Math Quizzes

Which ordered pair is between the x-axis and the line j?

(2, 3) Line j is a horizontal line through the point (0,5) on the y-axis. This is the graph of the equation y = 5. Only point (2,3), in quadrant I, is between the x-axis and line j.

Simplify the expression: 30 - 2 × 50 + 7030−2×50+70

0 To simplify the equation, follow the order of operations: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction (PEMDAS) and work left to right. The steps to simplify the expression would be: = 30 - 2 × 50 + 70 = 30 - 100 + 70 = -70 + 70 = 0

The images below are similar triangles. Solve for the missing value, x.

12 Since the triangles are similar, this question is best solved by setting up a proportion: \frac{15}{20} = \frac{x}{16}2015​=16x​ Solving leads to 20x = 24020x=240. This reduces to x = 12x=12

Which of the following is not a decomposed version of 2 \frac{3}{8}283​ ?

2/8​+3/8 A decomposed fraction expression must equal the original fraction. When these fractions are added together, they equal \frac{5}{8}85​. Since each whole unit would be \frac{8}{8}88​, the whole number 2 becomes \frac{16}{8}816​ not \frac{2}{8}82​.

Which of the following fractions has the smallest value?

3/7 3/7 is less than half because half of 7 is 3.5. The decimal equivalent is about 0.43.

What is the next step in this lattice multiplication algorithm?

add the diagonals Adding the numbers in each diagonal will lead to the final answer.

Which of the following is the best activity for reviewing percentages with fifth-grade students?

using a variety of methods and scenarios to determine percentage Presenting percentages in a variety of real-world scenarios helps students to review and fully grasp the concept as they practice using them.

If 18 pounds of tea were packed into boxes that each weigh \frac{1}{3}31​ pound, how many boxes were packed?

54 To find the number of boxes, divide 18 by the amount of tea packed in each box: 18\div \frac{1}{3}=18\times 3=5418÷31​=18×3=54.

If 2.2 lb = 1 kg, and Mary weighs 120 lbs, how much does she weigh in kg?

55 kg \frac{1 \text{ kg}}{2.2 \text{ lb}} = \frac{x \text{ kg}}{120 \text{ lb}}2.2 lb1 kg​=120 lbx kg​ Cross multiply and divide to find 54.54, which rounds to 55 kg.

The school day at Franklin Elementary begins at 7:45 am and goes until 3:04 pm. How long is the school day at Franklin Elementary?

7 hours, 19 minutes The simple conversion to military time makes subtraction between a "PM" time and an "AM" time straight-forward. In the case of this problem, 3:04 pm can be thought of as 15:04, and so the subtraction of the end time by the start time will be 15:04 - 7:45. In this case, 1 hour must be converted into 60 minutes so that the subtraction of minutes can be performed. Accordingly, 15:04 becomes 14:64 (1 hour less and 60 minutes more), and so the subtraction is 14:64 - 7:45. The difference is 7 hours and 19 minutes, the correct answer to this question.

John's car can drive 50 miles per gallon of gas, he wants to take a trip that is 750 miles. Gas currently costs $3.45 per gallon. He drives an average of 60 miles per hour during the trip. Which of the following expressions can solve for how many gallons of gas must he purchase for the trip?

750 \div÷ 50 750 \div÷ 50 represents the 750 miles traveled divided by the 50 miles per gallon his car can travel. The answer would provide the number of gallons needed.

There are 9 regular parallelograms that compose a single large one. If the perimeter of each of the regular parallelograms is 14, what is the perimeter of the large figure?

42 If the perimeter is 14 then each side is 3.5 (14 ÷ 4 = 3.5). There are 12 sides used to compose the larger parallelogram. 12 × 3.5 = 42

Which of the following is the product of 2 odd numbers and 1 even number, each of which is greater than 1?

30 The prime factorization of 30 is 2 × 3 × 5 which satisfies the need for 2 odd numbers and an even number.

The graph shows a linear relationship between x and y. Which of the following tables correctly shows values of x and y on this line?

Table D The line crosses each of these points.

Which of the following activities best helps students practice the process skill of predicting?

participating in a discussion on which soil conditions might help plants grow taller after examining plants in the schoolyard A prediction is a guess based on observation. Participating in a discussion about what might happen with different soil conditions helps students develop prediction skills.

Anytown School District wants all elementary students to be able to use computational strategies fluently and estimate appropriately. Which of the following learning objects best reflects this goal?

Students evaluate the reasonableness of their answers. If a student is able to use computational strategies, strategies for computing an answer, as well as estimate properly, then the student should be able to evaluate the reasonableness of his final answer. A student who is fluent in computational strategies and is good at estimating will know if his answer is about what he expected the answer to be, or if he should review his answer because it does not match what he expected.

Ms. Stacie asked her students to determine if the following relation was a function. As Ms. Stacie circulated the room, she overheard Jenny say to her partner "I think this is a function because it passes the horizontal line test." What is the best response Ms. Stacie could tell Jenny?

"Actually, in order to determine if a relation is a function, we use a vertical line test, not a horizontal line test. Do you think this relation would pass the vertical line test?" There is no such thing as a horizontal line test. A relation must pass the vertical line test in order to be a function.

An electronics store is offering a 20% discount on a pair of noise-cancelling headphones that normally cost $169.79. What is the price of the headphones, before tax, after the discount is applied?

$135.83 Convert the percentage to a decimal and multiply it by the original cost of the headphones to find the amount of the discount: 20\% = 0.220%=0.2 so (0.2)(169.79) = 33.96(0.2)(169.79)=33.96. Subtract the discount from the original price to find the new price: \$169.79 - \$33.96 = \$135.83$169.79−$33.96=$135.83.

12π ÷ 9 is approximately equivalent to:

4 Recall that a good estimation for π is 3. So, 12π ≈ 36.

Which expression can be used to solve the following word problem? Mr. Henry wants to purchase 24 hamburgers and 24 hotdogs for a Bar-B-Q he is having at his house. If hotdogs come in a package of 8 and hamburgers come in a package of 6, how many packages total of hamburgers and hotdogs will Mr. Henry have to buy?

824​+624​ B 24(\frac{1}{8}+\frac{1}{6})24(81​+61​) C 24(\frac{7}{24})24(247​) D All of the above All of the above answer choices are equal and represent equivalent expressions.

What is the digit in the hundreds place in the product of 63 × 31?

9 63 × 31 = 1953. The digit that occupies the hundreds place is 9.

What is the primary goal of summative assessments?

measuring student achievement Summative assessments are used to evaluate student learning.

Which of the following function tables would have points along the graphed line?

x-5,0,5,10 y-0,8,16,24 Identify 2 points along the line such as (0,8) and (-5, 0). Then determine the slope (rise/run). This allows to identify the equation as y = \frac{8}{5}x + 8y=58​x+8. The provided x and y points can then be tested.

Which of the following is not a rational number?

π The value of pi (π) never ends and does not repeat, making it irrational.

Solve: \frac{1}{3} + \frac{2}{5}31​+52​

1511​ When adding or subtracting fractions, a common denominator must be found first. Both fractions can be rewritten to use 15 in the denominator. \frac{1}{3} \times \frac{5}{5} = \frac{5}{15}31​×55​=155​ \frac{2}{5} \times \frac{3}{3} = \frac{6}{15}52​×33​=156​ Now the original expression can be re-written and solved: \frac{5}{15} + \frac{6}{15} = \frac{11}{15}155​+ 156​=1511​ This can't be simplified further since 11 is prime.

Solve: 1 \frac{3}{4} + \frac{1}{2}143​+21​

2 \frac{1}{4}241​ When adding fractions, a common denominator must be found first. Since 2 is a factor of 4, the second fraction can be rewritten by multiplying by 1 in the form of \frac{2}{2}22​. \frac{1}{2} \times \frac{2}{2} = \frac{2}{4}21​×22​=42​ The first fraction can be changed into an improper fraction by multiplying the whole number (1) by the denominator (4) and adding it to the numerator (3). 1 \frac{3}{4} = \frac{7}{4}143​=47​ Now the original expression can be re-written and solved: \frac{7}{4} + \frac{2}{4} = \frac{9}{4}47​+ 42​=49​ This can be simplified to 2 \frac{1}{4}241​.

If the value of A equals 1/5 and the value of B equals 1/2, which of the following equals C?

21/25 Point A is equal to 1/5 therefore each hash mark is equal to 1/5. C is closest to 4/5, however it is slightly more. 4/5 = 20/25 so 21/25 is the best answer.

Solve: \frac{2}{3} - \frac{1}{6}32​−61​

21​ When adding or subtracting fractions, a common denominator must be found first. Since 3 is a factor of 6, the first fraction can be rewritten by multiplying by 1 in the form of \frac{2}{2}22​. \frac{2}{3} \times \frac{2}{2} = \frac{4}{6}32​×22​=64​ Now the original expression can be re-written and solved: \frac{4}{6} - \frac{1}{6} = \frac{3}{6}64​− 61​=63​ This can be simplified to \frac{1}{2}21​ since both can be divided by 3.

Two angles are complementary. If the measure of one of the angles is 68°, what is the measure of the other angle?

22° because the sum of the measures of complementary angles is 90°. Complementary angles are two angles whose sum is 90 degrees. So, if one angle is 68 degrees, its complement would be 90 - 68 = 22 degrees.

What percent is represented by the shaded area of the decimal square?

24% There are 24 small squares shaded of the 100 total squares, therefore, 24% is the correct answer.

What is the area of the figure provided?

25 m2 One way to find the area is to find the area of the large triangle, then subtract the area that is cut out. A=A_{triangle}-A_{square}=\frac{1}{2}(10\times 10)-(5\times 5)=50-25=25 \text{ m}^2A=Atriangle​−Asquare​=21​(10×10)−(5×5)=50−25=25 m2. Similarly, the shape can be divided into 3 triangles, then the areas can be added together. The top triangle has a height of 5(10 \text{ m}-5\text{ m})5(10 m−5 m) and the bottom triangles are congruent and have a base of 2.5(\frac{10-5}{2})2.5(210−5​). A=A_{top triangle}+2A_{bottom triangle}=\frac{1}{2}(5\times 5)2(\frac{1}{2}(2.5\times 5))=12.5+12.5=25 \text{ m}^2A=Atop triangle​+2Abottom triangle​=21​(5×5)2(21​(2.5×5))=12.5+12.5=25 m2.

Simplify the expression: 3(10)2

300 The 10 must be squared first (order of operations) and then multiplied by 3. 3(10)2 = 3(100) = 300

A right triangle has one angle with a measure of 40 degrees. What is the measure of the other angle?

50 The sum of the interior angles of a triangle is always 180 degrees. Since the triangle is a right triangle, one measure is 90. The second angle is 40. 180 = 90 + 40 + x. Therefore, x must be 50 degrees.

Simplify the expression: 3x + 2(3x - 2) + 5 - 2(2x + 1)3x+2(3x-2)+5-2(2x+1)

5x-1 First, each value from the front of each set of parentheses must be distributed into the parentheses and multiplied appropriately, with attention to positive and negative signs: 3x + 6x - 4 + 5 - 4x - 23x+6x-4+5-4x-2. Next, like terms must be collected to be combined: (3x + 6x - 4x) + (-4 + 5 - 2)(3x+6x-4x)+(−4+5-2). Finally, like terms can be combined: 5x - 15x-1.

Mr. Johns gave a test last week and Ginny missed one question. She answered that 14.5 people would ride on each bus rather than 15. Her parents would like a conference because she did the math problem correctly and should receive credit even though her answer was not reasonable. How should Mr. Johns handle this situation?

Agree to meet, listen to their concerns, and then explain that one component of math is understanding reasonable answers. Meeting with the parents allows them to see what has been taught in the unit and to have a comprehensive idea of why there is more to mathematics than a computation.

For a student with strong addition skills, which subtraction algorithm is most suited their skill set?

Counting Up This method adds numbers to the smaller number to reach the larger number.

A first-grade teacher has been working with students on counting by twos, fives, and tens. The students are doing well with the concept, but the teacher is concerned that they are just memorizing the order of the numbers rather than applying the skill. What is one way that the teacher can encourage students to apply skip counting to their daily lives?

Give students a set of nickels and have them count by fives to find the total value. Counting coins is an excellent example of applying skip counting to real-world scenarios. Doing this would allow the students to apply what they have learned, while also showing them how skip counting will be used in their daily lives.

Ed graphs the point (3, 4) on the coordinate plane. Which quadrant is the point in?

I Since both coordinate values are positive, (3,4) is in the first quadrant.

In which quadrant is the point (-5, -3) located?

III Points with negative x and y coordinates are located in quadrant III.

Which situation could best be represented by the equation: 12x = 54?

Marty made car payments on her car for 54 months until it was paid off. What is x, the number of years it took Marty to pay off her car? To get the total months, 54, multiply the number of years, x, by the number of months in a year, 12; 12x = 54.

Which of the following terms best describes a polygon with 4 sides with only 2 angles of equal measure?

Quadrilateral A quadrilateral is a shape with 4 sides and 4 vertices. It can have any combination of equal angle measures.

A pre-K teacher is having students work in groups to count a set of small toys. She notices that one group of students has started playing with the toys instead of counting them. What would be an appropriate first step to take in this situation?

Remind students in the group of the expectations of the activity. A brief discussion and redirection is appropriate in this scenario and will likely be enough to get the group back on track with the activity.

If 6(3x+4) = 2(x+2) - 8, what is the value of x?

-7/4 Using distribution, 6(3x + 4) = 2(x+2) - 8 becomes 18x + 24 = 2x + 4 - 8. Combining like terms yields the equation 18x + 24 = 2x - 4. Subtracting 24 and 2x from both sides yields 16x = -28. Dividing both sides by 16 yields x = -28/16 which reduces to -7/4.

What is the first step in solving this equation? 3(y + 4) - 2(3y - 1) = 103(y+4)−2(3y−1)=10

3y+12−6y+2=10 The distributive property of multiplication allows the equation to be converted to this format. 3(y + 4)3(y+4) is equal to 3y + 123y+12 - 2(3y - 1)−2(3y−1) is equal to -6y + 2−6y+2

If the number 888 is written as a product of its prime factors in the form a3bc, what is the numerical value of a + b + c?

42 The prime factorization of 888 is 23 \times× 3 \times× 37. 42 is the correct answer because 2 + 3 + 37 is 42.

Maria solved a word problem and correctly gave 72 as the answer. Which of the following could not have been the question asked?

How many months did Alexa achieve perfect attendance last year? The number of months in a year can not exceed 12. Therefore, 72 can not be the answer.

Which of the following students would qualify as an English-language learner?

a student whose family speaks Choctaw at home A student whose dominant language at home is any language other than English would qualify as an English-language learner.

Which of the following is equivalent to the expression below? 2x+4y-3x+62x+4y−3x+6

−x+4y+6 In the expression, 2x and -3x are like terms and therefore can be combined by adding the coefficients and keeping the variables the same. 2x and -3x is -x. 4y and 6 cannot be combined, and are therefore left as is. The resulting expression is -x + 4y + 6.

It took Julie ¾ of an hour to run 3½ miles. What is her average speed in miles per hour?

4 ⅔ miles per hour 3 ½ needs to be converted to an improper fraction: \frac{7}{2}27​. Then divide \frac{7}{2}27​ by \frac{3}{4}43​. To divide by a fraction, multiply by the reciprocal: \frac{7}{2} \times \frac{4}{3} = \frac{28}{6} = \frac{14}{3} = 4 ⅔27​×34​=628​=314​=4⅔.

Which equation below models xª•xᵇ = xª⁺ᵇ?

5³ • 5⁴ = 5⁷ xª is a multiplication problem where "x" identifies the factor to be multiplied "a" times. These are some rules to follow when you are modeling an algebraic expression: 1) choose numbers other than 0 or 1 to replace the variables; 2) choose a different number for each variable; 3) replace the variables with the sample numbers you have chosen; and 4) evaluate to see if the relationship/equation is true. So, for this problem, the following sample numbers have been chosen: x = 5; a = 3; b = 4. Now, let's see if 5³ • 5⁴ = 5⁷. 5³ = 5 • 5 • 5 and 5⁴ = 5 • 5 • 5 • 5. So, 5³ • 5⁴ = (5 • 5 • 5) • (5 • 5 • 5 • 5) = 5 • 5 • 5 • 5 • 5 • 5 • 5 = 5⁷. This tells us that 5³ • 5⁴ = 5⁷ is a good model of the equation.

Which of the following is not a decomposed version of \frac{4}{9}94​ ?

62​+32​ When adding fractions, they need the same denominator and then numerators only are added. This expression assumes you add across both, which is incorrect. This expression simplifies to 1 so it is not equal to \frac{4}{9}94​.

What percent is represented by the unshaded area of the decimal square?

76% There are 76 small squares unshaded of the 100 total squares, therefore, 76% is the correct answer.

Mr. Jones has been teaching order of operations to his class and a group of students have mastered the concept quickly and easily. What would be the best way to offer them a challenge and increase the rigor of their lessons?

Introduce brackets and braces to go along with parentheses. This adds to the current concept and requires the students to use their knowledge in a more challenging way.

Which of the following steps in the scientific method is only completed after the experiment is completed?

communicating data After the experiment is concluded, the data is analyzed and then communicated.

What learning progression should be used when teaching math concepts to sixth-grade students?

concrete to symbolic to abstract Students need to be introduced to topics through manipulatives and concrete examples. Then, students can move on to symbolic representations such as drawings to represent equations. Finally, they can move to abstract that involves only numbers and variables in equations.

All of the following are equivalent to the number 16, except for which expression?

8(2) 8^{2}=8⋅8=6482=8⋅8=64, NOT 1616

The west wall of a square room has a length of 13 feet. What is the perimeter of the room?

52 feet A square has four sides of equal length. Perimeter is the total distance around an object. To find the perimeter of a square, follow the formula P = 4sP=4s, where PP = perimeter and ss = the length of a side of the square. In this case, P = 4(13) = 52 \text{ ft}P=4(13)=52 ft.

If the value of c is between 0.00082 and 0.0026, which of the following could be c?

0.0011 Larger numbers have larger values in place values to the left. This choice has 1 in the thousandths place, so is less than 0.0026, which has 2 in the thousandths place. This choice is less than 0.00082, which has 0 in the thousandths place.

A student is using an array to solve 12 ÷ 3. Which of the following shows the array that would be used to correctly solve this problem?

3x4 chart This array shows that when 12 items are divided into 3 equal columns, there are 4 items in each column. This correctly represents the problem 12 ÷ 3 = 4.

Danielle's third-period class began at 10:43 am and ended at 11:38 am. How long was the class?

55 minutes One option to determine the length of the class period is to see how long it is from the start of class to the next full hour (from 10:43 am to 11:00 am), and then add the minutes part of the end time. In this case, 11:00 am can be thought of as 10:60 am so that subtraction with 10:43 is easy: 10 - 10 = 0, so 0 hours and 60 - 43 = 17, so it is 17 minutes until 11 am. Then, from 11:00 am to 11:38 am is 38 - 0 = 38 minutes. The total length of the class is 17 + 38 = 55 minutes. Another option to determine the length of the class period would be to reason that if it were an hour long and started at 10:43 am, it would end at 11:43 am. But this class ends at 11:38 am, five minutes before 11:43 am (43 - 38 = 5), and so this class is 5 minutes shorter than 1 hour, or 55 minutes long.

Which of the following is not a decomposed version of 5 \frac{4}{9}594​ ?

95​+94​ A decomposed fraction expression must equal the original fraction. When these fractions are added together, they equal \frac{9}{9}99​, which is the same as 1. Since each whole unit would be \frac{9}{9}99​, the whole number 5 becomes \frac{45}{9}945​ not \frac{5}{9}95​.

Mr. Murphy is planning a lesson designed to meet the needs of all learners in his science class. The goal of his lesson is to help the learner enjoy learning science. Which of the following should Mr. Murphy incorporate first into the lesson in order to reach his goal?

activities focused on a variety of interests and learning styles In order for all students to enjoy the content, a variety of activities should be incorporated into the lesson. When these activities focus on the students' interests and learning styles, the students become more engaged in the lesson and enjoy learning.

Mr. Chappel hangs posters in each corner of the room with different names of number categories. One corner has a sign that says integers, another has a sign that says rational numbers, another says irrational numbers, and the last says whole numbers. Students are assigned a corner to start and on the first rotation they must add a definition to the sign. On the second rotation, they must add numbers that are examples to the sign. What should be the third rotation task?

adding a picture that helps students remember what is included in the number set This continues to familiarize students with the number sets.

Mrs. Hoyt is excited to be teaching fifth-grade math this year. She would like to encourage her students' independent skills. How can she facilitate this in her classroom?

allow for a variety of choices when it comes to assignments This increases autonomy while still accomplishing the teacher's goal of work and concept mastery.

A third-grade teacher gives her students an exit ticket in which they are asked to find the area of the rectangle below: A summary of student responses is shown below: Solution Number of students with this response 56 square feet 5 15 square feet 1 30 feet 12 Other response 2 Based on these responses, the teacher should address student misconceptions related to:

area vs. perimeter The most common incorrect response was 30 feet, which would be the perimeter of the rectangle. This means that students are most likely confusing the two terms.

A kindergarten teacher ends each day by having students march, jump, or run in place as they count out loud from zero to 30. What skill is she trying to promote by doing this?

counting by ones Students are practicing counting in order by ones while incorporating physical activity.

Which of the following units represents the shortest distance?

nanometer A nanometer is equal to one-billionth of a meter.

The following word problem was given to Mr. Trout's fourth-grade class: The Hotel Vacay is hosting a Wintertime Brunch for families. Each child that attends gets to decorate a gingerbread house and use the ice slide 3 times. Every family gets 2 snowballs per person. If 108 people can be seated and there are an equal number of adults and children, how many gingerbread houses and snowballs do they need? Morgan solved the problem using this equation: \frac{108}{2} + 108 \times 22108​+108×2 Julia solved the problem using this equation: 108 \times 2 \frac{1}{2}108×221​ Which child is correct?

Both children Both are correct. Morgan found the number of gingerbread houses and then the number of snowballs and added them. Julia determined that each parent-child pair gets a gingerbread house which is the same as ½ a house per person so she multiplied 2 ½ by the total number of seats.

Peter babysits in the evenings for neighborhood children. He charges a flat rate of $12 per evening plus $7 for each hour he sits. If E represents his total earnings for an evening of babysitting and t is the number of hours that Peter babysits that evening, which of the following equations represent the relationship between the amount of time he babysits and his total earnings?

E=7t+12 Multiply $7 by the number of hours Peter babysits and add the $12 additional flat rate. The number of hours is represented by t and his earnings are represented by E=7t + 12E=7t+12.

Which of the following statements best describes a formative assessment?

Formative assessments measure what students know along the way. Formative assessments measure what students know along the way. They should be given on a regular basis. These are not summative assessments, which are used to determine what students know at the end of the year or at the end of a unit.

A teacher prompted her students to write an example of an expression on their papers. One student wrote the following on their paper: 2x+3=52x+3=5 The student raises her hand and wants to know if her answer is correct. Of the following, which is the best teacher response to the student?

It is incorrect; this is an equation because it contains an equal sign. There is an expression on either side of the equal sign, which could be possible correct answers. The student response is incorrect because they wrote an equation, not an expression. Because an equation is a statement that two expressions are equal, either expression on each side of the equal sign could be an example of an expression.

Ms. Trask wants to create an authentic assessment to test her students about angles in triangles. Which of the following should she do first?

Look at the standards to determine what a meaningful task that students could complete to demonstrate their knowledge. Looking at the standards to design the assessment is a great first step.

Ms. Davis teaches a fifth-grade math class primarily composed of English language learners (ELL). Which of the following can support her ELL students? Select all answers that apply.

Make a word wall. A word wall is helpful for English language learners to visualize a word. B Use gestures, pictures, and models to explain terms. Use of gestures, pictures, and models are helpful to English language learners.

Mr. Douglas is introducing fractions to his third-grade class. He gives his students blocks to begin exploring fractions. They look at parts of a whole and then move to looking at pictures like the one below. What is the next step in displaying their knowledge?

Solving problems using numbers without pictures The next step in progression is solving problems without a visual prompt.

In which of the following assignments would students most likely find the Venn diagram to be a useful tool in organizing their information?

The teacher has asked the students to compare and contrast plants and animals. Venn diagrams are typically used when students are comparing and contrasting. The traditional Venn diagram has two circles that overlap. The area overlapping in the middle of the two circles is where you would record commonalities and the portions of the two circles outside of the overlapping area would contain the differences.

Which of the following equations satisfies the data table?

y = x2squared This equation works for all sets of numbers. 1 = (-1)2 = 1 0 = (0)2 = 0 4 = (2)2 = 4

What is the perimeter of the shaded portion of the figure?

$$68 \text{ in}$ To find the perimeter, add the perimeter of the outside with the perimeter of the inside. P=[2(11)+2(8)]+[2(9)+2(6)]=38+30=68 \text{ in}P=[2(11)+2(8)]+[2(9)+2(6)]=38+30=68 in

Which of the following sentences is true? Select all answers that apply.

All irrational numbers include a symbol such as square root or pi. Irrational numbers must be written with a symbol or radical. B Integers include all natural numbers, whole numbers, and their opposites. Integers are positive and negative counting numbers and zero.

Mr. Bielenberg asks students to measure 5 different objects from home using different units of measurement. He does not receive a wide variety of objects. How could he improve this activity in the future?

Give clear guidelines for expected objects. Students need to know what is expected of them.

What is 5/18 as a percent?

27.78% To convert a fraction to a percent, divide the numerator by the denominator and multiply by 100. 5 ÷ 18 = 0.2778 × 100 = 27.78%

A sixth-grade teacher discovers that each student in his class receives an allowance from their parents. Which of the following examples would best demonstrate to the students the power of saving their allowance instead of spending all of their allowance?

Show students the expected return of 5% allowance savings over a 10-year period. Demonstrating how much money students could make by saving their allowance would best demonstrate the power of saving money.

Which of the following principles is demonstrated by the figures below?

When the denominator stays the same and the numerator decreases, the fractional value decreases. The denominator remains 4 throughout the figures. As the numerator decreases, the fraction also decreases.

Which of the names below is not a proper classification for \frac{48}{3}348​ ?

irrational Irrational numbers can not be written as a fraction. Therefore, this number is not irrational.

Which of the following is a developmentally appropriate activity for an average sixth grader to establish number sense?

using positive and negative numbers to represent financial situations Students in sixth grade should be able to use positive and negative numbers in real-world scenarios such as money owed or money earned.

Solve for aa. 2a - 12 + a = 182a−12+a=18

10 Combine like terms: (2a + a) - 12 = 18(2a+a)−12=18 3a - 12 = 183a−12=18 Add 12 to both sides: 3a - 12 + 12 = 18 + 123a −12+12=18+12 3a = 303a=30 Divide both sides by 3: \frac{3a}{3} = \frac{30}{3}33a​=330​ a = 10a=10

How many terms are in the expression 3x² + 6x +3?

3 A term is either a single number, a variable, or numbers and variables multiplied together. The equation 3x² + 6x +3 has three terms: 3x², 6x, and 3.

Which sequence of steps, when completed, will solve the equation -3y + 4 = -2-3y+4=-2 ?

Subtract 4 from each side and then divide both sides by -3. This will solve for yy by isolating it on one side.

Solve: [5(6+5) + 475]/{-3[3+ 7(5)] + 119}

106 [5(6+5) + 475]/{-3[3+ 7(5)] + 119} = (5(11) + 475) / (-3(3 + 35) + 119) = (55 + 475)/(-114 + 119) = 530/5 = 106

If a number ends in zero, what number(s) can it be divided by? Select all answers that apply.

2 A number that ends in zero is even and therefore divisible by 2. B 5 A number that ends in zero (or 5) is divisible by 5.

What is the perimeter of the figure provided?

29 cm The perimeter of the figure is 2 × (l + w) = 2 × (5.5 + 9) = 29 cm.

Which of the following has the least value?

483 ones This is the same as multiplying 483 × 1 which equals 483.

Which metric prefix indicates a factor of 10?

Deca- Deca- indicates a factor of 10.

A child is using a geoboard and creates a shape with 6 sides. What is the name of this shape?

Hexagon A shape with 6 sides is called a hexagon.

Eddie graphs the point (-4, -8) on the coordinate plane. Which quadrant is the point in?

III Since both coordinate values are negative, (-4, -8) is in the third quadrant.

In Ms. Suzi's math class, she asks the students to look at the following pattern and find the next three terms. 1, 2, 4, 5, 7, 8, 10, 11, 13, ...1,2,4,5,7,8,10,11,13,... What type of thinking are the students using to solve this problem?

Inductive reasoning With inductive reasoning, students look for patterns and then make generalizations.

Which metric prefix indicates a factor of 1000?

Kilo- Kilo- indicates a factor of 1000.

Which activity would best support third-grade students in developing an understanding of the Solar System and the positions of the planets relative to the Sun?

Making a physical model showing the order of the planets and three properties of each planet. This inquiry-based activity is tied directly to the learning goal. Students would interact with the planetary positions and also note some distinguishing features for each planet.

Jocelyn bought an ice cream sundae for $2.67 (including tax and tip) by giving the cashier a $20 bill. If she received 8 bills and 7 coins, which combination of bills and coins did she receive as change?

One $10 bill, seven $1 bills, two dimes, two nickels and three pennies Jocelyn should be receiving \$20-\$2.67=\$17.33$20−$2.67=$17.33 in change from her purchase. One $10 bill and seven $1 bills makes 8 bills total and \$10+\$1+\$1+\$1+\$1+\$1+\$1+\$1=\$17$10+$1+$1+$1+$1+$1+$1+$1=$17. Two dimes, two nickels and three pennies makes 7 coins total and \$0.10+\$0.10+\$0.05+\$0.05+\$0.01+\$0.01+\$0.01=\$0.33$0.10+$0.10+$0.05+$0.05+$0.01+$0.01+$0.01=$0.33. Combined, the bills and coins add up to \$17.33$17.33.

Students in Mr. Jaffrey's class were discussing in pairs if the following mapping diagram represents a function: As Mr. Jaffrey was circulating, he overheard Reena tell her partner that the relation is not a function because every input gives the same output. Of the following, which is the best response for Mr. Jaffrey to give Reena?

Reena, you are incorrect. Even though each input gives the same output, there is only one output for every input, so the relation still represents a function. The only thing that determines if a relation is a function is if each input gives only 1 output. This is true for this relation, so it is a function.

Mrs. Rogers is teaching her students about volumes of regular rectangular prisms. She has students work with pieces of wood and measure their length, width, and height to determine volume. She asks students to analyze nets of prisms to determine their volume. While students have been successful using pieces of wood, they seem to be having issues using nets. How should Mrs. Rogers intervene?

She should demonstrate how to cut out and assemble the nets and then ask students to determine area of the nets in 3D form. Cutting out and assembling the nets will make them similar to the pieces of wood. This will allow them to connect new material to a skill they have already mastered. This is the best next step.

Which of the following terms best describes a polygon with 4 sides whose angles are all of equal measure?

Square A square has 4 sides and 4 angles measuring 90\degree90°.

Susan's second-grade class is studying fact families. Each student is purposefully assigned a fact card and asked to find other members of their family. Above are the cards received by 5 students. Students in the same fact family then work in a group to create fact family houses that are displayed at the school's Open House where parents come by to see the classroom and the student's work. Why is this an effective way to group students?

Students are discussing the concept before working on it. They have been studying fact families and this gives them an opportunity to discuss it among themselves as they find their group. This shows mastery of the concept which is then displayed in the project.

Ms. Hughes wants students to be familiar with quantities from everyday life. She asks all students to report their height and weight so the class can calculate their mean, mode, and range. What are all of the weaknesses of this approach? Select all answers that apply.

Students might not know that information. Not all students measure themselves regularly. C Students are not actively engaged in a hands-on activity. Students would be more engaged if they measured quantities themselves. D Students might not be comfortable disclosing that information. Weight is generally information people keep private about themselves.

Mrs. Herschend decided not to give a test about ratios and instead had her students do a project to display their knowledge. She has decided that she will do this for every unit going forward. What is the main disadvantage to this approach?

Students need to practice test taking skills periodically. Students need to practice these skills for standardized testing.

Which of the following is an appropriate skill for a second-grade student to master during a unit on numbers and operations?

Students will be able to place a given whole number in the correct position on an open number line. This correctly identifies a TEKS for second-grade math. It describes what the student will be able to do as a result of instruction.

Mr. Marshall is a math teacher and a student council sponsor. He has encouraged student council to do a service project, but they are struggling with ideas. He decides to assign his math class a project where they research local non-profits. How can he align this project with the curriculum?

Teach a lesson on how math can be used to inform people about social issues and have students find numbers that can help tell the story of the agency Math can be used in powerful ways and teaching students this helps connect the real world to the classroom

Jaylene is trying to solve the equation 5x+7=725x+7=72. She raised her hand to get help from her teacher. When the teacher comes over, the following is written on her paper: Jaylene wants to know if her first step is correct. Of the following, which is the best teacher response to Jaylene?

The first step is incorrect; while subtracting 7 is the correct inverse operation, the subtraction property of equality states that in order to keep an equation balanced, you must apply the subtraction on both sides of the equal sign. She should also subtract 7 from 72. This is correct; she is not correctly applying the subtraction property of equality because she is not subtracting 7 on both sides of the equal sign.

Billy and Sally perform the same experiment ten times to observe if variations occur in the results from the experiment. After they perform the experiment ten times, they notice a large variance of results, but they hypothesized a small variance in results. When they discuss the experiment with their teacher, the teacher directs them to identify any deviations from the original experimental procedure. Which of the following best describes the benefit of the teacher's directions?

The task helps Billy and Sally connect deviation in procedure to variance in results. By reviewing any deviations from the original experimental procedure, Billy and Sally can identify any procedures which might result in a large variance in the results of the experiment.

Many of today's education experts recommend that teachers move away from the "sage on the stage" approach and become more of a "facilitator of learning." What does this most likely mean?

This means that teachers need to move away from long lectures and move toward facilitating the classroom while allowing students to become active participants in learning. Today's educational leaders recommend that teachers move away from long lectures and give students more opportunities to become active participants in the classroom. Teachers need to become the "facilitator of learning" instead of being the person "doing the most learning". Lectures rarely involve students---the teacher is doing more learning than the students.

A student asks a teacher when calculating percentages of numbers will be useful in real life. Which of the following examples would be the most appropriate response for the student?

a mother going shopping at a store sale A mother shopping on at a store sale will often be buying items market as a certain percentage off.

There is a line AB defined by two points A and B. If Carly draws a point M that is not on line AB, which geometric figure is defined by the point M and the line?

a plane A plane is defined by non-collinear points. In this case points A, B, and M do not reside on the same line; therefore, they define a plane.

What is the next shape in this pattern?

circle The pattern is square, 2 circles, triangle, 2 circles, pentagon, 2 circles. After the last square, there was only 1 circle, so there needs to be another circle before moving on to another triangle.

A pre-K teacher has her students pretend to be a rocket ship as they squat down and then "blast off" as they say, "10, 9, 8, 7, 6, 5, 4, 3, 2, 1." What skill is the teacher promoting by doing this?

counting backwards By counting down from 10, students are practicing the skill of counting backwards.

A school fundraiser is selling candy bars to raise money for a new gymnasium. If Billy sells a total of $650 worth of candy bars for $d per candy bar, which expression could be used to represent how many candy bars Billy sold?

d650​ To find out how many candy bars were sold, simply divide the total amount of money by the price per candy bar to find the total number of candy bars sold. This would be 650 / d. Another way to write this is d*N = 650, where x is the price per candy bar and "N" is the number of candy bars sold.

After learning about organisms and adaptations, a teacher asks students to describe what they learned about how a particular organism might survive during a drought. She finds that many of her students cannot think of any ways the organism might adapt. She decides she will extend the lesson to the next class period. Which phase of the 5E model is the teacher implementing when she asks for descriptions of adaptation?

evaluate During the evaluate phase, students demonstrate their understanding and teachers evaluate their learning to inform their next lesson.

Which is the most appropriate unit to measure the height of the average adult human?

inches Inches are of an appropriate scale to measure the height of a human because most human adults measure between 50-80 inches, which are whole numbers that are not too large nor too small. Numbers between 0-100 are easy to understand and conceptualize.

Of the following, which is most appropriate to do after testing a hypothesis?

organize data After testing a hypothesis it is best to organize the data so that conclusions can be drawn.

Which of the following cannot form a regular tessellation?

pentagon A regular tessellation must be able to tile a plane with no overlaps or gaps by repeating a regular polygon. The only regular polygons that can form a regular tessellation are the triangle, square, and hexagon. A regular pentagon does not form a regular tessellation.

According the 5E model, an ideal full lesson cycle should start by ___ and end with ___.

piquing students' interests; some sort of evaluation The full lesson cycle needs to start with an activity that piques students' interests and should end with an activity that evaluates what they have learned.

A second-grade teacher is planning to teach a lesson on measuring mass. What would be the best introductory activity for his students?

providing balance beam scales and various objects to compare This inquiry-based activity allows the students to explore the idea of weighing mass. The balance beam scale will easily show students which object is heavier.

The table below gives the area of several squares with different side lengths. Which of the following graphs best represents the data in the table? Side length Area 1 1 2 4 3 9 4 16 5 25

small slope - This, a quadratic relationship, is the correct relationship. According to the data table, as side length doubles, area quadruples.

The semester exam administered to students at the end of the term is considered to be a:

summative assessment. A semester exam is a form of summative assessment.

Who is credited with creating much of what we consider geometry?

the Greeks The ancient Greeks are responsible for much of what is studied in Geometry, most famously the Pythagorean Theorem by Pythagoras.

A student is working through a double-digit multiplication problem and turns in the work pictured. Which of the following best describes the student's error? 15x19=135+25=385

the student carried over the hundreds value from the 9 and 15 multiplication The student placed a two in the hundreds place on the second row of the addition instead of a one. The student carried the additional hundreds value from the (9 * 15) calculation when calculating the tens product (1 *15) or (10 *15). The student should add 135 and 15 (or 150) not 25 or (250). The correct answer would be 285.

During a unit on Earth and space, Ms. Bosshardt wants her students to work on recognizing patterns by observing, describing, and illustrating clouds. Which of the following is the best way to incorporate technology into this lesson?

Have students go outside to observe clouds and use a phone camera to take pictures of a type of cloud that was previously discussed in the classroom. It is difficult to draw a cloud well enough to distinguish its type. By using a phone camera, students can observe real clouds and show with their photos that they understand different types of clouds.

Mrs. Stallings wants her students to learn the divisibility rules before committing them to memory. Using Bloom's Taxonomy levels, how can she elevate her lesson from "Remembering"?

Have them explain how to use the rules for large numbers. This allows them to analyze the rules which is a higher level of Bloom's Taxonomy.

Mr. White displayed 3 sequences on his whiteboard during math class: 20, 10, 5, 0, -2.5, ...20,10,5,0,−2.5,... 324, 108, 36, 12, 4, ...324,108,36,12,4,... -6, 1, 8, 15, 22, ...−6,1,8,15,22,... He asked his students to pick one of the sequences, determine if it was arithmetic or geometric, and explain their reasoning for their answer. Which student answer correctly identifies the sequence and has a sufficient explanation?

"-6, 1, 8, 15, 22, ...−6,1,8,15,22,... is an arithmetic sequence because if you add 77 to each term, you get the value of the next term in the sequence. When you have a common difference, the sequence is arithmetic." An arithmetic sequence has a common difference. In -6, 1, 8, 15, 22, ...−6,1,8,15,22,..., 77 is added to each term to continue the sequence. This statement is correct.

The graph shows the relationship between the number of hours that the Torres' babysitter watches their children and the amount of money that the Torres family owes the babysitter. According to this graph, how many dollars per hour does the Torres family pay their babysitter?

$12.50 The dollars per hour is the rate of change and, therefore, the slope of the line, which can be calculated by finding \frac{change in y \left( \$ \right) }{change in x \left( hours \right) }changeinx(hours)changeiny($)​. First, identify at least 2 points on the line, for example, (0, 0) and (4, 50). The change in y-values is the change from 0 to 50, which is 50. The change in x-values is the change from 0 to 4, which is 4. So the slope is \frac{\$50}{4 hours}=\frac{\$25}{2 hours}=\frac{\$12.50}{1 hour}=\$12.50/hour4hours$50​=2hours$25​=1hour$12.50​=$12.50/hour.

A sweater is on sale for $43.75. It is 30% off the original price. What is the original price?

$62.50 Set up a ratio to solve this problem: 43.75/x = 7/10. Cross multiply so you have 43.75 * 10 = 7x. Divide both sides by 7 to isolate x. So, 437.5/7 = $62.50.

The scatterplot shows the relationship between sales at an ice cream shop and temperature. Based on the best fit line, shown, which of the following is the best estimate of the sales when the temperature is 21°C?

$450 When the temperature is 21°C (found on the x-axis), the sales are about $450 (the corresponding y-value).

Maria has recently moved from Mexico City to the U.S. She is a secondary student who speaks little English, but who came from her school in Mexico City with excellent grades. Which of the following would be the most appropriate accommodation for Maria's math teacher to use with Maria?

Pair Maria with another student who speaks Spanish, to clarify instructions in Spanish as needed. If possible, pairing Maria with a student who speaks Spanish would be an excellent strategy.

The Payday Lending industry has faced increased criticism and scrutiny for which of the following practices?

charging high interest rates Payday lenders charge high interest rates which locks many low-income individuals into cycles of debt and repayment, a practice for which these companies have faced much criticism.

Bobby is buying gumballs for 7 of his friends. There are 51 gumballs before Bobby makes his purchase at the store. Bobby wants to give each of his friends the same amount of gumballs and not have any gumballs left. Which of the following approaches can Bobby use to find the greatest number of gumballs he can purchase to give his friends?

Make a list of the multiples of 7 and then purchase the highest multiple of 7 that is less than 51. This is the best answer as Bobby will know the number of gumballs to purchase.

Miss Wilson's class is learning about unit rates. They are comparing costs from the grocery store to see if the store brand is a better deal than the name brand. Douglas and Kaitlyn are volunteering to answer questions during class, but few others are. What should Miss Wilson do?

Provide wait time before calling on someone to answer Providing this wait time allows more students to think through the question and their answer. It is especially helpful if students are told they cannot raise their hand until asked to do so. This gives students additional think time and builds confidence.

Mrs. Doloff's third-grade class has learned about ordering people according to age when given a word problem such as "John is older than Mei and Mei is older than JD. Who is oldest?" What is the next concept for Mrs. Doloff to teach about ordering?

adding numbers to the problem to solve for exact age This is the next step in scaffolded learning.

What is the correct formula for the line depicted on the graph below?

y = 3x - 3 This graph has a slope of 3. With a point at (0, -3) and (1,0) the slope must be 3. The y-intercept is -3 because that is where it crosses the y-axis.

In a science center, students who stand in front of a wall when a light flashes will see a picture of their shadow on the wall afterward. Which phase of the 5E model is being implemented in this activity?

engage During the engage phase, students become mentally engaged and make connections to previous learning.

The 5E Model of Instruction is routinely recommended as one of the best practices in science classrooms. Which of these E's is generally the first step of the lesson cycle?

engage Engage is generally the first step of the lesson cycle if you are using the 5E Model of Instruction. (Engage, Explore, Explain, Elaborate, and Evaluate)

Cara would like to research the effects of plants on students' self-reported stress levels. She places potted plants in student common areas for two weeks, taking surveys before and after. She then makes a graph of her findings. Which parts of the scientific method is Cara performing?

experimentation and data analysis Cara conducts an experiment (placing plants in common areas) and carries out data analysis (creating a graph of the results).

Which of these is not a decomposed version of ⅚?

⅔ + ⅙ + ⅙ ⅔ is equal to 4/6 and when added to ⅙ and ⅙ it equals 6/6 or 1.

Caitlin knows that all birds have a beak. Adam is a bird. Therefore, Caitlin concludes that Adam has a beak. What type of reasoning is Caitlin using?

deductive reasoning Deductive reasoning involves statements such as: every dog is happy; Sally is a dog; therefore Sally is happy. Caitlin is using exactly this type of reasoning.

In a fourth-grade class, students are making cookies to learn about fractions. They are measuring using measuring cups and spoons. This learning is best described as:

formal standard measurement. Feet, inches, cups, gallons, meters, centimeters, grams, etc. are standard measurement. This is the correct answer.

A second-grade teacher gives students a short assessment on subtracting two- and three-digit numbers and collects the following data: Problem Solution 1 (correct answer) Number of students with solution 1 Solution 2 (incorrect) Number of students with solution 2 Solution 3 (incorrect) Number of students with solution 3 314 - 53 261 4 361 13 367 1 546 - 28 518 3 528 13 574 2 193 - 31 162 15 152 2 224 1 Based on this data, the teacher should plan to reteach concepts related to:

regrouping or "borrowing" In the majority of incorrect answers, the error is due to students not decreasing the value of the neighboring digit when they regroup to subtract. Note that in the third problem no regrouping needs to be done and that the majority of students got this problem correct.

Which of the following is NOT considered a benefit of cash?

security Cash is the least secure form of payment, as it cannot be tied to your personal identity and thus is not replaceable if lost.

Sixteen teachers placed a book order for books to be used in their classrooms. The bill, totaling $350, is to be shared equally. Which is the most appropriate representation for how much will each teacher pay?

16350​=21.875→21.88 This situation involves money. We are looking for an answer that can be "translated" into money.

A model of an equation is shown. What is the value of MM?

M=3 The equation modeled is: 4M - 8 = M + 14M-8=M+1. First add 8 on both sides of the equation: 4M = M + 94M=M+9. Subtracting M on both sides: 3M = 93M=9. Divide both sides by 3: M = 3M=3. To check, if M = 3M=3, the model becomes 4(3) - 8 = 3 + 1 \rightarrow 4 = 44(3)-8=3+1→4=4, which is a TRUE statement.

Mr. Jones is hosting a career day for his sixth-grade class. Jeremy tells him that his father cannot come present because his job has nothing to do with math because he did not attend college. Mr. Jones asks Jeremy what his dad does for a living. Jeremy says his dad is a carpenter. What should Mr. Jones tell Jeremy?

Carpentry involves a lot of math including accurate measurements, determination of angles, and geometry. B Carpentry involves algebra to determine how much raw material to buy. C Mathematics is used by people throughout their lives, whether or not they attend college. All of the above. All of these statements are true descriptions of how math is used in daily lifeticism and scrutiny for which of the following practices?

Ms. Hobbs is planning to introduce long division to her students for the first time. Which of the following would be the best first instructional step for this topic?

quiz students on their understanding of basic division before proceeding It is best for Ms. Hobbs to find out the level at which her students understand division so she can fill knowledge gaps before moving on to the more difficult topic of long division.

What fractional part of the diagram is shaded?

48/100 48 of 100 squares are shaded. This can be represented as the fraction: 48/100. Fractions compare part to whole.

The sequence has the 4th and 5th terms of 33 and -51 respectively. Each term is found by adding the previous 2 terms and multiplying by -3. What is the value of a2? a2, a3, 33, -51...

5 To solve, work backwards using opposite operations. -51 ÷ -3 = 17, so 17 is the sum of 33 and a3. 33 + a3 = 17 so the value of a3 is -16. This process must be repeated using 33 and -16 for an answer of 5.

A student uses a number line to solve a problem. Their work is shown below: Based on their work, the student was most likely solving which of the following problems

5 × 2 Number lines are often used as a way to represent multiplication as repeated addition. This number line shows five groups of 2, or 2 + 2 + 2 + 2 + 2, which is the same as 5 × 2.

A restaurant charges $7.00 for a bowl of noodles and $1.25 for each topping selected. Let D represent the total cost of a meal and let T represent the number of toppings selected. Which of the following is an equation for the total cost of a meal in dollars, D?

A D=7.00+1.25TD=7.00+1.25T The total cost of the meal equals the base cost of $7.00 for the noodles plus $1.25 times each topping T added to the noodles.

Which of the following units is most appropriate to measure the volume of a solid?

Cubic centimeters Cubic centimeters are the most appropriate unit to use for the volume of a solid object.

Ms. Miller is a student teacher in a fourth-grade classroom. She has heard that group work is important so she wants to plan for group activities. On her first day student teaching, she briefly says "today we'll be doing group work about fractions" before she sends the students to stations. How could she best improve her teaching?

Give a whole group lesson on fractions before breaking into groups. Ms. Miller did not give enough whole group instruction before letting the students work in small groups. At a minimum she should give a whole group lesson relating to the content of the day before sending students to work at stations.

A first-grade teacher is working with a small group of students on skip counting by tens. The students are able to recite numbers from 10 to 100 while skip counting, but they struggle when asked what ten more than 40 is. Which of the following strategies would help students improve their mathematical reasoning skills related to this concept?

Guide students in highlighting multiples of ten on a number line or hundreds chart as they skip count out loud. This gives students a visual representation of what is happening when they skip count by tens. The students have likely memorized, "10, 20, 30 ... etc." without understanding what they are actually doing. By highlighting the numbers on a number line or hundreds chart, students will be more likely to see that each number is ten more than the one before it.

Which of the following statements is false?

Inductive reasoning never leads to a correct conclusion. Inductive reasoning, or reasoning from specific examples to end with a more general conclusion, may or may not lead to a correct conclusion. It is incorrect to say that inductive reasoning never leads to a correct conclusion.

A parent is complaining about the math homework. They feel that their ELL child is at a disadvantage because they cannot afford internet at home and the homework is best completed using online software. The teacher is providing students time in class to complete the work that requires online resources, however, this student has not been using it stating that he will do it at home. What is the best strategy the teacher should use to prepare for meeting with the parent?

Open communication with the parents that does not involve educational jargon. Open communication that encourages parental involvement is best.

As shown below, a figure was cut along the dotted line to form a second figure. What statement is true about the figures?

The area of the 2 figures is congruent, but the perimeter of the second figure is greater. The area is the same because the shapes occupy the same amount of space, but the perimeter is greater for the second figure because it has 2 new external lines where it was cut.

After observing the behavior of ants in an ant farm, students present their drawings and ideas about ant behavior to each other in small groups. Which phase of the 5E model is being implemented in this activity?

explain During the explain phase, students explain what they know and verbalize their understanding.

Mr. Stiles is introducing measurement to his third-grade class. He has rulers, stopwatches, scales, and graduated cylinders available for them to use. Based on previous lessons, he knows that most students do not know how to use these tools correctly. What is the best introductory lesson for this unit?

providing students time to explore the items and then creating a K-W-L chart This allows students to figure out what they already know and what they would like to learn about the topic.

Aaron went to sleep at 8:35 pm Tuesday night. He woke up at 7:00 am. How much sleep did he get?

10 hours, 25 minutes Calculate the time until midnight, and then add the additional time to get to the end time in the morning. Specifically, in this case, one can count full hours to get from 8:35 pm to close to midnight [9:35 pm (1 hour), 10:35 pm (2 hours), 11:35 pm (3 hours)], and then add minutes in easy-to-work-with increments, such as 5 or 10 minute intervals in this case, to get the minutes to move from :35 to :00 [ :40 (5 minutes), :45 (10 minutes), :50 (15 minutes), :55 (20 minutes), :00 (25 minutes)]. Therefore, the time from 8:35 pm to midnight is 3 hours and 25 minutes. Then, because the time from midnight to 7 am is simply 7 hours, one can add 7 full hours to 3 hours and 25 minutes to get the correct answer of 10 hours, 25 minutes.

A rectangle has a length that is twice the size of its width. If the perimeter of the rectangle is 48 inches, what is the area of the rectangle in square inches?

128 in2 Since the length is twice the size of the width, the equation for the perimeter would be P=w+w+l+l=w+w_{}+2w+2wP=w+w+l+l=w+w​+2w+2w. Since the perimeter is 48, 48=6w48=6w so the width is 8 and the length must be 16. The area would then be A=lw= \left( 16 \right) \left( 8 \right) =128A=lw=(16)(8)=128 in2.

What is the total surface area of the figure provided?

132 in2 The total surface area is the surface area of all of the sides combined. The surface area of the two triangular bases is ½ × b × h = ½ × 3 × 4 = 6. There are two bases so their surface area is 12. There are three rectangular faces to the prism. 3 × 10 + 4 × 10 + 5 × 10 = 120. The sum of the lateral faces and the bases is 120 + 12 = 132 in2.

Hailey's mom wants to help her practice using fractions. They decide to make their famous chocolate chip cookie recipe, but it will need to be tripled so that she will have enough for all of the third-grade students. The original recipe calls for 2 ½ cups of flour and ¾ cup of sugar. How much more flour than sugar does she need to make enough cookies for her grade?

5 ¼ cups 2 ½ × 3 = 7 ½ which is the total amount of flour needed. ¾ × 3 = 2 ¼ which is the amount of sugar needed. 7 ½ - 2 ¼ = 5 ¼.

What words describe the polygon below?

Regular and convex This heptagon is equiangular and all sides are congruent. It is also convex as all interior angles are less than 180°.

What is the volume of the provided right rectangular prism?

1¼ m3 The volume of a right rectangular prism is equal to l \times w \times hl×w×h. Therefore, the volume of this right rectangular prism is 2.5 \times 0.5 \times 1 = 1.252.5×0.5×1=1.25 m3.

What is the volume of a ball that is 12 cm in diameter?

288π cm3 The volume of a sphere is equal to 4/3 × π × r3. Since the diameter of the ball is 12 cm, the radius of the ball is 6 cm. Therefore the volume of the sphere is equal to 4/3 × π × 63, which equals 288π cm3.

What is the perimeter of the figure provided?

48 cm To find the perimeter, add the lengths of all sides. Since the right side has a length of 88 and the square cutout has side lengths of 44, the left edges must have a combined length of 44. P=8+12+4+4+4+4+12=48 \text{ cm}P=8+12+4+4+4+4+12=48 cm

Below is an example of a student's work: 4/16 - 1/8 = 3/8 10/13 - 3/8 = 7/5 3/5 - 2/3 = 1/2 If the student continues making the same error, the student's most likely answer to the problem 9/16 - 3/4 would be:

6/12 In each example the student is subtracting both the numerators and denominators. When subtracting fractions, the student should find a common denominator and then subtract only the numerators. The student is not finding a common denominator but subtracting both the numerators from each other and the denominators from each other. Thus the most likely answer if the student performed (9/16) - (3/4) would be (6/12).

A second-grade teacher encourages her students to add two-digit to one-digit numbers by "grabbing the larger number in their mind" and using their fingers to count up to find the total. What counting technique are students using when they do this?

counting on By starting with the larger number in their head and counting up with their fingers, students are using a strategy of counting on.

Mr. Harris has several English-language learners in his classroom. He is currently beginning a unit about circuits. Which of the following activities will be most effective in engaging Mr. Harris' English-language learners in a lesson?

giving students bulbs, batteries, and connecting wires and asking them to try to make the bulbs light up Experimentation is one of the most engaging ways to start a lesson for English-language learners because it does not rely on their language skills. Later, Mr. Harris could help the students learn vocabulary associated with what they observed.

The teacher provides a word problem for her students: Sandra is making sandwiches for her family's camping trip. She has 72 slices of turkey, 48 slices of cheese, and 96 pieces of lettuce. What is the greatest number of sandwiches she can make if each sandwich has the same filling of turkey, cheese, and lettuce? Which of the following mathematical concepts is she most likely teaching in this lesson?

greatest common factor The greatest common factor is the largest number that can be evenly divided into a set of numbers. Finding the greatest common factor is the first step to solving this problem.

A third-grade student draws the following array: Based on this image, the student is most likely solving what problem?

3 × 5 The array shown has 3 rows and 5 columns, which correctly models the problem 3 × 5.

Which math expression is not represented by the array below?

48 × 1/8 This array does not show any fractions.

Which of the following options shows a logical and correct first step to solving the algebraic equation given? 3(2x + 1) - 5(x + 4) = 113(2x+1)−5(x+4)=11

6x+3−5x −20=11 The equation 3(2x + 1) - 5(x + 4) = 11 is best approached by distributing the values from outside of the parentheses into each set of parentheses. It is important to note that the 3 distributed into the first set of parentheses is a positive 3 and so will not change the signs of the quantities it is multiplied with. However, the quantity following that first set of parentheses shows that 5 times a quantity will be subtracted. Therefore, the 5 distributed into the second set of parentheses is a -5, which will change the sign on the x and the +4. Therefore, the left side of the equation becomes: 3(2x + 1) - 5(x + 4) = 3(2x) + 3(1) - 5(x) - 5(4), which results in the equation becoming 6x + 3 - 5x - 20 = 11.

Christopher had a basketball tournament on Saturday from 10:45 am to 6:15 pm. How long was tournament?

7 hours, 30 minutes The easiest way is to add hours from 10:45 am to 5:45 pm and then add minutes from 5:45 pm to 6:15 pm. Using this method, counting can begin from 10:45 am to 11:45 am (1 hour) to 12:45 pm (2 hours) to 1:45 pm (3 hours) to 2:45 pm (4 hours) to 3:45 pm (5 hours) to 4:45 pm (6 hours) to 5:45 pm (7 hours) and continue with 5:45 pm to 6:00 pm (15 minutes) to 6:15 pm (30 minutes), to come up with the correct final answer of 7 hours, 30 minutes.

What is the area of the figure provided?

80 cm2 One way to find the area is to find the area of the large rectangle, then subtract the area that is cut out. A=A_{rectangle}-A_{square}=(12\times 8)-(4\times 4)=96-16=80 \text{ cm}^2A=Arectangle​−Asquare​=(12×8)−(4×4)=96−16=80 cm2. Another way to find the area is to separate the shape into rectangles, one large rectangle on the right and two smaller, congruent, rectangles on the left. A=A_{large rectangle}+2A_{small rectangle}=(8\times 8)+2(2\times 4)=64+16=80 \text{ cm}^2A=Alargerectangle​+2Asmallrectangle​=(8×8)+2(2×4)=64+16=80 cm2

Which symbol most accurately reflects the relationship between the two numbers below? 0.8 ☐ 4/3

< Since the numerator (4) is more than the denominator (3) of the fraction, it is more than 1.0.

A teacher wants his students to learn about different forms of energy in everyday life. Which of the following is the most engaging way to start a lesson that relates to the lesson goals and encourages students to see themselves as scientists?

Give students time to rotate through several hands-on science experiments that demonstrate the transformation of energy from one form to another. Not only does this pique interest in energy transformations, it also allows students to be scientists as they form theories and ideas about the different forms of energy present in the experiment.

Which activity would best support kindergarten students in developing the ability to ask questions and seek answers through investigations?

Telling students that there is a problem with litter in the city and that the city planners would like a solution, and then guiding students into asking questions about the problem and suggesting ways to test solutions. This inquiry-based activity is tied directly to the learning goal. Students would be learning what makes a testable question.

The following sequence is an example of which type? 81, -27, 9, -3, 1, -\frac{1}{3},...81,−27,9,−3,1,−31​,

a geometric sequence, - \frac{1}{3}−31​ is used as the common ratio. Geometric sequences have a common ratio. In this case, every term is multiplied by - \frac{1}{3}−31​ to find the value of the next term.

Which of the following terms would be used to describe a polygon with six sides whose angles are all of equal measure?

a regular hexagon Since all angles are of equal measure, the polygon is regular. Since it has six sides it is a hexagon.

What is the next shape in this pattern?

triangle The pattern is circle, square, two triangles, circle, square, triangle. The sequence starts again with circle, square, triangle, so the next shape needed would be a second triangle.

A first-grade class has been working on place value for several days. The teacher notices that some students are still struggling with the basic concept, some students are improving but still need additional practice, and some students have caught on quickly and are becoming bored. She plans to work with students in small groups while the rest of the class works in stations or independent work. What would be the most appropriate way to group students in this scenario?

homogeneously Homogeneous grouping is appropriate for this scenario because it allows the teacher to target specific skills with each group or provide enrichment opportunities for students who have mastered the skill.

A mathematics teacher gives her class a two-question clicker quiz at the end of each class period and tabulates their answers according to their mathematical understanding, misconceptions, and error patterns. If her goal is improvement in her students' mathematical proficiency, her best use of the data would be to use it to:

inform upcoming instructional strategies. Data on student understanding, misconceptions, and error patterns is best used to inform instructional strategies on the same or subsequent topics.

Which of the following are equivalent to dividing 144 by 9? Select all answers that apply

(121 ÷ 11) + (55 ÷ 11) 144 ÷ 9 = 16 and (121 ÷ 11) + (55 ÷ 11) = 11 + 5 = 16 C (24 ÷ 12)(64 ÷ 8) 144 ÷ 9 = 16 and (24 ÷ 12)(64 ÷ 8) = (2)(8) = 16 D (16 ÷ 4)2 144 ÷ 9 = 16 and (16 ÷ 4)2 = 42 = 16

A classroom is 7.5 meters wide. How many centimeters wide is the room?

750 cm Remember that Centi- means 1/100. 1 m = 100 cm therefore, 7.5 m = 750 cm.

Jordan was simplifying the expression: 3x^{2}-4+8x-5x^{2}+63x2−4+8x−5x2+6. She simplified it to 8x^{2}+8x+108x2+8x+10, and then raised her hand to have her teacher check her work. Of the following, what is the best response from the teacher to Jordan?

Jordan is not correct. Every term has a sign to the left of it. When she combined 3x^{2}3x2 and -5x^{2}−5x2, she disregarded the sign of the 5x^{2}5x2 term and got 8x^{2}8x2 when she should have simplified it to -2x^{2}−2x2. She made the same mistake when adding the constants. She dropped the negative in front of the 4; -4 and 6 combine to 2. Jordan had a sign errors for the terms that were negative. Every term has a sign to the left of it.

A number x is squared and then multiplied by 2, then 7 is subtracted and that result is divided by 4. Which of the following sequential steps would reverse that procedure?

Multiply the final number by 4, add 7, then divide by 2. Then take the square root of the result. These are the inverse operations used in reverse order.

A student asks the teacher who invented the number system we use today. Which of the following answers would be most appropriate?

The base-ten number system was developed by the Hindu-Arabic civilizations. The base-ten number system, which is the foundation of the modern number system, was developed by Arabic and Hindu civilizations.

A second-grade class has been learning about using appropriate units to measure length. They have learned about inches, feet, and yards. Which of the following would be the most effective set of questions to have students answer in a group discussion?

What unit would you use to measure your pencil? Why? This set of questions encourages students to think about the reasons for using different units. By explaining why they would use a specific unit to measure a pencil (likely inches), students are able to demonstrate their reasoning for selecting that unit of measurement.

Technology is best utilized in the classroom when it can accomplish which of the following?

enhances the learning objective Technology is best used to enhance the learning objective of the lesson.

Which of the following best describes a high-stakes assessment, such as state mandated exams?

formal summative assessment The purpose of the state standardized assessments is to determine the progress of students, based on state mandated, grade specific criteria. It is a formal assessment and is summative because it comes after instruction is completed.

Mr. Habib bought 8 gifts. If he spent between $2 and $5 on each gift, which is a reasonable total amount that Mr. Habib spent on all of the gifts?

$32 Mr. Habib spent at least $16 and at most $40: $16 if every gift cost exactly $2 and $40 if every gift cost exactly $5. So only amounts within this range are reasonable.

The graph shows the relationship between the cost of a wedding and the number of people attending the wedding. According to the graph, what is the initial cost to host a wedding without any guests in attendance?

$400 This is the y-intercept of the graph, which is the initial cost (0 guests).

Simplify the expression: 82 - 100 \div 4 + 6 \times 1282−100÷4+6×12

129 Remember to do both multiplication and division before addition or subtraction. 82 - 100 \div 4 + 6 \times 1282−100÷4+6×12 82 - 25 + 6 \times 1282−25+6×12 82 - 25 + 72 = 12982−25+72=129

A student asks the teacher, "Why is the area of a triangle formula ½bh?" Which of the following would be the most appropriate answer for the teacher to provide

A parallelogram is the combination of two congruent triangles. Since the area of a parallelogram is bh, one half of the area of a parallelogram equals the area of a triangle. Every parallelogram is made up of two congruent triangles. The area for a parallelogram is base × height (bh), so the area of each of the two congruent triangles is one half of the parallelogram, or (1/2bh).

A teacher wants her students to demonstrate mastery of combining and dissecting figures. Which of the following is the best activity to determine if they have mastered this concept?

A project where students determine the area of 10 oddly shaped objects they have encountered in the last week and describe the process. This allows students to demonstrate mastery both in the objects they choose and their approach to determining the area. This also relates math concepts to the real world.

A teacher wants to introduce her students to three dimensional figures. Which of the following is the best first activity to do?

Give students models of various three dimensional figures and have them write what they observe about the figures. Starting with something concrete that students can interact with will help them understand what three dimensional objects are.

A teacher is introducing the concept of volume to his fifth-grade class. Which of the follow is the best initial activity?

Give students several hollow objects and ask them which they think can hold more water and why they think that. Then allow them to determine the volume of water that fits inside each object. This is an engaging activity at the concrete level of learning.

Which of the following is a main benefit of using inquiry-based learning in the classroom?

Inquiry-based learning encourages students' scientific inquiry and develops their skills using the scientific method. Encouraging scientific inquiry and developing scientific method skills are main benefits of using inquiry-based learning.

Suppose Mike's actual weight is 165 lbs. His scale says his weight is 164 lbs. What can be said about his scale?

It is accurate. This scale is accurate because it gives a weight close to his actual weight.

Mr. Harris assigns his students to create a factor tree of the products of a number. One student turns in the product factor tree of 32 shown here. Which of the following best describes the error in this factor tree?

The factor tree identifies the sums and not the product factors of many of numbers. The third level of factors is the sum of the second level numbers (4 + 4 = 8). The correct factors of eight would be either (4 and 2) or (1 and 8).

John made a circular garden in his backyard. The garden has a diameter of 20 feet. He used ⅓ of the garden for tomatoes, his favorite vegetable. He enclosed the entire garden with a picket fence that was 12 inches high. Which of the following questions could NOT be answered with the information provided?

What is the volume of the dirt in the garden? Only this question cannot be answered with the information given because we do not know the depth of the soil to be planted.

Which term best describes the figure shown?

a trapezoid Trapezoids have one pair of parallel lines and one pair of non-parallel sides.

Students are plotting improper fractions on a number line. Quincy places a fraction between the 5 and the 6 on the line. If the denominator is 3, which of the following could be the numerator?

17 The fraction must be greater than 5, which is equal to 15/3, and less than 6, which is equal to 18/3. 17 is the only number that meets the requirements.

A sixth-grade class is asked to estimate the answer to the following question: 75.8 + 326.79 + 488.92 ÷ 11 = _____. Which of the following would be the best answer?

450 This question checks for understanding of estimation and the order of operations. Since this problem involves both addition and division, division MUST be done first. 75.8 + 326.79 + 488.92 ÷ 11 is more clearly written as (75.8 + 326.79) + (488.92 ÷ 11) where the division will be done first. Since this is an estimation problem, it would be about 500 / 10, which is 50. Then 75.8 + 326.79 is about 400. Adding the 50 and 400, we get about 450.

Sabrina finds a coat on sale for 18% off the original price of $85. She computes her potential savings in the following way: \$85 \times 0.18$85×0.18 Which of the following methods could Sabrina also use to correctly determine the potential savings?

$85×10018​ The percentage 18% is equivalent to the fraction \frac{18}{100}10018​ and to the decimal 0.18.

Mrs. Janie asked her class to write their own geometric sequence. As she walked around the room, she noticed Brad had 3, 6, 2, 4, \frac{4}{3}, \frac{8}{3}, ...3,6,2,4,34​,38​,...written on his paper. When Mrs. Janie asked Brad to explain his sequence, he replied, "My sequence is a geometric sequence because you multiply by 22, then multiply by \frac{1}{3}31​, then you multiply by 22 again, then multiply by \frac{1}{3}31​ again and so on." What is the best teacher response to Brad's statement?

"Your reasoning has an error. In order for a sequence to be a geometric sequence, you must multiply by the same common ratio each time. You can not use two different ratios." This is correct, you must multiply by the same common ratio each time to calculate the next term in the sequence. Brad created a complex sequence.

The ΔABC in the coordinate plane will be translated 3 units to the right and then 4 units down. Which of the following points correctly expresses the location of vertex C after the translations?

(-2, -2) The original coordinates of point C are (-5, 2). A translation to the right increases the first coordinate, in this case, by 3 units: -5 + 3 = -2. A translation down decreases the second coordinate, in this case, by 4 units: 2 - 4 = -2.

Triangle ABC has been plotted on a coordinate graph with the points A (-3, 1), B (-1, 3), and C (-1, 1). If the triangle is translated 5 units right and 2 units down, what are the new coordinates of point A?

(2, -1) A translation of a geometric figure moves the entire figure to a new location in the same coordinate plane. If the movement is a shift to the right, the x-coordinate (first coordinate) should be increased. If the movement includes a shift down, the y-coordinate (second coordinate) should be decreased. Therefore, if the point (-3, 1) is shifted 5 units to the right and 2 units down, the new point will be (-3 + 5, 1 - 2) = (2, -1).

What is the prime factorization of 36?

(2²) × (3²) The prime factors of a number are the prime numbers that divide the integer exactly. The prime numbers then can be multiplied together to equal that number. The prime factors of 36 are (2²)*(3²). For 36, the factor tree would be: 36 = 4 × 9 = (2²) × (3²).

Which expression can be used to solve the following word problem? Mrs. Bussey has planned a field trip for the third grade students. They have 2 buses and 49 people that need rides. There are also 2 coolers that will carry the lunches that need to be stored on the bus. On the morning of the field trip, 3 students are absent. How many people will be on each bus?

(49−3)​/2 First, 49 people needed rides but then 3 students were absent, leaving 46 people needing a ride. Since there are 2 buses, there will be 23 on each bus.

Isabella is creating a function by making a table of values. So far, her table looks as follows: x y -1 5 4 3 0 -6 ? 7 If inserted into the blank in the table, which value of x would invalidate her function?

-1 There is already an input of -1 in the table, which corresponds to the output of 5. Inserting another input of -1 that corresponds to 7 means that her function would violate the vertical line test.

The graph of the function f(x)f(x) is shown. For what value(s) of xx does f(x) = 1f(x)=1?

-4, -1, and 4 The expression "f(x)f(x)" means "the value of the function," which is the y-coordinate of the function for that x. So, "f(x) = 1f(x)=1" means that the y-coordinate equals 11. Therefore, the question is asking for the x-value(s) with a y-coordinate of 11. This question is answered with a simple look from left to right across the function for intersection with the horizontal line y = 1y=1. The x-values that have a y-coordinate of 11 are -4−4, -1−1, and 44.

In which of the following are the numbers ordered from greatest to least?

1, ½ , ¼ , -1 Since 1 is a positive, whole number, it's the largest. Since -1 is negative, it's the smallest number. With fractions, if the numerator (top) is the same, then the smaller denominator is a larger fraction; for example, 1 out of 2 is 50% but 1 out of 4 is 25%. Therefore, 1 > ½ > ¼ > -1.

What is 19,968 rounded to the hundreds place?

20,000 19,968 is rounded by looking at the digit to the immediate right of the place value being rounded to. In this case, look at the 6 and know that the number rounds up. Because there is a 9, it rounds to 0 and the one is carried over. The thousands place also has a 9 so when 1 is added, it becomes 0 and the one is again carried over. The ten thousands place is now 2 for a final answer of 20,000.

If \frac{1}{5}x + 3 = 651​x+3=6, what is the value of x?

15 To solve, isolate x. \frac{1}{5}51​x + 3 = 6 \frac{1}{5}51​x = 3 x = 15

Juan is 5 feet tall and casts a shadow that is 10 feet long. If the flagpole casts a shadow that is 30 feet long, how tall is the flagpole?

15 feet Since Juan and the flagpole are in the same setting, they are creating similar shapes. A proportion can be used. Juan is 5 feet tall and casts a 10 foot shadow, while the unknown height flagpole casts a 30 foot shadow. So, 5/10 = x/30. Rearranging, x = (5/10)30, or 15.

Put these fractions, decimals and percentages in order from greatest to least: 15%, 0.34, 245%, 2 ¾, 1.5, 1/15

2 ¾, 245%, 1.5, 0.34, 15%, 1/15 It is easiest to convert these numbers to decimals and then order them. 15% = 0.15, 0.34 = 0.34, 245% = 2.45, 2 ¾ = 2.75, 1.5 = 1.5, 1/15 = 0.067

Mrs. Keller writes down the following numbers on the board: 4, 2, 6, 8, 9, 1, 3 She instructs her students to write down the smallest number possible with the 8 in the thousands place and the 1 in the tens place. Which of the following would be the correct answer?

2,348,619 This is the smallest number that has the number 8 in the thousands place and the number 1 in the tens place.

Which of the following depicts the operation 1\frac{1}{2}+\frac{4}{5}121​+54​?

2103​ First convert 1\frac{1}{2}121​ to a mixed fraction. 1\frac{1}{2}\rightarrow \frac{3}{2}121​→23​. To add two fractions, find a common denominator. Since 2 and 5 are prime numbers, their least common multiple is their product, 2\times 5=102×5=10. \frac{3}{2}\times \frac{5}{5}=\frac{15}{10}23​×55​=1015​ \frac{4}{5}\times \frac{2}{2}=\frac{8}{10}54​×22​=108​ Then the original expression can be rewritten and solved: \frac{15}{10}+\frac{8}{10}=\frac{23}{10}1015​+108​=1023​ This can be simplified to 2\frac{3}{10}2103​.

Jessica is having 42 friends over for her party. She baked 7 extra-large pizzas with 12 slices each. If everyone shares equally, how much of one pizza will each friend eat?

61​ To find how much each person eats, we need to split 7 pizzas into 42 portions, so \frac{7}{42}=\frac{1}{6}427​=61​, so each person will eat \frac{1}{6}61​ of a pizza.

Which of the following word problems is a valid question to prompt writing the equation: 8 - 5 + 3 = n8−5+3=n?

8 birds were sitting on a fence. 5 birds flew away and 3 more birds landed on the fence. How many birds are on the fence now? The best response begins with 8 items, uses language to lower the initial amount of items by 5, then to raise the resulting amount by 3, and finally asks how many items there are in the end. Only the answer choice with the birds begins with 8 items (8 birds), has 5 removed (5 fly away), 3 added in (3 more birds landed on the fence), and then asks "How many birds are on the fence now?"

A teacher draws a 10x8 grid on the board without any "X"s in the grid. The teacher then writes "X"s in one and a half rows of the grid. The teacher asks the students to create an equation to represent blocks left on the grid, if the "X"s represent the blocks that have been removed. Which of the following is the best equation in response to the teacher's question?

80 - 15 There are 80 blocks on the grid. If 15 are removed, then the equation 80 - 15 represents this.

Which symbol most accurately reflects the relationship between the two numbers below? 0.6 ☐ 3/5

= Since 0.6 and 3/5 (0.6) are equal, this is the correct symbol.

A diagram of Layla's backyard is provided. The blue square represents a pool recently installed. Her backyard has a total area of 1,800 square feet. Which equation could be used to determine A, the area of Layla's backyard remaining for landscaping?

A=1800−(20 ×15) To find the area of the yard after the pool was installed, you would need to subtract the area taken up by the pool from the total area of the yard. The area of the yard taken up by the pool is 15 x 20 = 300 ft², so the area remaining left for landscaping is the difference.

Ms. Nakaroti wants to teach her students about properties of points, lines, planes, and angles. Which of the following should she include in her planning for the unit?

Analyze the standards to determine learning objectives before she starts writing lesson plans. The standards should always be consulted before beginning lesson planning.

Which of the following best describes the polygon shown?

Concave hexagon A concave hexagon has 6 sides and at least one angle larger than 180\degree180°. This hexagon has one, the bottom middle interior angle.

Mr. King gives his students this figure and asks students to determine its perimeter. About 80% of the students give the correct response, but he receives several responses of 100. How should he address the issue?

During group work, pull aside the students who go the answer incorrect and review the difference between perimeter and area. This allows students to correct their misunderstanding without delaying the progress of the entire class.

Which of the following comparisons between equations and inequalities is NOT true?

Equations are solved using inverse operations while inequalities cannot be solved with inverse operations. This is false; both equations and inequalities can be solved using inverse operations to isolate the variable.

A third-grade teacher wants students to learn about the structures that help organisms survive within their environments. Which of the following activities best supports critical thinking and relates to the lesson goal?

Have students find similarities and differences in the breathing apparatus of fish, amphibians, and reptiles and connect their findings to life underwater versus life on land. This activity supports critical thinking by having students look for and find patterns, and it relates directly to the learning goal.

Mrs. Wheelan is teaching geometric shapes and wants to use informal reasoning questions for discussion. What question is best to start with?

How do geometric shapes play a role in daily life? This is an open-ended question and it allows for real-world connections.

Students were asked to name point B. Zoe wrote that B equals -2.4, Julio responded that it equals -2 ¼, Sage said that it equaled -3 ¾ and Kaitlyn said that Zoe and Julio were both correct because the numbers were equivalent. Which student was correct in their response?

Julio Point B is between -2 and -3. It is halfway between -2 and -2 ½ which means it is located at -2 ¼.

Ms. Todd gives students a project where she gives all students in her class a single set of ordered pairs numbered 1 through 30. They need to graph ordered pairs in order and then connect the dots in the order in which they are graphed to make a picture. This serves as their final unit project on graphing points on the coordinate plane. Is this a suitable project?

No, because students can easily copy each others work. Since all students receive the same ordered pairs copying may be rampant and students may not be demonstrating mastery.

As part of a lesson on electricity, Mrs. Garcia has her students complete the concept map shown here. If one student erroneously placed "lightening" in the box marked with an asterisk (*) and colored yellow, what is the best activity for Mrs. Garcia to do?

Partner that student with one that had this bubble correct and have them discuss and edit their maps. Lightning is a form of electricity, but not a source. This term should be in a bubble on the right hand side. By partnering with another student to discuss, the student can receive peer feedback.

Mrs. Smith is teaching 2 digit by 2 digit multiplication to her class. By assessing her class with exit slips, she notices that 10 of her 22 students have achieved the same solution, seen here. What should Mrs. Smith teach tomorrow? 16x18= 128+16=144

She should reinforce placeholder zeros. Students forgot to put a placeholder zero and therefore added the two products incorrectly.

Jessica starts to count by 3's: 3, 6, 9, 12, 15, 18, ... Which counting technique is she using?

Skip counting Skip counting is counting by something other than one, such as counting by 5's or 10's.

Mr. Wheeler has taught prime factorization to his class this week. In an effort to differentiate instruction, he decides to block off time to provide remediation for students with learning disabilities. What is the main problem with this approach?

This targets only one group of students, which may or may not have struggled with this specific concept. He needs to evaluate who struggled with this concept before providing additional instruction.

Which of the following is the best way for elementary students to learn inverse operations?

Use a number line to illustrate adding and subtracting the numbers in a fact family. This allows students to visualize the concept and understand opposite operations.

A student asks a teacher when would knowing the likelihood of a six being rolled on a dice be useful in real life. Which of the following examples would be the most appropriate response for the student?

a casino estimating the expected number of jackpot payouts over the next fiscal year Companies of chance (like casinos, insurance companies, etc) estimate the number of claims they will have to pay over the course of a given time period. This is a great example of probability and statistical analysis.

A kindergarten class is finishing a lesson on two-dimensional shapes. Which of the following would be the most beneficial activity that creates real-world connections for students to complete?

a scavenger hunt in which students work in pairs to find examples of different shapes in the classroom This activity would be the most beneficial for students because it allows them to apply what they have learned about 2D shapes to their daily lives and the objects that they see in the real world.

Anytown School District provides a 50 multiple-choice question mathematics assessment to all students. The students complete the assessment, the tests are scored, and the scores are compared throughout the school district. Which of the following mathematics component is most likely the goal of this type of assessment?

accuracy The assessment most likely is designed to measure the students' accuracy of answering questions since it is multiple choice.

Which of the following would be an appropriate time for a classroom teacher to use a formative assessment?

all of the above are good times for a formative assessment Formative assessments should occur regularly in every classroom. Effective teachers are always watching and assessing their students' progress in order to adjust instruction and address misunderstandings as they occur.

A third-grade teacher is working with a small group of students on representing fractions. She asks students to use the method of their choice to represent ¾. All of the students choose to draw a circle divided into 4 equal parts and color 3 parts. She then asks students to represent the same fraction in another way. Which of the following is NOT a method that the students could use to represent ¾?

an array Arrays are used to represent multiplication or division problems, not as a way to represent fractions.

A second-grade teacher is planning an introductory lesson on ordering numbers on open number lines and wants to incorporate technology into the lesson. Which of the following would be the most effective use of technology in this scenario?

an interactive number line on which students can drag and drop numbers to the correct place This allows students to be actively engaged in the lesson. Students are completing an activity that helps them achieve the learning goal of ordering numbers on a number line.

Which of the following activities will best allow students to self-identify their misconceptions?

applying the scientific method to an idea in class and designing an experiment This method will best allow students to self-identify their misconceptions.

A third-grade teacher is working on multiplying one-digit numbers with a small group of students and plans to have the students solve three different multiplication problems. Which of the following would be the best way for the teacher to promote mathematical reasoning skills while working with the small group?

asking students to solve one problem using two different strategies of their choice and then having each student explain their reasoning to other students in the group Having students solve one problem in more than one way is a great way to improve mathematical reasoning skills because it allows students to see the problem from multiple angles. Having students explain their thought process encourages metacognition and also gives them the opportunity to hear other strategies from their peers.

If -¼ is the 11th term in a geometric sequence where r = -½, then what is a₁?

a₁ = -256 Since this is a geometric sequence, the formula t_n = a_1r^{(n - 1)}tn​=a1​r(n-1) can be used. Here, n = 11n=11, r = -½r=−½, and a(11) = -¼a(11)=−¼. a(11) = a_1r^{(n - 1)} a(11)=a1​r(n-1) -¼ = a_₁(-½)^{(¹¹⁻¹)}−¼=a₁​(−½)(¹¹⁻¹) -¼ = a_₁(-½)^{10}−¼=a₁​(−½)10 -¼ = a₁(\frac{1}{1024})−¼=a₁(10241​) The final answer is found by dividing 1/1024 on each side of the equation. The result of that step of division or multiplication by a reciprocal is -256−256, so a_₁ = -256a₁​=−256.

Based on the figure, which of the following is true?

line EF is perpendicular to line ST It is given that line EF is perpendicular to line UV. ST is parallel to line UV because the alternate interior angles of its transversal, AB, are congruent. Therefore, Line EF is also perpendicular to line ST.

In the figure, which line represents a line of symmetry?

line m Line m is the line of symmetry in this sketch. If you were to fold the figure on line m, the two halves would match up perfectly - much like the wings of a butterfly. One half would become a reflection of the other half when folded on m. This is not true of any of the other lines.

Which is the most appropriate unit to measure length of the average football field?

meters A meter is close to a yard which is the actual unit for measuring a football field.

Mrs. Brooks sets up a few math stations for her kindergarten students. One station has a 10-sided dice, a bowl of beads, and a recording sheet with a row of 3 boxes. When the students arrive at this station, they roll the dice and place that number of beads in the center box of their recording sheet. Then, they create one number to the left and one number to the right of the number on the dice, using the beads, in the other two boxes on their recording sheet. They record all 3 numbers the beads represent, then repeat the activity. Which of the following topics are the students most likely exploring in this station?

one more and one less In one more and one less relationships students subtract one and add one to a number.

Which of the following is the most appropriate unit for expressing the volume of an average glass of milk?

pint A standard serving of milk is 1 cup, which is equal to 1/2 of a pint.

Which of these has the greatest value?

0.435 This has the highest numbers in each of the place values.Therefore, the number is overall greater than any of the other choices.

Tia participates in marching band before school and plays volleyball after school. She arrived at school at 6:52am today and did not leave until 5:34pm. How many hours and minutes did she spend on the school campus?

10 hours 42 minutes 10 hours after her arrival is 4:52pm. It is another 42 minutes until 5:34pm, when she left.

Solve: 2 \frac{1}{2} \times \frac{1}{6}221​×61

125​ The first fraction can be changed into an improper fraction by multiplying the whole number (2) by the denominator (2) and adding it to the numerator (1). 2 \frac{1}{2} = \frac{5}{2}221​=25​ When multiplying fractions, you don't need a common denominator, so the original expression can now be re-written and solved by multiplying across: \frac{5}{2} \times \frac{1}{6} = \frac{5}{12}25​ ×61​=125​ This can't be simplified further.

At Memorial High School, 60 of the 240 freshmen students are on an athletic team sponsored by the school. If the ratio is the same for the sophomore class, how many of the 220 sophomores are NOT athletes?

165 The ratio 60/240 = ¼ so ¾ of students are not athletes. Since this can be applied to the sophomores, ¾ × 220 = 165 sophomores.

Consider the algorithm below: Step 1: Select a numerical value for n. Step 2: Subtract 4 from n. Step 3: Square the result Step 4: Multiply the result by 3 Step 5: End Which of the following is an equivalent algebraic expression?

3(n-4)2 The key steps are #3 and #4. Only (n-4) is squared and then multiplied by 3.

Which symbol most accurately reflects the relationship between the two numbers below? 1.21.2 ☐ \frac{9}{10}109​

> Since the numerator (9) is less than the denominator (10) of the fraction, it is less than 1. Therefore, 1.2 is greater than \frac{9}{10}109​.

The function f(x) = 26.00 + 13.75xf(x)=26.00+13.75x describes the rental fee for an air compressor, where f(x)f(x) is the total cost and xx is the number of rental hours. The equation models which of the following situations?

A fixed rental charge of $26.00 plus an additional charge of $13.75 per hour. The total rental fee f(x) equals the $26.00 base rate plus $13.75 times the number of hours, x

Which of the following sequences of steps will yield the valid solution for x to the equation -8 + 5x = 12?

Add 8 to each side of the equation, then divide by 5 on each side of the equation. Of these options, only adding 8 and then dividing by 5 will yield the correct final answer to the equation. 8 is the additive inverse of -8 and so adding it simplifies the equation to 5x = 20. Then, dividing by 5 (or multiplying by its reciprocal, 1/5) will get the x completely alone because 5/5 = 1 and 1x is the equivalent of simply x. None of the other proposed sequences of steps would result in a valid solution.

Mrs. Dobbs is teaching students to skip-count by 2s, 5s, and 10s in her second-grade class. Earlier in the year, she evaluated her students learning style and assigns them one task based on this evaluation. Visual learners have been given a number line and they are to draw the hops across the top. Auditory learners have been given a list of the even number to 20, numbers divisible by 5 to 50 and numbers ending in 0 up to 100. They are told to say them over and over aloud to memorize the skips. Kinesthetic learners have been given a large number line on the floor. They are jumping to the next number as they skip-count. What can Mrs. Dobbs do to improve her teaching?

Allow all students to participate in all three activities by rotating through them. This encourages students to exercise different parts of their brain and strengthen different learning styles.

Ms. Miles is teaching her students about circles. Students are having problems with determining area because many of them are confusing the formulas for circumference and area. What should she do to address the problem?

Create an activity where students determine area and circumference in a hands on way to activate a concrete level of understanding. A hands on activity will help students remember the formulas and how they are used in a meaningful way.

Mr. Romeo wants his students to understand that math is very important and used in the real world all the time. He wants them to understand that math is used outside of school on a regular basis. Which of the following is the best way to have students learn about this?

Have students interview two adults about how they use math in their everyday life. Interviewing adults is helpful to demonstrate that people use math past school age.

At Ball High School, 70% of students are in an extracurricular activity. Which of the following circle graphs shows a shaded region that most accurately displays this data?

The shaded region is slightly less than ¾ or 75% of the circle. Therefore, it represents 70%. (almost 3/4)

A fifth-grade student was asked to multiply 15 and 35. His work is provided below. 35x15=1525+35=1560 As his teacher, what remediation would you plan on providing?

a remedial lesson on place value The errors come from a lack of understanding of place value. When the student multiplied 5 and 5, they should have decomposed the 25 into 20 and 5. The 20 would have carried as a 2 above the 3 and added to the product of 5 and 3. The student should have added an additional zero at the end of the result when he multiplied the 1 in the number 15 because its actual value is 10, not merely 1.

Which of the following activities would be most effective in helping first-graders understand partitioning 2-dimensional shapes into equal parts?

cutting out different shapes and having students fold them into 2 or 4 equal parts This activity provides a visual for the students to use when thinking about dividing a shape into equal parts.

Which of the following is an inquiry-based activity that could be used during a unit on specific heat?

measuring and graphing temperature versus time for different materials placed under a heat lamp Conducting an investigation, measuring, and analyzing data develops student inquiry skills.

What is the next shape in this pattern?

pentagon

Joshua is learning about volumes of three-dimensional figures. First, his teacher explains what volume is. Then, she writes the formula for area of a cube on the board v = s3. Next, she has the students recite "the volume of a cube is the side length cubed". Finally, she has students take six-sided dice of various sizes and measure them to determine their volume. Which best describes the teaching method is the teacher attempting to use?

task variety The teacher is using task variety because she is presenting the same material in multiple ways.

Interest is best defined as:

the cost associated with borrowing from the bank which issues a credit card. Using a credit card is essentially taking out many small loans, and interest is the cost of borrowing the money from the bank which issued your credit card.

Use the table below to answer the question that follows. x y 1 -2 3 4 5 10 9 22 Which of the following equations correctly models the relationship in the table?

y=3x−5 This equation correctly models the relationship in the table. Anytime the x value in the table is substituted for the "x" variable in the equation, the y value in the table is the result of the equation. 10 = 3(5) - 5; 22 = 3(9) - 5.

Which of the following numbers is neither prime nor composite?

1 One is neither a prime number nor a composite number.

In the image below, the area of the triangle is 1 unit2. What is the total area of the figure?

11 unit2 Dissecting the figure, it becomes apparent that each square consists of two triangles. The hexagon consists of 6 triangles. Therefore, the total area is 2 + 2 + 6 + 1 = 11 units2

How many edges does a rectangular prism have?

12 A rectangular prism has 12 edges.

If the measure of angle 1 = 70°, which angle also measures 70°?

3 Angles 1 and 3 are vertical angles. Vertical angles are made with 2 intersecting lines that cause two opposite pairs of congruent angles. Congruent means equal, therefore, making angle 3 also measure 70°.

Solve: 3 \frac{2}{5} + \frac{1}{3}352​+31​

31511​ The first fraction can be changed into an improper fraction by multiplying the whole number (3) by the denominator (5) and adding it to the numerator (2). 3 \frac{2}{5} = \frac{17}{5}352​=517​ When adding fractions, a common denominator must be found first. Since 3 and 5 are both prime, their least common multiple is their product (15). \frac{17}{5} \times \frac{3}{3} = \frac{51}{15}517​×33​=1551​ \frac{1}{3} \times \frac{5}{5} = \frac{5}{15}31​×55​=155​ Now the original expression can be re-written and solved: \frac{51}{15} + \frac{5}{15} = \frac{56}{15}1551​+155​=1556​ This can be simplified to 3 \frac{11}{15}31511​

What is the greatest odd factor of 2,496?

39 The prime factorization of 2,496 is 26 × 3 × 13. When multiplying the odd numbers (3 and 13), the greatest odd factor is 39.

Solve: \frac{6}{7} - \frac{2}{3}76​−32​

4/21​ When adding or subtracting fractions, a common denominator must be found first. Since 3 and 7 are both prime, their least common multiple is their product (21). \frac{6}{7} \times \frac{3}{3} = \frac{18}{21}76​×33​=2118​ \frac{2}{3} \times \frac{7}{7} = \frac{14}{21}32​×77​=2114​ Now the original expression can be re-written and solved: \frac{18}{21} - \frac{14}{21} = \frac{4}{21}2118​− 2114​=214​ Since 21 and 4 share no factors, it can't be simplified any further.

How many faces does a cube have?

6 A cube has 6 faces.

What is the value of the "8" in the number 17,436,825?

800 In a base 10 system, each place location for a number has a value that is a power of 10. Specifically, the ones place is properly understood to be 10⁰ (because any nonzero number raised to the zero power equals 1). The tens place is 10¹, the hundreds place is 10², the thousands place is 10³, etc. When a digit is in a specific position, its value is equal to the product of that digit and the power of 10 that is assigned to its position. Therefore, in the number 17,436,825, the 8 represents 8 × 10^2 = 8008×102=800.

Jemma likes to earn spending money through babysitting her neighbor's child and helping with extra chores at home. The expression 8b + 6c represents the total amount of money (in dollars) that Jemma can earn, where b is the number of hours of babysitting she completes and c is the number of chores she finishes. Which term represents the total amount of money that she earns from babysitting?

8b The full expression, 8b + 6c, represents the total money that Jemma can earn from a combination of activities. The portion of that which represents Jemma's earnings from babysitting is simply the 8b because b is defined in the given information as "the number of hours of babysitting she completes."

The Trout family just purchased a large table in the shape of a perfect circle. It is 600 cm across. John helps set one side of the table for dinner and walks exactly halfway around the table. Which of the following is closest to how far has he walked?

950 cm Since John walked halfway around the table, we are solving for half of the circumference, C = 𝜋d. Since the table is 600 cm across, d = 600 cm and therefore P = 600𝜋cm. John walked halfway around, so John walked \frac{1}{2}(600)\pi21​(600)π which is about 950 cm.

Ms. Netterville wants to find an engaging activity for students to demonstrate their understanding of United States currency. Which of the following activities is likely to be the most engaging and help ensure that all students are meeting the learning objectives?

Have students run a classroom store where they have to give appropriate change. This activity will be engaging and meet the learning objectives.

Which activity would best support first-grade students in developing an understanding of force and motion?

Have students use a ruler to push a low-friction object across their desks and describe the kind of push needed to make the object move in a straight line, in a zigzag pattern, and at different speeds. This inquiry-based activity is tied directly to the learning goal. Students would compare the strength and direction of the pushes needed to obtain each motion.

Ms. Ludgate would like her students to participate in an Engagement activity for a unit on vascular and nonvascular plants. Which of the following is the most appropriate for an Engagement activity in the 5E Instructional Model?

Have students pair up, and give each pair a sample of a nonvascular plant and a vascular plant. Ask students to make observations and notice differences, then have each pair share their findings with the class. This activity does not require prior knowledge. It is an effective engagement activity.

Formative assessments provide information that can be used for which of the following?

to change and improve instruction The purpose of formative assessments is to determine what students know about what they just learned. They are intended to be administered frequently throughout learning, not at the end. The teacher should use this information to change and improve instruction. In most instances, it is not appropriate to use a formative assessment as a grade.

Which of the following is the best way to use data collected from pre-assessment activities?

to drive instruction Pre-assessing student knowledge helps the teacher focus the direction of the lesson where needed and adjust the pacing to meet the needs of the learners.

A third-grade teacher is planning a lesson on representing data using dot plots. She plans to introduce the concept of dot plots, show examples, and create a class dot plot that shows how many siblings the students have. Which of the following would be the best way to incorporate technology into this lesson?

an online program that allows students to plot their data point on a dot plot Of the answer choices, this is the most effective use of technology because it involves student participation. By using an interactive online dot plot, the teacher is using technology for the most student-centered aspect of the lesson.

What equation describes the linear relationship shown in the table? x 2 6 9 12 y 7 19 28 37

y = 3x + 1 The table above is correctly represented by the equation y = 3x + 1 because each (x, y) pair presented in the table makes the equation true. 7=3 \left( 2 \right) +1; 19=3 \left( 6 \right) +1;28=3 \left( 9 \right) +1;37=3 \left( 12 \right) +17=3(2)+1;19=3(6)+1;28=3(9)+1;37=3(12)+1.

A survey is taken of students in a math class to determine what pets the students have. 7 students have birds; 15 students have cats; 18 students have dogs. Some students have more than 1 animal. For example, 3 students have cats and dogs and 4 students have cats, dogs, and birds. All students have at least one of these three types of pets. Which of the following would be the best strategy to use to answer a question about how many total students are in the class?

draw a Venn diagram A Venn diagram is a visual strategy.

Mrs. Marshall grades tests from the last unit and realizes most students are missing word problems because they do not identify the correct operation to use. They did demonstrate mastery on questions that provided the equation. How should she address this issue?

Provide a warm-up question each day and students must underline key terms that help decide what operation to use. If students understood the concepts being taught in the last unit at a basic level, providing practice through warm-ups allows her to address this issue and assess improvement on the next test.

Second-grade students, Bryan and Alexander, are working together to count money raised by the school's student council. They know the value of the penny, quarter, and dollar, but they consistently confuse the value of the nickel and dime. How can the teacher address this?

Provide hands-on examples where they act out different scenarios using nickels and dimes. Concrete examples where they handle and practice using the value of the money will help them master identifying the value of coins.

Number of Sales, x Monthly Salary, y 0 250 1 325 2 400 3 4 Mr. Miller gives students the table above and tells them about a commissioned sales person. He asks students to fill in the missing boxes and write a summary of how the number of sales, x, is related to the monthly salary, y. Which of the following best demonstrates how x and y are related?

y = 75x + 250 This equation satisfies the data table.

Which of the following equations satisfies the data table? x y -1 1 0 0 2 4

y = x2 This equation works for all sets of numbers. 1 = (-1)2 = 1 0 = (0)2 = 0 4 = (2)2 = 4

Which equation most closely represents the line of best fit for the scatterplot shown?

y=3/2​x+1 Graphing this equation will produce a line that has about half the points from the scatter plot above the line, and half below the line, and so is a good line of best fit.

x 3 4 6 9 11 y 12 15 21 30 36 The table above shows a linear relationship between x and y. Which of the following equations correctly defines the relationship?

y=3x+3 A linear equation is written in the format: y = mx + b. To determine the slope, m, find the change in y divided by the change in x. The slope is 3, so that must be in front of the x. Then, substitute one point in the problem to find b. 12 = 3(3) + b. 12 = 9 + b. b = 3

Ms. Monroe is teaching her students about counting money and change. In her morning class, she gives several word problems as practice. In her afternoon class, she has students run a school store and practice giving change. She finds that students in her afternoon class perform much better on the unit test. What could explain the difference?

Students found the school store engaging and learned the material better than students given word problems. Running the school store likely engaged the students and they found it interesting. The practice likely deepened their knowledge.

A class of sixth-grade students is given the following problem: 1/2 + 3/4 = Many of the students arrive at the answer: 1/2 +3/4 = 4/6 =2/3 What should the teacher NOT consider with respect to remediation?

Students need more work reducing fractions. The student reduced the answer correctly, but the answer was not accurate.

Which of the following is the best rationale for using formative assessment?

Students will show what skills they have mastered and what skills still need to be practiced. A formative assessment is used by teachers to determine what concepts students have mastered following instruction and then identify areas in which additional practice is needed. Teachers use formative assessment data to plan subsequent lessons.

Which of the following equations is written in slope-intercept form?

y=3x+5 Slope-intercept form of the equation of a line is y = mx + by=mx+b where mm and bb are numbers representing the slope of the line and its y-intercept, respectively.

Which of the following equations are linear? Select all answers that apply.

y=−3x−5 This equation will create a straight line so it is linear. - y=x−2 This equation will create a straight line so it is linear. - y=3 Since this equation only contains a constant, it is linear. Note that the equation could be written y=3+0xy=3+0x. - y=−(1/3)x−(5/3) This equation will create a straight line so it is linear.

Solve: \frac{-4(3-5) + 2}{-3[3+ 7(4)] + 8}−3[3+7(4)]+8−4(3−5)+2​

−172​ First, resolve the parenthesis on the top and bottom: \frac{-4(-2) + 2}{ -3(31) + 8}−3(31)+8−4(−2)+2​ Now, multiple terms outside the parenthesis with the term inside: \frac{8 + 2} {-93 + 8}−93+88+2​ Last, add, then simplify the fraction. \frac{10}{-85} = -\frac{2}{17}−8510​=−172​

A third-grade student is asked to find the best estimated answer for the problem below by rounding to the nearest ten. 162 + 287 + 395 The student gets an answer of 840. Which of the following best describes the student's error?

The student added the numbers first, then rounded the answer. Adding the numbers first and then rounding the answer would lead to the student's answer of 840 rather than the correct answer of 850. When estimating totals, students should be taught to round first, then add.

A second-grade student is given the problem 38 + 94. The student's work is shown below: 38 + 94 1212 Which of the following best describes the student's error?

The student did not regroup or "carry" the tens value when adding 8 + 4. From the work that is shown, it appears that the student added 8 + 4 to get 12, but wrote the number 12 under the line rather than placing the 1 ten above the 3 in the tens place. They then added 3 + 9 to get 12 and wrote it next to the original 12. Their incorrect answer resulted from not regrouping the 1 from 8 + 4 = 12.

For homework, Mr. Waters asked students to bring in 3 receipts from home. In class, they practiced rounding the prices of items and then totalling them to compare to the final price paid. What is the best reason this is good teaching method?

This makes connections between the classroom and the real world. This connection helps students see when they will use math throughout their lives.

Which of the following is the best way for elementary students to be introduced to rectangular arrays?

Using manipulatives such as 10-blocks to create their own arrays This gives them an opportunity to explore the concept concretely before having to put it into practice.

Which is the best way to help elementary students learn the scientific method?

Use ideas from the scientific method, with explicit instruction, in hands-on investigations throughout the year. Enabling students to repeatedly follow the scientific method, along with explicit instruction focusing on what they are doing and what they could do next, leads to real student understanding about the process of doing science.

A tennis ball has a diameter of about 3 inches. What is the approximate volume of a cylindrical container if it holds three tennis balls?

about 64 in³ To find the volume of a cylinder, the B (area of the base) is multiplied by the height. The tennis ball can is three tennis balls high or about 9 inches. B, the area of the base, would be the area of the circle with the diameter of the tennis ball, or 3 inches. If the diameter is 3 inches, the radius would be 1.5 inches and the area would be: B = A of circular base = πr² = π(1.5)² = π(2.25) ≈ 7.07 in². So, the volume of the cylinder would be: V = Bh ≈ 7.07(9) = 63.63 in³. 64 in³ is the best approximate answer to this question.

A first-grade class is finishing a unit on counting sets of coins. Which of the following would be an effective use of technology at the end of the unit?

an online assessment in which students select the set of coins needed to purchase different items This allows students to apply their knowledge of counting coins and actively involves them with the technology, making it the most appropriate option.

A third-grade teacher is planning a lesson on representing multiplication facts. She wants students to be able to model multiplication problems using a variety of different representations. Which of the following includes ways that the students could model a basic multiplication fact?

arrays, equal-sized groups, number lines All of these are common ways to represent multiplication problems. Arrays are used to arrange pictures in columns and rows to represent a multiplication problem. Equal-sized groups are a way for students to draw a picture to represent a multiplication problem. Number lines are used to model a multiplication problem in terms of repeated addition.

In a unit on personal finance, a sixth-grade teacher wants students to be able to identify the difference between fixed and variable costs. Which of the following examples would best highlight this difference?

categorizing the expenses of a local restaurant into expenses that depend on the number of customers and expenses that do no not depend on the number of customers This will help students highlight the differences between variable and fixed costs because the student is actively having to categorize an expense into one of the two categories.

Kate is starting a new babysitting job in which she will make $7 per hour that she works. Currently, she owes her parents $15, which she will have to pay back from her earnings. Below is a table of the amount of money Kate has saved since starting her job. Which of the following equations could best be used to demonstrate the relationship between x and y?Total hours worked, x Amount of Money Saved, y 0 -15 2 -1 4 13 6 27

y=7x−15 This matches the values in the table. If Kate makes $7 per hour, this represents her slope. The $15 she owes her parents represents the y-intercept and is negative.

A math teacher plans her instructional delivery method on resolving the difficulty students have distinguishing between mode and median. She plans to have students first work alone calculating the mode and median of sets of performance results from the school track team. Next, her students will work in groups of 2 or 3 to discuss and interpret their results, and record a summary of the significance of the results on whiteboards. Finally, the groups will present their summaries to the class, along with a teacher-led discussion of the findings. By planning such an activity, the teacher demonstrates that she understands:

how to apply a variety of instructional delivery methods that can help students develop their mathematical thinking. The teacher's plans show she understands how to use individual, small-group, and large-group instruction methods to help students develop their mathematical thinking.

Students are working to solve the following question: ½ - x = ¼. The teacher then gives the following as an example: "If you are sharing a pizza with somebody and there is half a pizza left, how much must the other person eat so that you only have one quarter of the pizza left?" As the teacher engages with several students, the teacher observes students are still having difficulty understanding the concept of fractions. The teacher then uses a pie chart to help explain the concept. Which of the following types of assessments has the teacher used?

formative This is correct because a formative assessment involves teachers adjusting their instruction based on the assessment of students; a formative assessment helps form a teacher's instruction. The teacher engages with the students, observes student difficulty with fractions, and then adjusts instruction.

A teacher has her students graph multiple linear equations with the same slope, and then record their observations about the equations and graphs. Which of the following goals is the teacher most likely to achieve?

have students connect the relationship between equations with the same slope and parallel lines Having students graph a series of equations with the same slope and record their observations will help students connect that all equations with the same slope but different y-intercepts will produce parallel lines.

The mathematics teacher and art teacher work together to create an interdisciplinary lesson using tessellations, which are basic geometric shapes set to a repeating pattern. The students cover a large piece of poster board with the patterns they create. Which of the following mathematical concepts is most closely reflected in this activity?

infinity The tessellations will continue in infinity. The teacher is introducing a mathematical concept that does not end, but repeats continually. This is the concept of infinity.

A student-athlete can run 10 yards in 6 seconds. Which equation shows the number of yards that can be run in s seconds?

s/0.6 If 10 yards can be run in 6 seconds, 1 yard can be run in 0.6 seconds. Therefore, the total number of seconds divided by 0.6 will give the number of yards run.

Mr. Swan wants to ensure that his students truly understand the material he is teaching. When students get questions incorrect on a test, he presents them the opportunity to correct their answers for half credit. He asks students questions such as "what if I changed this number?" and "why did you do this?" What process is Mr. Swan trying to get his students to engage in?

metacognition Metacognition is reflecting on one's thought process to deepen understanding. This is what Mr. Swan is attempting to do.

Miguel is playing with his model cars. Which transformation is represented in the picture of his cars?

rotation This is a rotation because the top car has been rotated 180° about the point at the center, which is the transformation between the two cars, leaving you with this position and orientation of the bottom car.

Which line segments appear to be perpendicular in the figure?

segment AB and segment BC Segment AB and segment BC appear to be perpendicular; they seem to intersect at a right angle to each other.

Which of the following scatterplots is most likely to have a line of best fit represented by the equation below? y=-4x+3y=−4x+3

short long decrease, The given equation has a y-intercept of (0, 3) and a slope of -4. If a line with these characteristics were to be graphed on the scatter plot, about half the points from the scatter plot would be above the line, and half below the line, making the given equation a suitable line of best fit.

A first-grade student is finding the value of a set of six nickels. What counting skill will this student most likely need in order to complete this task?

skip counting In order to efficiently count the value of six nickels, the student will need to already be familiar with skip counting by fives.

What is x in terms of y for the equation: 74 - 6x = 9y

x = (9y -74) ÷ -6 To isolate x, first subtract 74 from each side so the equation is -6x = 9y -74. Then divide both sides by -6: x = (9y -74) ÷ -6

Line QR is graphed on the xy-plane. Which of the following data tables corresponds to the graph?

x-1,0,1,2 y-1,1,3,5 These points are all found on the line.

Which equation best represents y in terms of x?

y = 1 - 2x The expression y = 1 - 2x is the only expression that satisfies ALL the possibilities on the chart.

Mr. Marlowe wants his students to be able to interpret word problems relating to geometry. He has many ELL students. What is the best way to clarify the meaning of various prepositions such as: above, below, together, apart, inside, etc.?

Give students a visual diagram that explains these terms. Visual diagrams will help students understand these terms.

Mrs. Blue wants her students to be able to write two column geometric proofs. Which is the most appropriate way to determine their mastery?

Give students an open ended exam where they write multiple two column proofs. Asking students to write a proof is the best way to determine if they can write a proof.

Mrs. Matthews is teaching her sixth-grade class about areas of regular geometric figures. How should she best introduce this topic to her students?

Give students pattern blocks to manipulate. Tell them the area of the smallest figure is one and ask them to determine the area of the larger figures. This method would allow students to engage with manipulatives they had used in earlier years and connect them to newer knowledge. This would be a good engaging experience that allows them to connect prior knowledge to new learning goals.

A second-grade teacher is planning a lesson on measuring length using standard units. Which of the following would be an effective way to engage students in the lesson while allowing them to practice measurement strategies?

Going outside to measure various parts of the playground in inches, feet, or yards. This is the best answer choice because it gives students the opportunity to apply what they have learned about measurement to real-world items that they are already familiar with.

Ms. Rose's class is learning about order of operations. While practicing this new concept, a student simplifies the following expression. 8-(4+3)^2 \times 68−(4+3)2×6 8-16+9 \times 68−16+9×6 8-16+548−16+54 -8+54−8+54 4646 Which of the following best describes the student's error?

The student evaluated the power of exponents before adding within the parentheses. With the order of operations, the expression inside the parentheses must be simplified before the exponent is evaluated.

What is the y-coordinate of the point on the line drawn when x = 125?

175 First, write an equation that gives the output, y, for any input, x. This is a straight line, and so the equation can be a linear equation in the form y=mx+by=mx+b. The line passes through the origin, so b=0b=0. The slope can be found using the two points on the graph: (25, 35) and (50, 70). Therefore, m=\frac{rise}{run}=\frac{35}{25}=\frac{7}{5}m=runrise​=2535​=57​. So the equation y=\frac{7}{5}xy=57​x represents the line. The question asks for the value of y when x=125x=125, so substitute 125 in for x in the equation to get y: y=\frac{7}{5} \left( 125 \right) =\frac{875}{5}=175y=57​(125)=5875​=175.

The time allowed for Elliot's lunch was 11:42 am to 12:10 pm. How many minutes was lunch?

28 minutes One option to determine the length of the lunch period is to see how long it is from the start of lunch to the next full hour (from 11:42 am to 12:00 pm), and then add the minutes part of the end time. In this case, 12:00 pm can be thought of as 11:60 am so that subtraction with 11:42 am is easy: 11 - 11 = 0, so 0 hours and 60 - 42 = 18, so it is 18 minutes until 12 pm. Then, from 12:00 pm to 12:10 am is 10 - 0 = 10 minutes. The total length of the lunch period is 18 + 10 = 28 minutes. Another option to determine the length of the lunch period would be to reason that if it were an hour long and started at 11:42 am, it would end at 12:42 pm. But this lunch hour ends at 12:10 pm, 32 minutes before 12:42 am (42 - 10 = 32), and so this class is 32 minutes shorter than 1 hour, or 60 - 32 = 28 minutes long.

A pancake recipe requires 1 tablespoon of baking powder per 2 cups of flour. If 2 cups of flour make 4 pancakes, how many tablespoons of baking powder are needed to make 12 pancakes?

3 1 tablespoon of baking powder per 2 cups of flour makes 4 pancakes -> 1 tablespoon of baking powder is used to make 4 pancakes. To make 12 pancakes, 3 tablespoons of baking powder are needed. To find this, divide 12 by 4 to the proportional increase in pancakes. 12 / 4 = 3 -> because the number of pancakes is 3 times as many as the recipe size of 4; multiply 1 tablespoon by 3 to get 3 tablespoons of baking powder.

The graph of the function f(x)f(x) is shown. For what value of xx does f(x) = -4f(x)=−4?

3 The expression "f(x)f(x)" means "the value of the function," which is the y-coordinate of the function for that x. So, "f(x) = -4f(x)=−4" means that the y-coordinate equals -4−4. Therefore, the question is asking for the x-value(s) with a y-coordinate of -4−4. This question is answered with a simple look from left to right across the function for intersection with the horizontal line y = -4y=−4. There is only one x-value intersecting here, 33.

Which of the following is equivalent to 3 meters?

300 centimeters 1 meter is equal to 100 centimeters. "Centi" sounds like "century" which has 100 years

The varsity basketball team has 3 freshmen, 5 sophomores, 3 juniors, and 4 seniors. Approximately what percentage of the basketball team is comprised of sophomores?

33% A total of 15 students are on the basketball team: 3 + 5 + 3 + 4 = 15. There are 5 sophomores on the team. The ratio of sophomores to the whole team can be represented by 5:15 = 1:3. 1/3 = .33 or 33%.

What is the area of the shaded region?

34 in2 One way to find the area is to find the area of the large rectangle, then subtract the area that is cut out. A=A_{\text{large rectangle}}-A_{\text{ small rectangle}}=(11\times 8)-(9\times 6)=88-54=34\text{ in}^2A=Alarge rectangle​−A small rectangle​=(11×8)−(9×6)=88−54=34 in2 Similarly, the shape could be divided into 4 rectangles, then the areas can be added together. A=2A_{rectangle_{1}}+2A_{rectangle_{2}}=2(11\times 1)-2(6\times 1)=22+12=34\text{ in}^2A=2Arectangle1​​+2Arectangle2​​=2(11×1)−2(6×1)=22+12=34 in2.

If the pattern below is continued, how many blocks will be in the 7th term?

36 The first model is made with three blocks, 1 in column 1, and 2 in column 2; the second term is made of 1 block in column 1, 2 blocks in column 2, and 3 blocks in column 3. So, term #1 = 1 + 2 blocks; term #2 = 1 + 2 + 3 blocks; term #3 = 1 + 2 + 3 + 4 blocks. Each term, n, is the sum of the numbers from 1 to (n + 1); the sum of the consecutive integers from 1 to (n + 1). So, the 7th term would be: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 or 36 blocks. This is a small enough number that you could actually sketch the model and count the blocks.

What is the volume of an ice cream cone that is 6cm wide at the top and 12cm tall?

36π cm3 The volume of a cone is equal to ⅓ × π × r2 × h. Since the diameter of the base of the cone is 6 cm, the radius of the base of the cone is 3 cm. Therefore the volume of the cone is equal to ⅓ × π × 32 × 12, which equals 36π cm3.

Mr. Feeny has been teaching fifth-grade math for thirty years. He will only accept answers from his students that follow his algorithmic procedures. If a student determines a correct solution by any method other than the way they were taught in class they will not receive credit. How could Mr. Feeny improve his teaching practice?

Teach students multiple varied ways to achieve the right answer and accept any correct answer as long as there is mathematically reasonable supporting work. This is the best choice. Students should be encouraged to think through a variety of ways to solve problems.

Solve the following equation. Write the solution as a fraction in simplest form. 3(4x - 5) + 8 = 9(2x - 1)

1/3 The first step in solving this equation is to simplify each side completely. The first step of simplification requires distributing into each set of parentheses to get 12x - 15 + 8 = 18x - 9. Next, like terms on each side are combined to the extent possible to get 12x - 7 = 18x - 9. Finally, solving can begin. While several steps would be valid at this point, the smaller variable part is often moved to join the larger and so 12x can be subtracted from each side to get -7 = 6x - 9. Now, the variable can be isolated by adding 9 to each side (2 = 6x) and dividing by the coefficient of x, 6, on each side. The resulting solution, 2/6 = x, should be reduced completely by the common factor of 2 in the numerator and denominator of the fraction, yielding the best answer: 1/3.

Put the following fractions in order from least to greatest: \frac{1}{2}, \frac{3}{4}, \frac{5}{7}, \frac{3}{16}21​, 43​, 75​, 163​

163​, 21​, 75​, 43​ The easiest way to order these is to convert them to decimals and round to the hundredths place: 1/2 = 0.5 3/4 = 0.75 5/7 = 0.71 3/16 = 0.19 Then order the decimals and pair with their fraction equivalent.

Tom wants to mentally calculate a 20% tip on his bill of $40. Which of the following is best for Tom to use in the mental calculation of the tip?

40 × .1 × 2 Tom can quickly find 10% of 40 and then double it. In this case the answer is $8 because 10% of 40 is 4 and 4 × 2 is 8.

Solve: 7 \frac{2}{5} - 2 \frac{1}{3}752​−231​

5151​ The fractions can be changed into improper fractions by multiplying the whole numbers by the denominator and adding it to the numerator. 7 \frac{2}{5} = \frac{37}{5}752​=537​ 2 \frac{1}{3} = \frac{7}{3}231​=37​ When subtracting fractions, a common denominator must be found first. Since 3 and 5 are both prime, their least common multiple is their product (15). \frac{37}{5} \times \frac{3}{3} = \frac{111}{15}537​×33​=15111​ \frac{7}{3} \times \frac{5}{5} = \frac{35}{15}37​×55​=1535​ Now the original expression can be re-written and solved: \frac{111}{15} - \frac{35}{15} = \frac{76}{15}15111​−1535​=1576​ This can be simplified to 5 \frac{1}{15}5151​

A fifth-grade teacher wants to assess students' ability to calculate the area of nonstandard polygons. Which of the following figures would assess a student's ability to find the area of non-standard polygons?

Figure 5 Figure 5 is a non-standard polygon because it does not have a standard geometric structure, such as a triangle, square, or rectangle do.

A first-grade teacher gives each table 68 unifix cubes to count. She observes one table organizing the unifix cubes into groups of 10 and counting the sets of 10 that were made. What counting technique was this group utilizing?

counting collections The students have organized the groups into sets of 10 and counted the sets, which is an example of counting collections.

For a unit assessment on fractions, students are given 3 choices to display their knowledge. They can create a building using interlocking blocks and then label fractions within their building, they can take a teacher-created test, or they can write a short story with fractions. Why is this a best teaching practice?

This allows students authentic ways to display and practice their knowledge. Authentic methods of assessment give students the opportunity to display their knowledge at the highest level.

A teacher is monitoring her class while the students are involved in a group activity exploring the size of angles in a set of triangles. She moves from group to group, pausing and watching the group dynamics. What the teacher is doing can best be described as:

informal formative assessment. The teacher is listening and watching as she informally assesses student understanding of the concept: angle measures in triangles.

Janine is trying to determine who to vote for in the class president race. She thinks that candidate A is friendlier to her, but candidate B is better at convincing adults to do things. What type of reasoning is she using when she decides who to vote for?

informal reasoning Informal reasoning is used to answer questions and solve problems that are complex and open-ended without a definitive solution by using everyday knowledge to synthesize information and reach a conclusion. Janine is using feelings rather than true logic in her decision making here.

Jessica is working on adding 8 to 25. She starts counting at 25, using her fingers to count 8 more numbers out loud. Which counting technique is she using?

Counting on When counting on, a student starts at one number and counts until a second number is reached.

Mr. Allenye wants to determine if his students understand parallel and perpendicular lines. He tells them to draw a picture of a city and write in the measure of all of the angles. How could he improve his project?

Have students write a small essay about how they designed their city and explain why it relates to parallel and perpendicular lines. Incorporating writing in math can allow students to demonstrate mastery.

What is the next number in the sequence? 5, 10, 20, 40, 80...

160 The pattern is the previous number multiplied by 2. Since the previous number was 80, the next number will be 80 × 2 = 160.

In Anytown ISD, 13 out of every 20 students ride the bus. Which ratio compares the number of students who ride the bus to those who do not?

13:7 This is the ratio that compares riders to non-riders. 13 out of 20 ride the bus. This means that the complement of this relationship, those who do not ride the bus, is 20 - 13 = 7. So, the ratio of those who ride the bus to those who do not ride the bus is 13:7. When writing ratios, remember that order is important and matters. 13:7 is not the same as 7:13.

Which of the following is the same as this expression? 1y + 8x -2 + 2x + 1 -3y1y+8x−2+2x+1−3y

10x - 2y - 110x−2y−1 This correctly combines like terms.

How many faces does a square pyramid have?

5 A square pyramid has 5 faces. Remember that a pyramid only has one base.

Asher makes $240 every pay period plus 15% on all sales. He determines his paycheck using the expression 240 + .15x240+.15x. Which of the following is equivalent to Asher's expression?

5(48+.03x) This expression factored (essentially "pulled out") the 5 from both terms. The distributive property proves this true: 5 × 48 = 2405×48=240 and 5 \times .03x = .15x5×.03x=.15x

How many faces does a rectangular prism have?

6 A rectangular prism has 6 faces.

Mr. Miller is teaching his students about the volume of rectangular prisms. He writes the formula volume = length × width × height on the board and tells his students to get to work. He notices two of his students arguing over which leg represents length and which represents width. What should he do? Select all answers that apply.

Allow each student to select which means length and which represents width on their own and then do math and compare the volume they compute. The students will realize their choice does not matter when they arrive at the same solution. B Remind students that multiplication is commutative so it does not matter which leg they select to represent each variable. This is a good way to tie current learning back to essential properties of mathematics.

Which of the following civilizations is most closely associated with the development of algebra?

Arabian Al-Khwarizmi (770 - 840 C.E.) is generally accepted as the Father of Algebra even though there is evidence that many concepts from algebra were known many thousands of years before Al-Khwarizmi. The word "algebra" comes from the Arabic al-jabr, meaning to unite or combine.

Mr. Sudu is a waiter. His total weekly earnings consist of a wage of $6 per hour plus approximately 15% in tips on his total sales for the week. One week Mr. Sudu worked 25 hours and had total sales of z dollars. Which of the following represents his total weekly earning in dollars, E, for that week?

E=0.15z+150 To find Mr. Sudu's earnings, multiply the percentage in decimal form (0.15) by the total sales in dollars (z) and add this to his wage of 150, which is the product of his hourly rate (6) and the number of hours he worked (25)

Which activity would best support third-grade students in developing an understanding of measuring with the metric system and creating graphs?

Having students use a metric ruler to measure the height of blades of grass growing in the schoolyard and then guiding them as they make bar graphs of their recorded results. This inquiry-based activity is tied directly to the learning goal. Students would measure, record, and graph metric data.

Rather than give a unit test, Mrs. Kirby decides to assign a major project to her students. They are provided a rubric that sets the expectations and guidelines. Students will be given 2 class periods to work on it and the rest must be completed at home. Students will then present their projects in class. What is the main advantage to giving a project rather than a test?

Projects require higher level thinking and can demonstrate greater concept mastery than tests. Projects with clear guidelines require students to think on a higher level and display mastery in a variety of ways.

A child is using a geoboard and creates a shape with 3 angles. What is the name of this shape?

Triangle A triangle has 3 sides and 3 angles.

A first-grade teacher is planning a lesson on solving problems with an unknown addend, such as 3 + __ = 8. She knows that students have struggled with this concept in previous years and is looking for a way to engage students with technology while still improving their understanding of the concept. Which of the following could she do in order to achieve this?

Use an interactive part-part-whole model that allows students to drag items from the "whole" to the "parts" to find the unknown addend. This would be a good way to show students a visual representation of how the problem is solved while involving them in the activity. It would also provide them with a strategy to use in the future for these types of problems.

Trapezoid ABCD is shifted 3 units to the left and 5 units up. What will be the coordinates of Point B after the shift?

(5, 12) Point B is located at (8, 7). To shift left, subtract 3 from the x value. To shift up, add 5 to the y value.

Mr. Kim shares with his geometry class the triangle sum property - The sum of all angles in a triangle always add to 180\degree180°. Then, he asks the students to find the missing angle in the triangle below: What type of thinking are the students using to solve this problem?

Deductive reasoning With deductive reasoning, students start with a proven fact, rule, or definition to arrive at a conclusion.

Mr. Macrow's first-grade class is having a hard time understanding prepositions for directionality. What is the most effective lesson for his students?

Provide an anchor chart and objects. Have students move two objects to form each relationship on the chart. Young children learn a new concept best using a concrete manipulative. By providing objects to move and describe, students can connect the vocabulary to the directionality of the two objects.

Which symbol most accurately reflects the relationship between the two numbers below? 0.4 ☐ 2/5

= Since 0.4 and 2/5 (0.4) are equal, this is the correct symbol.

Mrs. Perkins is beginning to teach her class about congruent shapes. Which of the activities below is the best activity to introduce the subject?

Allow students to use cutouts of shapes that have been magnified to different dilations and compare and contrast their attributes. This teaches students at the concrete level since they are interacting with physical manipulatives. This is the best first activity.

Students in a math class are working on the following problem: Julio can answer 3 math problems in 10 minutes. He completed his math homework after school, which consisted of 14 questions. Assuming he worked at the same rate the entire time, how long did it take Julio to complete his math homework? One student called the teacher over to see if she set up the problem correctly. The following was on her paper: \frac{3}{10}=\frac{x}{14}103​=14x​ Which of the following suggestions should the teacher give the student to guide them to realize their mistake?

Write the units of each value in each ratio. The problem with the student's proportion is the units for each value in the ratio do not match. Writing the units next to each value in the proportion the student wrote will show her the the units are not aligned in the proportion she wrote.

If a number is divisible by 6 and 8, what other number(s) can also divide into it? Select all answers that apply.

3 Using divisibility rules, it can be determined that a number divisible by 6 and 8 is also divisible by 3. C 4 Using divisibility rules, it can be determined that a number divisible by 6 and 8 is also divisible by 4. D 2 Using divisibility rules, it can be determined that a number divisible by 6 and 8 is also divisible by 2.

Tosha has 8 coins in her pocket. She has a mixture of pennies, nickels, dimes and quarters, but she has no more than 3 of any coin. What is the largest amount of money she could possibly have?

$1.11 To satisfy the prompt given, there must be at least one of each coin. She will need to have the most number of the coins with the greatest value: quarters and dimes. So, that would be 3 quarters, 3 dimes, 1 nickel, and 1 penny. This totals $1.11.

Two color counters are often used to model addition and subtraction of integers. The red counters represent negative integers; the yellow represent positive integers. If the counters above were used to model the addition, what would be the result?

-2 The problem pictured above is -7 + 5 = -2. Using the chips, a red and a yellow chip are paired together to form a "zero-pair"-a model of -1 + 1 = 0. Pairs are matched and removed from the group leaving two red chips unmatched. This results in a representation of an answer of -2.

Students are working on measurement principles. Kali measures a countertop in the classroom that is 5,743 mm long. Lauren finds that the distance on a map between New York City and Washington D.C. is drawn as 364.1 mm. How does the 3 in Kali's number compare to the 3 in Lauren's number?

1/100 Kali's digit is in the ones place and Lauren's digit is in the hundreds place. Therefore Kali's digit is 1/100 of the value.

After a lesson on rounding and estimation, a teacher tells students that the football concession stand has purchased 590 candy bars to sell for the 6 football home games this year. The teacher asks the students to estimate the average number of candy bars that will be sold at each home game. Which of the following would be the correct estimation?

100 An estimate is finding an approximation of a value. Estimates are used to quickly find an answer that is close, but probably not precise. 590 can easily be rounded to 600 which is divisible by 6. This means that about 100 candy bars will be sold per game.

Sheila has a large collection of stickers. She gives ½ of her collection to Sue, ½ of what is remaining to Sandra, and then gave ⅓ of what was left over to Sarah. If she has 30 stickers remaining, how many stickers did she begin with?

180 stickers This is a problem that can be worked backwards. Sheila is left with 30 stickers after she gave ⅓ of what she had to Sarah. That means that 30 stickers represent ⅔ of what Sheila had before she gave any stickers to Sarah. 30 is ⅔ of 45; so, Sheila had 45 stickers before she gave any to Sarah. 45 is half of what was left when half of the collection was given to Sandra. This means that Sandra received 45 stickers and that Sheila had 90 stickers before she gave any to Sandra. 90 stickers is how many Sheila had after she gave ½ of what she had to Sue; this means that Sue received 90 stickers and that Sheila had 180 stickers before she gave any away to Sue.

What is the prime factorization of 18?

2 × (3²) The prime factors of a number are the prime numbers that divide the integer exactly. The prime numbers then can be multiplied together to equal that number. The prime factors of 18 are (2 × (3²) ). Solving prime factors of most integers involves completing the factor tree of an integer until only prime numbers are used. For 18, the factor tree would be: 18 = 2 × 9 = 2 × (3²).

Which numbers are divisible by 2, 3, 6, and 7? Select all answers that apply.

252 Using divisibility rules, it can be determined that 252 is factored by 2, 3, 6, and 7. C 1,260 Using divisibility rules, it can be determined that 1,260 is factored by 2, 3, 6, and 7. D 2,772 Using divisibility rules, it can be determined that 2,772 is factored by 2, 3, 6, and 7.

If ⅙x-4=1⅙x−4=1, then x =

30 The first step to solve this equation is to add 4 to each side, as +4 is the additive inverse of the -4 that is preventing the variable expression from being alone on its own side of the problem. The resulting equation is ⅙x⅙x == 55. At this point, 6 should be multiplied on each side of the equation in order to eliminate the factor ⅙ from in front of the x, as 6/1 is the multiplicative inverse of the fraction ⅙ that is preventing the variable from being alone. When 6 has been multiplied to each side, the result is x = 30.

What is the value of the "3" in the number 17,436,825?

30,000 In a base 10 system, each place location for a number has a value that is a power of 10. Specifically, the ones place is properly understood to be 10⁰ (because any nonzero number raised to the zero power equals 1). The tens place is 10¹, the hundreds place is 10², the thousands place is 10³, etc. When a digit is in a specific position, its value is equal to the product of that digit and the power of 10 that is assigned to its position. Therefore, in the number 17,436,825, the 3 represents 3 \times 10^4= 30,0003×104=30,000

Susan is planning for volunteer day at the high school. Every person that signs up gets a free lunch for volunteering. This year, lunch includes 3 slices of pizza and a soda. If x = number of volunteers and one pizza has 8 slices, which equation can help her to determine the correct number of pizzas (n) to order?

3x/8 = n This equation multiplies the number of slices by the number of people. Then, it divides that amount by 8 (number of slices in a pie) to account for the number of pizzas needed.

In the diagram below, each rectangle is ½ the height of the rectangle immediately to its left. The area for the first figure is 135.355cm². All of the triangles are congruent. If the pattern continues, what will be the area of the fourth figure?

47.855 cm² In the first diagram, the rectangle on the bottom has an area of 100 cm². This means that the triangle on the top has an area of 135.355 - 100 = 35.355 cm². The triangle has a constant area - it is always 35.355 cm². So, the area of each successive figure is 35.355 + area of the rectangle. After the first figure's area is determined, the area of the rectangle is ½ of the area of the preceding rectangle. For the second figure the area would be 35.355 + ½(100) = 35.355 + 50 = 85.355 cm². For the third figure the area would be 35.355 + ½(50) = 35.355 + 25 = 60.355 cm². For the fourth figure the area would be 35.355 + ½(25) = 35.355 + 12.5 = 47.855 cm².

Mrs. Fields' science class takes care of a plant at school. The class is responsible for watering the plant and measuring its growth. The students' measurements are charted in the table. Number of Months (m) Height of the Plant (h) in inches 1 8 2 13 3 18 4 23 Which of the following equations relates the height of the plant, h, and the number of months, m, assuming a constant rate of growth?

5m + 3 = h The difference between the growth of each month is 5 inches; looking at the growth of each month, the plant's height increases 5 inches each month. If the rate of growth is constant, then the beginning height of the plant is 3 inches; the height at the first month (8 inches) minus the growth of that month (5 inches) would equal 3 inches. If the growth of each month is 5 inches, then one can find the height of the plant by the growth of each month (5 inches) multiplied by the month (m) and then add 3 inches to account for the initial height. 5m + 3 = h.

Which of the following correctly simplifies the left side of the equation below? 3x - 4 + 6x + 5 - 4x - 2 = 16

5x - 1 = 16 This is the only answer option that combines the terms correctly. Another way to write the problem is 3x + 6x - 4x - 4 - 2 + 5 = 16; this can then be written 5x - 1 = 16.

A gas pump can pump a quarter gallon of gas every five seconds. If a person is filling up an empty gas tank that can hold 18 gallons of gas, how long will it take the gas pump to fill the empty gas tank?

6 minutes If a gas pump can pump a quarter of a gallon every five seconds, then the pump can deliver a gallon of gas every 20 seconds, and 3 gallons of gas every minute. If the tank is 18 gallons, then it will take 6 minutes (3 gallons per minute × 6 minutes = 18 gallons).

There was a big sale and Branden bought 9 items of clothing. Shirts were selling for $15 each and pants were $20. If he bought at least one of each item and spent $150, how many of each did he purchase?

6 shirts and 3 pants Two equations are needed to solve this: x + y = 9 and 15x + 20y = 150 where x is the number of shirts and y is the number of pants. The first equation can be manipulated to isolate y so that y = 9 - x. This can then be substituted into the second equation: 15x + 20(9 - x) = 150. When distributed, the equation is 15x + 180 - 20x = 150. Combine like terms: -5x = -30. Divide by -5 to isolate x and find x = 6. If there are 6 shirts, then there must be 3 pants (since x + y = 9).

Solve: 3 \frac{3}{4} \div \frac{1}{2}343​÷21

721​ The first fraction can be changed into an improper fraction by multiplying the whole number (3) by the denominator (4) and adding it to the numerator (3). 3 \frac{3}{4} = \frac{15}{4}343​=415​ When dividing fractions, flip the second fraction and multiply across: \frac{15}{4} \div \frac{1}{2} = \frac{15}{4} \times \frac{2}{1} = \frac{30}{4}415​÷21​=415​×12​=430​ This can be simplified to 7 \frac{1}{2}721​.

A third-grade teacher notices that a student got nine out of ten multiplication problems correct, but on the missed problem they wrote 24 × 3 = 27. What would be the best step for the teacher to take next?

Ask the student if 27 seems like a reasonable answer to 24 × 3. This option encourages the student to think about whether or not their answer "makes sense." A student who usually does well with multiplication will likely be able to reason that 27 is too small of a number for 24 × 3.

A first-grade teacher is planning a group project in which students will work in groups of three to create a survey question to ask their peers, collect data from the class, and create a picture graph using the data collected. Which of the following should the teacher do to help ensure successful group collaboration?

Assign roles to each group member, such as recorder, speaker, and materials manager. Assigning roles to each group member is a good strategy for group collaboration because it encourages each group member to contribute to the project and gives students a sense of individual responsibility.

The 4th-grade students are going on a field trip to the science museum. There are 4 classes with 23 students and 3 adults in each class. They will take 5 buses with an equal number of people on each bus. How many people will be on each bus? Which of the following statements about the solution must be true?

Because of the real-world context, the solution must belong to all the set of all natural numbers. Therefore the solution is unacceptable. Natural numbers are whole counting numbers beginning with 1 and used in real word problems. In this problem, 26 people from 4 classes → 104 people on 5 buses. Because this problem requires 20 ⅘ people to ride the bus, the solution is unacceptable.

x 1 4 7 10 13 y 9 3 -3 -9 -15 The table above shows x and y values that have a linear relationship to each other. Which of the graphs below could illustrate the relationship between these variables?

Graph C The table shows x-coordinates that increase by 3 units at a time and y-coordinates that decrease by 6 units each. The progression from one point to the next includes moving down 6 units and 3 units to the right. This constant change as the values in the table go from one ordered pair to another is the slope of the line. Any pair of points can be selected from the table to perform the calculation and the (reduced) result will be the same. Here, the points (1, 9) and (4, 3) are being used: (y2 - y1)/( x2 - x1) = (3 - 9)/(4 -1) = -6/+3 = -2/1. If this slope is applied to fill in a value from the table to the left of the first point given, (1, 9), the y-intercept (value of y when x = 0) can be determined to be 11 (because the x-coordinate is reduced by 1, the y-coordinate must be increased by 2 units). With a y-intercept of 11 and a slope of -2, the equation for this line is y = -2x + 11, and so the graph must have a point on the y-axis at (0, 11) and a slope of down two units for every movement to the right one unit. Alternatively, the graphs can be inspected to determine which contains at least two points from the table. The point (1, 9) appears in several different graphs, but only one graph also contains the point (4, 3).

After reading a story about a world that runs out of natural resources, a second-grade teacher wants students to think deeply about what they could do to prevent this in our world. Which of the following activities best supports critical thinking and relates to the lesson goal?

Have small groups of students discuss and evaluate their own thoughts about what they could do personally to conserve resources. This activity meets the lesson goals and requires students to think about their own lives, find connections, and evaluate the thoughts of others in their groups.

Using money in mathematical examples is a good strategy to promote student engagement in activities. A first-grade teacher decides to begin teaching about place value by using money, specifically with the example of 10 pennies = 1 dime and 10 dimes = $1. Why is this strategy probably not a good beginning strategy? Select all answers that apply.

The relationships above are too abstract for young learners. Money can be a good motivator, but very young children do not have a grasp on the value. They tend to be more interested in "how many" and not "how much." B The coins are not proportional with respect to shape and size. There is also a problem because there is no proportional relationship. Why are ten pennies worth less than ten dimes, especially when a penny is physically larger than a dime? C Most young learners would rather have 8 pennies rather than 1 dime. Money can be a good motivator, but very young children do not have a grasp on the value. They tend to be more interested in "how many" and not "how much."

A second-grade class has been working on solving multi-step word problems using a variety of strategies. The teacher plans to give students a multi-step word problem to solve and have the students explain the steps they took to solve it. How can the teacher best incorporate technology into this activity?

Use a website that allows students to record themselves explaining the steps they took to solve the problem. This is the best option because it allows students to interact with the technology while still achieving the desired goal of explaining how they solved the problem.

Elementary students use flashlights with opaque and transparent objects as they investigate shadows. Which phase of the 5E model is being implemented in this activity?

explore During the explore phase, students work with the materials to develop their knowledge. In this task, students manipulate materials and work to make sense of their findings.

Colin is a child learning about animals. He notices that dogs have four legs and a tail. When he sees a cat he incorrectly calls it a dog. What type of reasoning is Colin using?

inductive reasoning Inductive reasoning or generalizing knowledge from one area to another is used to make predictions. This is what Colin is doing when he predicts that a cat is a dog.

Mrs. Adamson's student asks her how much space a cube takes up. Mrs. Adamson said to answer this question, the student would need to calculate the volume of the cube. Which of the following measurable attributes is the formula for a cube based upon?

length Before the volume of a cube can be calculated, the length, width, and height must be measured. Length is the best answer.

Mrs. Campbell, a third-grade science teacher, is teaching conservation practices. What can her class do to demonstrate they have learned to make informed choices, based on the needs of the environment?

start a paper and plastic recycling program The best way to demonstrate that information was learned about conservation is to put the information into practice by recycling.

A fifth-grade teacher is beginning a unit on equivalent fractions with her students. If this is an introductory lesson, which of the following activities would be the most effective in helping the students understand the concept of equivalent fractions?

use pattern blocks to model different fractions equivalent to ½ Since this is an introductory activity, concrete, proportional manipulative materials like this should be used for concept development. It is important not to rush past this step and to use a variety of different materials to develop and reinforce understanding of this concept.

At the end of a lesson on factoring, Ms. Wilson gave her class an exit ticket. After she reviewed the responses on the exit ticket, Ms. Wilson realized that many of her students were still struggling with the concept of factoring. Which of the following strategies would be best for Ms. Wilson to use in her next lesson on factoring to help the students solidify their conceptual understanding of factoring?

using manipulatives to show factoring as the reverse, or un-doing, of distribution This activity uses concrete manipulatives to demonstrate the concept of factoring. Students can use prior knowledge of distribution to make connections to factoring.

James counted the coins in his piggy bank, and he has 19 quarters, 3 dimes, 11 nickels, and 9 pennies. How much money does he have?

$5.69 The sum of all of the money he counted was 569 cents, which is $5.69. 19 \text{ quarters} \times 25 \text{ cents} = 475 \text{ cents}19 quarters×25 cents=475 cents 3 \text{ dimes} \times 10 \text{ cents} = 30 \text{ cents}3 dimes ×10 cents=30 cents 11 \text{ nickels} \times 5 \text{ cents} = 55 \text{ cents}11 nickels×5 cents=55 cents 9 \text{ pennies} \times 1 \text{ cent} = 9 \text{ cents}9 pennies×1 cent=9 cents

Evaluate the expression: 5(4 - 1)2 - (4 + 3)2

-4 This question is about order of operations. First, solve what is inside the parenthesis: 5(3)2 - (7)2. Next, solve the exponents: 5(9) - 49. Then, multiply: 45 - 49. Finally, subtract: -4

If 2.54 cm = 1 in, about how many inches are in 1 meter?

39.4 in There are 100 cm in 1 m, so 100cm/m ÷ 2.54 cm/in ≈ 39.4 inches/m.

Mr. Marks gives his students a pop quiz on graphing on the coordinate plane. Sixty percent of his students fail the quiz. What should he do next?

Reteach the (x,y) coordinate structure and axes to the whole class. When the majority of the class does not understand a topic, it should be retaught in a different manner.

Before teaching multiplication, a teacher reviews skip counting on a number line. Students use different colored markers to show counting by 2s, 5s, and 10s. After introducing multiplication, they review their number lines and connect the concept to the jumps. Why did the teacher return to the number line as she taught?

This allowed students to connect prior knowledge to new concepts with a visual example. This method allows them to "see" multiplication.

When teaching geometric shapes, Mr. Gaines challenges his students to prove a statement right or wrong. He writes on the board, "All rectangles are parallelograms and all squares are rectangles; therefore, all squares are parallelograms". What type of thinking is trying to promote?

deductive reasoning Deductive reasoning requires the students to think through two or more known statements to determine if the conclusion is true.

During a lesson on using models in mathematics, a teacher asks the students to figure out how many hours they spend on homework for all their classes each year. In asking this question, the teacher has asked the class to:

demonstrate an understanding of the estimation process. Students will need to apply several estimates to determine the amount of time they spend on homework each year.

A first-grade student is asked to find the total value of the following coins: 3 dimes, 1 nickel, and 4 pennies. The student's response is that the coins are worth $0.12. Based on this response, what concept does this student likely need help with?

recognizing different coins and their respective values Based on their answer, the student most likely recognized the nickel as 5 cents but thought that the dime and pennies were all the same type of coin and worth 1 cent each. The teacher should plan on working with the student on recognizing the difference between dimes and pennies and recalling the values of each.

Which terms best describe the triangle shown? Select all answers that apply.

right Right triangles contain a right (90 degree) angle. scalene Scalene triangles have all sides of different length.

The pictograph above displays data for sports equipment sold last Saturday at a certain sporting goods store. At this store, basketballs sell for $12, volleyballs sell for $15, and the total sales made last Saturday on the items shown in the pictograph was $212. If each soccer ball sold for d dollars, what is the value of d?

$10 The total sales last Saturday is composed of the subtotals in sales for each type of ball: (number of basketballs sold × $12 each) + (number of volleyballs sold × $15 each) + (number of soccer balls sold × d each) = $212 in total sales. Because each ball symbol represents 2 balls sold, the pictograph offers the information that 6 basketballs (2 × 3 = 6), 4 volleyballs (2 × 2 = 4), and 8 soccer balls (2 × 4 = 8) were sold at this sporting goods store last Saturday. Because each basketball costs $12, with 6 basketballs sold, $12 × 6 = $72 gives the subtotal of $72 in basketball sales. Because each volleyball costs $15, $15 × 4 = $60 gives the subtotal of $60 in volleyball sales. Therefore, $72 + $60 = $132 of the total $212 in sales are accounted for by basketballs and volleyballs. This leaves $212 - $132 = $80 for soccer ball sales. According to the pictograph, 8 soccer balls were sold. Therefore, 8d = $80 is a valid expression for the monetary value of the soccer ball sales. This equation is solved by dividing by 8 on each side, yielding the correct final answer of $10 for each soccer ball.

The median home cost in the US in 1975 was $40,000. In 1990, an equivalent home cost $140,000. The trend continued into 2005 when the median home cost in the US was approximately $240,000. Assuming that this data's relationship is steady in the future, what is a reasonable estimate of the median home cost in the US in 2025?

$373,333 The data points (1975, 40), (1990, 140), and (2005, 240) all show a rise in home price of $100,000 for every 15 year passage of time. This constant change in dependent variable (y) compared to change in independent variable (x) is the slope characteristic of linear data. Therefore, if the linear trend continues, in 2020 (15 years after 2005), the median home price could be expected to be $340,000 ($100,000 more than $240,000). The year 2025 is 5 years after 2020, which is just 1/3 as much as the previous 15 year increments. Because of the linear trend of this data with its slope of +$100,000/+15 years, it would be reasonable to expect an increase in value of an additional 1/3 of $100,000, or approximately $33,333 past $340,000. Therefore, the final answer is $340,000 + $33,333 = $373,333. It would also be valid to reduce the slope of +$100,000/+15 years to a unit rate of $6,666.67/1 year, multiply that slope by the 20 years that pass between 2005 and 2025 to get $133,333.33, and add that amount of change to the last known data value of $240,000 in 2005 to get $373,333.33 in 2025.

James has saved $35.25. He wants to save his money to buy a bicycle that costs $85.00. His brother's bike cost $92.00. If sales tax is 8%, about how much more must he save to purchase his bike, including tax?

$60 The math used: 8% is close to 10% sales tax on $85.00, or about $8.50 tax. So $85.00 + $8.50 = $93.50. Notice this is an overestimate so James' target will be a bit more than he actually needs. James needs to save about $93. If he has saved about $35, he will need an additional $58. ($93 - $35 = $58) Therefore, if rounded up this would be the best choice: $60. When dealing with money, generally an overestimate is more reasonable.

The graph is a representation of the following situation: Marty purchased a car for $24,000; this included all interest, tax, and title fees. She made payments of $500 per month for 48 months until the car was paid off. What ordered pair would best represent point A at the top of the graph?

(0,24000) The point A, (0,24000), indicates that at the time "0" - or at the beginning of the loan - the amount owed was $24,000. In this situation, the x-axis (horizontal) represents the time in months and the y-axis (vertical) represents the amount of the loan. In the equation y = 24000 - 500x, the - 500 is the $500 paid (subtracted) each month on the loan. As you look at the graph moving from left to right, the line goes "downhill"; this graph represents a linear decrease. The point represented by B on the x-axis would be the point (48,0). This means that after the 48th month, the amount remaining on the loan was $0.

Solve: \frac{2}{3} + \frac{4}{5}32​+54​

1157​ When adding or subtracting fractions, a common denominator must be found first. Both fractions can be rewritten to use 15 in the denominator. \frac{2}{3} \times \frac{5}{5} = \frac{10}{15}32​×55​=1510​ \frac{4}{5} \times \frac{3}{3} = \frac{12}{15}54​×33​=1512​ Now the original expression can be re-written and solved: \frac{10}{15} + \frac{12}{15} = \frac{22}{15}1510​+ 1512​=1522​ Since the numerator is larger than the denominator, this can be simplified from an improper fraction to 1 \frac{7}{15}1157​ since 22 - 15 = 722−15=7.

What is the 8th term of the geometric sequence -3, 6, -12, 24, -48,...?

A(8) = 384 A(8) = 384 comes from seeing that the sequence is shown to have a₁ = -3, r = 6 ÷ -3 = -2, and n = 8. The question is answered correctly by keeping an appropriate variable expression in the place of A(n) and inputting all known values so that the formula A(n) = a₁(r)ⁿ⁻¹ becomes A(8) = -3(-2)⁸⁻¹. When the order of operations is followed correctly, exponents will be simplified before any multiplication occurs. The resulting equation becomes A(8) = -3(-2)⁷ and then A(8) = -3(-128). The final answer is the product of -3 and -128, and so A(8) = 384.

A kindergarten teacher is planning a lesson on comparing two numbers using "greater than" and "less than." After introducing the phrases "greater than" and "less than," she writes a 4 and 8 on the board and asks students to think about which number is greater. Which of the following activities should the teacher use next to promote and assess students' mathematical reasoning skills?

Ask students to explain why they think one number is greater than the other. Having students verbally explain their thought process is a great strategy for encouraging mathematical reasoning skills. This also allows the teacher to assess students' reasoning and correct any misunderstandings.

Mr. Zammit is teaching his class about shapes. One of his students incorrectly labels all rectangles as squares and all rectangular prisms as cubes. Which of the following should Mr. Zammit do in this situation? Select all answers that apply.

Make an analogy to help the student understand his mistake, for example calling every rectangle a square is like calling every girl a princess. Connecting to a real world example can help the student understand his mistakes and improve his future use of math terms. C Require his student to use correct mathematical vocabulary. Correct vocabulary is a very essential part of mathematics.

A student performed an experiment on three different types of paper towels. Each of the towels was soaked in a separate beaker, each containing 20 ml of water, for exactly 15 seconds. The towels were removed. What step should be next in the procedure in order to accurately identify the paper towel that absorbed the most water?

Measure the remaining water in each of the three beakers and compare the results. To accurately compare the paper towel absorption, the amount of water remaining in each of the beakers must be measured and compared after removing the soaking paper towels.

Mrs. Johnson lets her students choose between two word problems: Problem A: If you are digging for dinosaurs and need to fence off your dig site, what's the biggest site you can fence off with 40 ft. of fence? Problem B: What is the largest area you can create with 20 inches of rope? Mrs. Johnson finds a significant majority of her students chose to work Problem A. Which of the following is the most likely reason more students chose Problem A instead of Problem B?

Problem B is less interesting than Problem A. This is the best answer. Students are more likely engaged when presented with a problem about digging for dinosaurs than a simple mathematical word problem. The way problems are presented can impact students' engagement in the learning process.

Students in Mrs. Portock's class were trying to write an expression that represents the total number of cubes for any term number, n, for the sequence below. Diego raised his hand to get help from Mrs. Portock. He had the table following written on his paper: Term # (n) # of cubes 1 1 2 4 3 7 4 10 Diego said he recognized the pattern of adding 3 more cubes every time, but needed help writing an expression using n. Of the following, what is the best possible teacher response?

Re-write the number of cubes as an expression showing the amount of cubes being added every time. (Ex: 1+3 instead of 4 cubes, 1+3+3 instead of 7 cubes, etc.) Re-writing the cube numbers like this should help Diego to see that the 1 is always constant, and that you add another 3 for each term. The number of 3s added is always one less than the term number.

On a recent quiz in Mrs. Zehr's math class, the majority of students in the class incorrectly simplified the expression 2 \left( 3x-4 \right)2(3x−4), picking the answer choice 6x-46x−4. Of the following, which strategy for reteach would be the best course of action for Mrs. Zehr based on how her students answered this question?

Review the concept of the distributive property using real world examples: If a family meal at a fast food restaurant has 4 hamburgers, 3 chicken fingers, 2 fries, and 4 drinks, and someone orders 3 family meals, how many of each item will they receive? How can this be written mathematically using the distributive property? Providing real world examples of the distributive property will help students conceptualize that everything inside the parentheses is together in a group. It would not be fair if the hamburgers in the family meal were multiplied by 3, but the drinks were not! The same is true mathematically -- every term inside of the parentheses must be multiplied by the term on the outside.

A teacher prompted his class to write their own examples of arithmetic sequences on their papers. As the teacher is circulating, he sees the following written on one Tasha's paper: 2, 3, 5, 8, 12, 17, 23... When asked to explain her work, Tasha explains, " The sequence is arithmetic because to get the next number in the sequence, you +1, +2, +3, +4, +5, see? So you always add one more to get the next number." Which of the following is the best teacher response to Tasha's reasoning?

Your reasoning is incorrect; you must add by the same number every time for the sequence to be arithmetic. This is correct; arithmetic sequences require you to add by the same number every time to get the next number in the sequence (ex: adding +1 to get the next number every time, or adding +5 every time to get the next number).

Mr. Meadows is a third-grade teacher in a low performing school. There is a high rate of absenteeism and low rate of students doing homework. He makes a public star chart where students get a sticker for each assignment they complete. Which of the following learning theories best matches the use of a star chart?

behaviorism learning theory Behaviorism has to do with students learning new behaviors based on the response they get to current behaviors. The students are receiving positive reinforcement through the use of the star chart. This is the correct answer.

A teacher engages her class in a discussion of the coordinate plane. The students are asked to identify the quadrants, the coordinate axes, and the mathematical notation for various points in the plane. Students are asked to develop a way to quickly identify the quadrant in which various points lie. Which of the following objectives is the teacher most likely trying to address with this lesson?

developing precise mathematical language when expressing mathematical ideas The precise use of mathematical language is required when using and describing information in the coordinate plane.

Mr. Fischer, a bilingual teacher, teaches a mathematics class composed of native English speakers and English language learners (ELLs). He has introduced a new topic with new vocabulary words in which he presented the vocabulary words with several examples. Which of the following strategies should Mr. Fischer use next to check each student's understanding of the vocabulary words?

having students write a definition for each term in their own words in their native language It is best to have the students construct their own definition in their native language so Mr. Fischer can assess their knowledge of the vocabulary words.

What is the place value of the "5" in the number 15,436,129?

millions In a base 10 system, each place location for a number has a value that is a power of 10. Specifically, the ones place is properly understood to be 10⁰ (because any nonzero number raised to the zero power equals 1). The tens place is 10¹, the hundreds place is 10², the thousands place is 10³, etc. When a digit is in a specific position, its value is equal to the product of that digit and the power of 10 that is assigned to its position. In the direction of the positive powers of ten, the units are ones, tens, hundreds, thousands, ten thousands, hundred thousands, millions, ten millions, hundred millions, billions, etc. Therefore, in the number 15,436,129, the 5 represents 5 × 10⁶, or 5 × 1,000,000 = 5,000,000, which is pronounced 5 million. Therefore, the 5 is in the millions place.

What is the place value of the "9" in the number 6,587.9213?

tenths In a base 10 system, each place location for a number has a value that is a power of 10. In the opposite direction of the ones place, there is the tenths place from 10⁻¹ = 0.1 or 1/10, the hundredths place from 10⁻² = 0.01 or 1/100, the thousandths place from 10⁻³= 0.001 or 1/1,000, etc. When a digit is in a specific position, its value is equal to the product of that digit and the power of 10 that is assigned to its position. In the direction of the negative powers of ten, the units are called tenths, hundredths, thousandths, ten thousandths, hundred thousandths, millionths, etc. Therefore, in the number 6,587.9213, the 9 represents 9 × 10⁻¹, or 9 × 0.1 = 0.9 or 9/10, which is pronounced "nine-tenths". Therefore, the 9 is in the tenths place.

Students have learned about the energy stored in rubber bands and springs and now use provided materials to build and test gum-drop launchers. Which phase of the 5E model is being implemented in this activity?

elaborate During the elaborate phase, students extend their thinking by applying what they have learned to a new situation and practicing new skills that were developed during the unit.

Solve: [7(3 - 1)2 + (-8)]/{-3[3+ 6(½)] + 19}

20 [7(3 - 1)2 + (-8)]/{-3[3+ 6(½)] + 19} = [7(2)2 + (-8)] / {-3[3+ 3)] + 19} = [7(4) + (-8)] /{ -3(6) + 19}= [28 + (-8)] / {-18 + 19} = 20/1 = 20

Students in Miss Pappas' class each have a set of cards with numbers 0-9 on them. When they have a few minutes in class, she asks students to pull out the cards and they create large numbers with them. She will then ask students to hold up the card with a place value of 10, 100, 1,000, etc. Why is this a good teaching practice?

Every student participates and this reinforces the concept regularly. This is an easy way to review and engage all students.

A student is instructed to draw a four-pointed geometric shape on an xy-plane. After the shape is drawn, the student is instructed to add 5 to each x-coordinate and add 3 to each y-coordinate. Which of the following did the student perform?

translation A translation is simply moving the object from one point on a plane to another point on the plane. The shape of the object remains the same; the object is simply moved along the plane.

The Booster Club at Martin MS is selling spirit buttons for homecoming. The buttons cost $0.75 to make and will be sold for $2 each. How many buttons, b, must be sold to make a profit of $500?

$500 = $2b - $0.75b The profit is equal to the selling price minus whatever costs are applicable. So, if the profit is to be $500, then enough buttons must be sold to reach that profit. If we are selling the buttons for $2 each, but it costs $0.75 to make each one, then there is a profit of $2 - .75 or $1.25 on each button. How many buttons will we have to sell to reach $500 profit: $500 = $1.25b? $500 = $2b - 0.75 c = 1.25b, so the Booster Club will have to sell 400 buttons.

Which of the following has the least value?

0.0518 This has the least value of the set. The tenths place has a 0 while the other numerals have a 5 in the tenths place.

Angela has a stack of construction paper on her desk. Each day she takes one piece of paper, cuts it into 3 pieces to make 3 greeting cards for friends. If Angela has been making greeting cards for 12 days, how many greeting cards has she made? Which of the following equations could a student use to solve this problem?

12÷1​/3 Angela cuts each paper into thirds, so if 12 is divided by one third, we can find the number of greeting cards she made, 36.

Simplify: 15 - 3(8 - 6)²

3 What is inside parentheses must be addressed first and since 8 - 6 = 2, the problem becomes 15 - 3(2)². Exponents should be handled next, so the problem is 15 - 3(4). The multiplication of the 3 with 4 must be completed before subtraction can occur, leaving 15 - 12 = 3. Note that a common error in this problem may include erroneously distributing the 3 from the front of the parentheses into the quantity "8 - 6" inside the parentheses. Because distributing 3 is a form of multiplication, and because exponents must be used before multiplication can occur, the 3 cannot be distributed to the quantity in the parentheses, but must be multiplied only after the power is raised.

Which of the following are correct? Select all answers that apply.

1.045 < 1.45 The ones place is the same so look at the tenths place. 1.45 is greater than 1.045. C 1.54 > 1.45 The ones place is the same so look at the tenths place. 1.54 is greater than 1.45.

If the number 180 is written as the product of its prime factors in the form a²b²c, what is the numerical value of a + b + c, where c = 5 and a and b do not equal 1?

10 The prime factors are the numbers that, when multiplied together, equal a number. In this problem there are three prime factors, where two are squared. We know that c = 5 so the equation (a²)(b²)(c) can be written (a²)(b²)(5) = 180. We can then divide by 5 and simplify this to (a²)(b²) = 36. Take the square root from each side simplifies the equation further to (a)(b) = 6. We know that a and b do not equal 1, so they must equal 2 and 3. So (2²)(3²)(5) = 180 and a + b + c is 2 + 3 +5 = 10.

Of the following, which is most likely the distance from a classroom on the second floor to the playground outside at the end of the wing?

105 meters This is a reasonable distance as it is about the length of a football field.

Lily wants to compare the ages of the children in her family. The table below shows the children's ages. Which of the following compares the children's ages correctly? Lily's Family CHILD AGE Sarah 12 Anne 8 Ross 10

12 > 10 > 8 12 is greater than 10 is greater than 8

The Huang family is building a circular swimming pool in their backyard with a diameter of 8 meters. They wish to place a decorative rock border along the edge of the pool from point A to point B, as shown by the dotted curve in the diagram. As seen in the diagram, points A and B are directly across from one another. Approximately how many linear meters of rock will be needed to form the decorative border along the edge of the pool from point A to point B?

12.6 m The length of the edge of the pool from point A to point B is a portion of the perimeter of the pool. Because points A and B are directly across from each other and the segment which connects them passes through the center of the circular swimming pool, the segment AB is a diameter, and so the portion of the perimeter of the pool that will have a decorative rock border is exactly half. Because the pool is in the shape of a circle, its perimeter is calculated using the formula for C, the circumference of a circle. C = πd. The circumference of the swimming pool is simply C = π×8 ≈ 3.14×8 ≈ 25.12 meters. Given that the circumference is ~25.12 meters, half that amount is 12.56 meters. Therefore, the best answer option is 12.6.

The cement pipe used in a storm drain system is an 8-foot long right circular cylinder with a wall thickness of 3 inches and an outside diameter of 24 inches. Which of the values below best approximates the volume, in cubic feet, of the interior of the pipe? (The formula for the volume, V, of a right circular cylinder with radius r and height h is V = πr2h.)

14.1 If the diameter of the pipe is 24 inches, then the radius of the pipe is 12 inches (because d = 2r, where d = diameter and r = radius). If the wall of the pipe has a thickness of 3 inches, then the interior of the pipe has a radius of 12 - 3 = 9 inches. Because the calculation is to be performed in cubic feet and not in inches, 9 inches must be converted to feet. This can be done using the conversion factor 1 foot/12 inches to cancel inches and bring in feet. 9 inches × 1 foot/12 inches = 9 feet/12, which reduces to ¾ feet, or 0.75 feet. Therefore, the radius to use in the volume calculation is 0.75 feet. The length of the cement pipe was given as 8 feet. Accordingly, the value to use as the height of the right circular cylinder is 8 feet. Finally, substitutions can be made and the appropriate calculations performed, using 3.14 as an approximation for π in the formula V = πr2h so that the volume of the interior of the pipe is discovered to be approximately 14.13 cubic feet. The best answer to select from the options, therefore, is 14.1. V = π(0.75)2(8)= π(0.5625)(8)= π(4.5)≈14.13 cubic feet

Solve: 2 \frac{1}{4} - \frac{1}{2}241​−21​

143​ When subtracting fractions, a common denominator must be found first. Since 2 is a factor of 4, the second fraction can be rewritten by multiplying by 1 in the form of \frac{2}{2}22​. \frac{1}{2} \times \frac{2}{2} = \frac{2}{4}21​×22​=42​ The first fraction can be changed into an improper fraction by multiplying the whole number (2) by the denominator (4) and adding it to the numerator (1). 2 \frac{1}{4} = \frac{9}{4}241​=49​ Now the original expression can be re-written and solved: \frac{9}{4}-\frac{2}{4} = \frac{7}{4}49​−42​=47​ This can be simplified to 1 \frac{3}{4}143​

Values of the linear function f are listed in the table. What is the value of f(85)? x f(x) 30 5 45 8 60 11 85

16 Since it's stated that the pattern is linear, find the slope between any two points. slope = \frac{\Delta{y}}{\Delta{x}} = \frac{8-5}{45-30} = \frac{3}{15}= \frac{1}{5}=ΔxΔy​= 45−308−5​= 153​= 51​ This means that for every 5 unit increase in xx, there is a 1 unit increase in f(x)f(x). From 60 to 85, there is a 25 unit increase in xx so there will be a 5 unit increase in f(x)f(x) (since 25 ÷ 5 = 525÷5=5). Therefore, f(85) = f(60) + 5 = 11 + 5 = 16f(85)=f(60)+5=11+5=16.

What is the volume of a soup can that is in the shape of a cylinder, 10cm tall, and 8cm in diameter?

160π cm3 The volume of a cylinder is equal to π × r2 × h. Since the diameter of the can is 8 cm, the radius of the can is 4 cm. Therefore the volume of the can is equal to π × 42 × 10, which equals 160π cm3.

Simplify: 200 - 3(6 - 2)³ + 10

18 Parentheses be addressed first, so the first step in this problem is to perform the subtraction of 6 - 2 = 4. From there, the problem becomes 200 - 3(4)³ + 10. Exponents should be handled next. In this case, 4 is raised to the third power, resulting in 200 - 3(64) + 10. Multiplication of the 3 with 64 must be completed before subtraction or addition can occur, leaving 200 - 192 + 10. Subtraction and addition are to be simplified in the order in which they appear from left to right. Accordingly, 200 - 192 + 10 = 8 + 10 = 18.

Solve: 1 \frac{1}{4} \div \frac{2}{3}141​÷32​

187​ The first fraction can be changed into an improper fraction by multiplying the whole number (1) by the denominator (4) and adding it to the numerator (1). 1 \frac{1}{4} = \frac{5}{4}141​=45​ When dividing fractions, flip the second fraction and multiply across: \frac{5}{4} \div \frac{2}{3} = \frac{5}{4} \times \frac{3}{2} = \frac{15}{8}45​÷32​=45​ ×23​=815​ This can be simplified to 1 \frac{7}{2}127​.

If the 5th term in a geometric sequence is 162, and the common ratio is 3, what is the first term in the sequence?

2 2 comes from seeing that the sequence is shown to have n = 5, r = 3, and A(5) = 162, where A \left( n \right) =a_{1}r^{n-1}A(n)=a1​rn−1 and A \left( n \right)A(n) is the nth term, a_{1}a1​ is the first term, rr is the common ratio and nn is the term number. The question is answered correctly by keeping a variable expression in the place of a₁ and inputting all known values so that the formula becomes A(5) = 162 = a₁(3)⁵⁻¹. This equation will be simplified as far as possible and then solved for a₁. When the order of operations is followed correctly, exponents will be simplified before any multiplication occurs. The resulting equation becomes 162 = a₁(3)⁴ and then 162 = a₁(81). The final answer is found by dividing 81 on each side of the equation in order to isolate the unknown a₁. The quotient of 162 and 81 is 2, and so a₁ = 2.

Students are measuring various objects around the classroom. A pencil measures 8 ⅜ inches while a pair of scissors measures 5 ½ inches. How much longer is the pencil than the pair of scissors?

2 ⅞ inches First find the least common denominator for the fractions, which is 8. 8 \frac{3}{8}-5\frac{4}{8}= ?883​−584​=? The fractions cannot be subtracted as they are because \frac{4}{8}84​ is larger than \frac{3}{8}83​. Borrow one whole (\frac{8}{8}88​) to make the mixed number 7 \frac{11}{8}7811​. 7\frac{11}{8}-5\frac{4}{8}= 2\frac{7}{8}7811​−584​=287​ inches

Which expression can be used to solve the following word problem? John and Jose want to buy a pizza for dinner and then head to a movie. They will each pay for their movie ticket, which costs $12 each, and they will split the pizza cost of $9. John has $17 and Jose has $20. How much will Jose have left at the end of the evening?

20 - (9/2 + 12) Jose's starting amount is 20 and then the cost of his portion of pizza and his movie ticket are subtracted.

Solve: 5 \frac{3}{4} \times \frac{1}{2}543​×21

287​ The first fraction can be changed into an improper fraction by multiplying the whole number (5) by the denominator (4) and adding it to the numerator (3). 5 \frac{3}{4} = \frac{23}{4}543​=423​ When multiplying fractions, you don't need a common denominator, so the original expression can now be re-written and solved by multiplying across: \frac{23}{4} \times \frac{1}{2} = \frac{23}{8}423​×21​=823​ This can be simplified to 2 \frac{7}{8}287​

Simplify the expression: 4 \left( 7x-3 \right)4(7x−3)

28x−12 Apply the distributive property by multiplying the number on the outside of the parenthesis, 4, to each term on the inside, 7x and -3. 4 \left( 7x \right)4(7x) is 28x28x and 4 \left( -3 \right)4(−3) is -12. 28x-1228x−12 cannot be simplified further because the terms are like like terms because they both do not share the same variable/exponent combination.

Marvin is trying to get to his friend's house. He walks 4 blocks north to the park, then turns right and walks 3 blocks. Finally he turns right and walks 4 blocks. How far from his starting point does he wind up?

3 blocks east Turning right while walking north makes Marvin travel east. He travels east by 3 blocks. When he takes another right he heads south. He winds up in the same north/south position, but 3 blocks east.

The state sales tax is 7.5%. Which number could also represent 7.5%?

3/40 There is always the option of arriving at the answer by eliminating incorrect answer choices, but it is always a good idea to double-check the final choice. In the case of this question, 3/40 = 3 ÷ 40 = 0.075 = 75/1000 = 7.5/100 = 7.5%.

Jenny is baking cookies. Each dozen cookies requires 2 cups of flour and 0.75 lbs of butter. How many cookies can she make with 6 cups of flour and 3 lbs of butter?

36 She can make 36 cookies. 6 cups of flour allows for 6/2 = 3 dozen cookies to be made.

The ratio of Antone's height to arm span is the same as the ratio of his brother's height to arm span. About how tall is Antone?

39 inches The answer is found by solving the proportion: Antone's Brother's Arm Span/Antone's Brother's Height = Antone's Arm Span/Antone's Height, or (56/60) = (36/x). In this proportion, x is Antone's height. In the first ratio, 56 is Antone's brother's arm span and 60 is his height. In the second ratio, 36 is Antone's arm span, and x, his height. Proportions are solved by cross multiplying. When cross multiplication is performed on this proportion, we get: 56 ∙ x = 60 ∙ 36. When simplified, we get: 56x = 2160; then you divide each side by 56 resulting in x = 2160/56 = 38.57, but because the question says "about", you would use 38.57 ≈ 39".

Becky arrived at her babysitting job Saturday morning at 9:15 am. She left at 1:30 pm. How many hours did she work?

4 hours, 15 minutes It is easiest to simply add hours from 9 am to 1 pm and then add minutes from :15 to :30. Using this method, counting can begin from 9:15 am to 10:15 am (1 hour) to 11:15 am (2 hours) to 12:15 pm (3 hours) to 1:15 pm (4 hours), and continue with 1:15 to 1:30 by adding another 15 minutes, to come up with the correct final answer of 4 hours, 15 minutes.

Simplify the expression: 4(10)3

4000 The 10 must be cubed first (order of operations) and then multiplied by 4. 4(10)3 = 4(1000) = 4000

What is the area, in square units, of the figure?

45 units2 The area of the figure can be found using the information from the image. One way to address the question is to notice that the pentagon in the diagram is composed of a 6 × 6 unit square and a triangle with a length of 6 units and a height of 3 units. The area of the square and the triangle can be calculated and then added together to get the total area of the pentagon. The area of a square is found with the formula A = s2, where A is the area and s is the length of a side. Or, because a square is a specific type of rectangle, the area of the square can be calculated using A = bh or A = lw, where b is the base, h is the height, l is the length, and w is the width. In this case, the side length is 6 units, which can be seen either through counting boxes in each direction or using subtraction of coordinates on the ends of the square in the x-direction (-5 to +1 is 1 - (-5) = 1 + 5 = 6) and in the y-direction (-2 to 4 is 4 - (-2) = 4 + 2 = 6). Therefore, the area of the square is 62 = 36 square units. The area of a triangle is found with the formula A = 1/2bh, where A is the area, b is the base, and h is the height of the triangle. The base of this triangle can be measured by counting squares along the vertical line x = 1, or by subtracting the highest and lowest y-coordinates along the line x = 1: 4 - (-2) = 4 + 2 = 6 units. The height of the triangle can be measured by counting squares along the horizontal line y = 1, or by subtracting the x-coordinates from the points (1, 1) and (4, 1): 4 - 1 = 3 units. Therefore, the area of the triangle is 1/2(6)(3) = 3 × 3 = 9 square units.The total area of the pentagon is 36 + 9 = 45 square units.

Bill went to the store to purchase new clothes for the upcoming school year. Bill purchased 8 shirts, 4 pairs of shorts, and 2 pairs of pants. If a single outfit consists of one shirt and either one pair of shorts or one pair of pants, how many outfits can Bill create with the clothes he purchased?

48 The answer can be found by multiplying the number of shirts by the number of pairs of shorts and pairs of pants. This would create the equation (8 shirts) × (4 pairs of shorts + 2 pair of pants) = 8 × (4+2) = 8 × 6 = 48.

An isosceles triangle with a rectangle cut out is shown. What is the perimeter of the resulting figure?

48 m First, find the length of the legs of the isosceles triangle by dividing the triangle into two right triangles with height 12 and base 5. Use Pythagorean theorem (or Pythagorean triples) to find the length of the hypotenuse. 12^2+5^2=c^2\rightarrow c=13122+52=c2→c=13 Then, add the lengths of the perimeter of the shape. P=13+13+2.5+6+5+6+2.5=48 \text{ in}P=13+13+2.5+6+5+6+2.5=48 in

What is the area of the figure provided?

49.5 cm2 The area of the figure is l × w = 5.5 × 9 = 49.5 \text{ cm}^2l×w=5.5×9=49.5 cm2.

Susan travels at a rate of 60 miles per hour for 3 hours. Her car uses on average one gallon of gas per 30 miles. How many gallons of gas does she use on her trip?

6 The two unit rates: (30 miles per 1 gallon) and (60 miles per hour) can be used to convert from 3 hours to gallons of gas. Susan travels 180 miles (60 miles/hour × 3 hours). 180 miles/(30 miles/gallon) = 6 gallons of gas.

What is the volume of the triangular prism pictured?

60 in3 The volume of a prism is in general B*h. The base of this prism is a triangle. The area of a triangle is ½ × b × h. The area of the base is ½ × 3 × 4 = 6 and then it is multiplied by the heights so 6 × 10 = 60.

The Chen family loves to go to new places. They drove on the highway at an average speed of 60 miles per hour to try out a new restaurant. They had lunch there for about a half hour, and decided to take the scenic route home, driving on smaller roads and averaging 30 miles per hour for the return trip. If the restaurant is about 60 miles from their home, which graph best models the Chen family's journey?

60-90 If the Chens travel at 60 miles per hour while on the highway en route to the restaurant 60 miles away, then they will reach the restaurant in 1 hour, which is expressed as 60 minutes on this graph. During the half hour (30 minutes) that they spend eating lunch at the restaurant, their distance from home will remain constant. Accordingly, the correct graph shows a horizontal segment at 60 miles from home for 30 minutes, and so extending until the 90 minute mark. Finally, on their way home, the Chens travel at a rate of 30 miles per hour. At that rate, the 60 mile return trip will take 2 hours, or 120 minutes, from the 90 minute mark. Therefore, their arrival home occurs at 90 + 120 = 210 minutes. Upon their arrival home, the Chens are 0 miles from home, and so the graph shows a point at (210, 0), representing the 3.5 hours that the Chens spent on their excursion. None of the other graphs correctly illustrate this journey.

A tennis ball has a diameter of about 3 inches. The container that holds a stack of three such balls is a right cylinder with a circular base. What is the approximate volume, in cubic inches, of the container that holds three tennis balls?

64 To find the volume of a right cylinder with a circular base, the area of the base of the cylinder is multiplied by its height. The area of the base of this container is a circle and so the calculation for its area should follow the formula A = πr2, where A = the area of the circular base and r = the radius of the base. The radius of the circular base of the can should be approximately equal to (though slightly larger than) the radius of the tennis ball. The diameter of the ball is given as "about 3 inches". Because diameter is twice radius, the radius of the tennis ball must be approximately half of that amount, or about 1.5 inches. Therefore, the area of the base of the cylindrical can with a circular base can be calculated as A = π(1.5)2 = 2.25π ≈ 7.07 square inches. It was given that the can for the tennis balls fits a stack of three tennis balls. Therefore, the height of the can should equal the height of three 3-inch diameter balls stacked on top of each other: 3(3 inches) = 9 inches. Therefore, the height of the can must be about 9 inches. Now the volume of the container can be calculated by multiplying the area of the circular base, ~7.07 inches, with the height of the can, ~9 inches. 7.07(9) = 63.63 in³. This answer can be rounded to approximately 64 cubic inches for the best approximate answer to this question.

A runner is running a 10k race. The runner completes 30% of the race in 20 minutes. If the runner continues at the same pace, what will her final time be?

67 minutes To find the answer to this question, set up a ratio; remember that 30% = .3 and 100% = 1. Therefore, (20 / .3) = (x / 1) When you cross multiply to solve for x, you get the equation .3x = 20. Divide each side by .3 to isolate x and the answer is 66.66666. The best answer choice is 67 minutes.

What is the value of the "7" in the number 432.0769?

7/100 In a base 10 system, each place location for a number has a value that is a power of 10. In the opposite direction of the ones place, there is the tenths place from 10⁻¹ = 0.1 or 1/10, the hundredths place from 10⁻² = 0.01 or 1/100, the thousandths place from 10⁻³= 0.001 or 1/1,000, etc. When a digit is in a specific position, its value is equal to the product of that digit and the power of 10 that is assigned to its position.

Marsha asked all 72 children at recess and only ⅙ said that their favorite ice cream flavor was strawberry. Which of the following expression can be used to determine the number of children who told her strawberry was their favorite?

72 × 0.166 The fraction ⅙ can be converted to a decimal by dividing 1 by 6 for 0.166. This multiplied by the total number of children (72) will provide a solution for the number of children picking strawberry.

A teacher presents a right triangle to her class. She declares that the hypotenuse can be written as either 4x + 30 or as 6x + 14. Given this relationship, what is the value of x?

8 If both algebraic expressions can be used for the length of the hypotenuse, they must be equivalent expressions. Therefore, the value of x can be found by solving the equation 4x + 30 = 6x + 14. This equation should be solved by grouping all x values on one side of the equation and all constant terms on the other, and then dividing by the coefficient of x. One way to accomplish this process is to subtract 4x on each side to get 30 = 2x + 14. Next, 14 can be subtracted from each side to get 16 = 2x. Finally, 16 = 2x can be simplified to 8 = x by dividing both sides by 2.

A third-grade class begins working on a mathematics project at 9:50 a.m. and stops working on the project at 11:10 a.m. How many minutes did the class work on the project?

80 minutes There are 10 minutes from 9:50 to 10:00 and 11:00 to 11:10 and one hour from 10:00 to 11:00. There are 60 minutes in every hour. Between 9:50 a.m. and 11:10 a.m. is one hour and twenty minutes, or 80 minutes.

A painter charges $10 fixed initial charge plus $20 per hour of painting. If the total bill comes to $190, how many hours did he paint for?

9 The bill for 9 hours would be $10 + 9 \times× $20 = $190. To solve this problem, you can work backward. $190 - $10 initial charge = $180 charge for the hours. Since $180 / $20 = 9, he worked for 9 hours.

Which symbol most accurately reflects the relationship between the two numbers below? 0.7 ☐ 4/5

< Convert 4/5 to a decimal (0.8) to compare more easily. Since 0.7 is less than 0.8, this is the correct symbol.

Ms. Colon, a new fifth-grade teacher, is planning her math lessons for the grading cycle. She thinks of all of the topics she needs to teach and makes discrete daily lessons. Each unit has an opening pre-test. Each lesson has instruction, guided practice, and independent practice. Which of the following are methods she should incorporate into her lesson planning? Select all answers that apply.

A Instead of making single lesson plans, first create a thematic unit around which to frame her lessons. Planning discrete lessons does not leave much room for repetition of ideas. Planning lessons around a thematic unit allows students to be exposed to the ideas multiple times. Plan time each day for students to explain concepts they have learned to their peers. Planning a time for students to explain concepts to each other is good practices. D Plan each lesson with a closure activity. Planning for a closure activity is good practice.

Which of the following relations represent a function? Select all answers that apply.

A relation is a function if every input has exactly one output. In an (x, y) ordered pair, the x is the input and the y is the output. None of the x values repeat in the set of ordered pairs, so each x value corresponds with only one y value, and so the relation is a function. In order for a graph to represent a function, it must pass the vertical line test. A vertical line pass through any part of the graph must only intersect the graph at one point. This graph passes the vertical line test, and so it is a function. flat numbers graph

Jason solved the equation 3x-2=13+1x-73x−2=13+1x−7 below: What property of equality was misused in Jason's work

Addition property of equality In the first step, Jason added 2 to the left side but 4 to the right side of the equation (he added 2 twice). The addition property of equality only works if the same number is added to both sides of the equation.

Mrs. Jones is teaching a lesson on slope-intercept form. She requires each student to find the slope and y-intercept of a set of graphs, then put them into a formula that describes the graph. The students work one problem at a time and Mrs. Jones circulates to check their work. If a student has the correct answer, Mrs. Jones gives them a checkmark and they move on to the next question. If the student has the wrong answer, Mrs. Jones directs them to the incorrect portion of their work and they revise their answer. Mrs. Jones continues to circulate the room until all students have finished the assignment. Which of the following learning theories best matches the activity Mrs. Jones uses with her students?

Behaviorism learning theory The students are learning by receiving feedback with positive reinforcement.

Maria baked 6 dozen cookies for her classmates. There are 28 students in her class, each child received 2 cookies and Maria gave 6 cookies each to her teacher and her principal. Which equation could be used to find C, the number of cookies she had left over?

C = 6 • 12 - (2 • 28 + 2 • 6) 6 • 12 gives us the total number of cookies in 6 dozen: 72 cookies. Then if each child receives 2 and there are 28 children, 2 • 28 = 56; if the teacher and the principal each receive 6, that is another 12. So, we have 72 - 56 - 12 = 4. Maria will have 4 cookies left

Which of these statements correctly describes the coefficients and degrees of the polynomial shown? 5x7 + 5x5 - 3x - 2

Coefficients: 5, -3, -2 Degrees: 7, 5, 1, 0 The coefficients are the whole numbers preceding a variable. The degrees are the exponents. For example, 5x7 has a coefficient of 5 and a degree of 7. For the degrees, unwritten exponents such as -3x are noted as 1 (because x1 = x) and constants are noted as 0 degrees (because x0 = 1).

Students in Mr. Walton's class were independently trying to solve the problem below. The graph above shows the amount of money in dollars, y, that Bobby has saved after x weeks. If he continues saving money at the same rate, how much money will Bobby have saved after 12 weeks? Gabriel is a student in Mr. Walton's class. He is struggling to get started on the question, and raises his hand to get some help. Gabriel says he knows he needs to figure out the value of y when x = 12 weeks, but is stuck because the graph is cut off after x=6. Which of the following is not a possible responses to help Gabriel know how to start the problem?

Create a proportion using an ordered pair from the graph and solve for $y in 12 weeks. For example, \frac{1 week}{\$2}=\frac{12 weeks}{\$y}$21week​=$y12weeks​. Using a proportion to solve for a missing value will work only if the relationship is proportional. You can tell if a relationship is proportional if the graph is a straight line that goes through the origin. This relationship is not proportional because it does not go through the origin, and therefore setting up and solving a proportion will not give the correct value of y when x = 12.

Mr. James plans to assess his students' knowledge during a unit on linear functions and would like feedback from the students on how well they feel they are learning the concepts. Which of the following assessment would be the most appropriate for Mr. James to use during the unit?

Daily open-ended formative assessment in which the students complete a problem, with justification and any questions they still have about the material from that day. These assessments would best allow Mr. James to assess student learning and gain insight on where they are struggling.

Mr. Sexton has been trying a variety of teaching methods to engage his class, but it seems to make things more out of control. How can he increase engagement while maintaining an orderly classroom?

Establish a daily procedure for class and vary the activities used for instruction. Students will be more on task when provided a routine to follow .

Mr. Muldoon is teaching about converting between metric and English units. One of his students refuses to engage in the activity and states "I am never leaving America so I don't need to learn this." How should he respond?

Explain the many ways in which people in America use the metric system. Relating current learning to the real world is always a good idea. Information should be shown to be relevant.

Which of the tables best corresponds to the graph?

From the given image, the following points can be found on the line: (6, 10), (18, 25), and (30, 40). Of those points, two are in the table for the correct answer. The other two points in that table can be estimated to be on the line using the graph.

Mr. Grubb is teaching about accuracy and precision. He asks students to write an essay explaining the difference between the two. He gets a couple of essays that are two sentences long. How can he improve this?

Give a rubric which clearly communicates expectations. Rubrics help clarify expectations and should be given for most open ended assignments.

Mr. Macdonnel is teaching about elapsed time. He asks students to make a daily schedule and calculate how long they do each activity for the week. Several students list only: sleep, school, and home as their activities. How can he improve this activity in the future?

Give a rubric which clearly communicates expectations. Rubrics help clarify expectations and should be given for most open ended assignments.

A kindergarten class is beginning a unit on data collection. Which of the following would be the best first activity?

Give each student a collection of colored tiles to sort by color. This is an excellent activity to begin a unit on data collection. After sorting, students can begin to answer questions like, "What color of tile do I have the most of?", and "And the least of?" They can even begin comparing what they have with what another student has.

Ms. Klein is teaching her students about tessellations. She brings in magnetic tiles for her students to create their own tessellations as an introductory activity. She hands them out to the students and then begins to explain the activity for the day. Students are not paying attention and instead building whatever they want. How can she improve her teaching practice?

Give the students clear instructions and a worksheet that accompanies the activity prior to handing out the tiles. It is vital to give out guidelines for use prior to handing out manipulatives.

Veronica noticed that the more time she spent practicing her piano recital piece, the more of the music she had memorized. Which of the following graphs could represent the relationship Veronica noticed between her time spent practicing and her knowledge of her recital music?

Graph D Since time is the dependent factor, it will be on the x-axis. This graph that shows the Portion of Recital Music Memorized rise as Time Spent Practicing for Piano Recital increases, reflecting the situation that Veronica observed.

A teacher wants students to understand how environments can support a population of plants and animals in an ecosystem. Which of the following is the most engaging way to start a lesson that relates to the lesson goals and encourages students to see themselves as scientists?

Have students observe and record the interactions of plants and animals in a terrarium over a span of several days or weeks. The interactions in a terrarium will best engage students by stimulating interest in the topic. It also allows students to be scientists by making, recording, and discussing their observations over a period of time.

During a unit on organisms and environments, Mr. Woodland wants his second-grade students to identify factors in the environment that affect plant growth. Students design investigations that involve growing bean plants in paper cups and exposing the plants to environmental variables of their choice. After the beans sprout, the students measure and record the heights of their bean plants. At the end of the investigation, students will be asked to present their data in a way that will be quick and easy to understand. Which of the following is the best way to incorporate technology into this lesson?

Have students record and graph their data in a spreadsheet that they can access each time they make a measurement. A spreadsheet is the best use of technology for this activity. It will allow students easy access to data that is collected over a period of time. Making a graph with a spreadsheet can be quick and students can experiment with different types of graphs and select the best graph for their presentation.

A third-grade class has been working on adding increments of time smaller than 60 minutes. The majority of students are able to correctly add 15- and 30-minute increments in both isolated problems and word problems. What activity could the teacher add to the next lesson to increase student engagement?

Have students work in pairs to create a new daily schedule with 30 more minutes of recess, 15 more minutes of lunch, and 15 more minutes of PE. This activity will encourage students to apply their knowledge to a familiar real-world scenario and will likely be an appropriate challenge for students to complete.

In a first-grade class, the students have been working with manipulative materials and pictures as they investigate the concept of addition. Through both formative and summative assessments, the teacher has determined that the students are ready to move to more abstract (pencil and paper) ways to represent addition. How should she begin this process?

Have the children model pictorial representations of problems like 7 + 2 = 9 that include the numbers that represent each step. Relating the symbolic representation of addition facts references models students have done in the past but has only the teacher involved in the actual modeling. Students must be in control as much as possible of their own learning. Remember that students learn best by doing, not by watching others do.

A math teacher wants to introduce a lesson on the use of decimals and fractions. Which of the following strategies is most likely to increase the students' understanding of the concepts?

Highlight examples of decimal and fraction use from the students' lives. By relating the concept to a familiar situation in the students' lives, the teacher takes an abstract example and provides students with a real-world context through which to understand it.

A student is investigating the growth of Elodea under different light sources. Which of the following is the best research question for this student?

How does the type of light source affect the rate of photosynthesis of Elodea plants? This is the best and most testable research question.

Mr. Erikson has his friend Ted, who is an architect, come present to the class about how he uses math in his job. What is Ted likely to talk about?

How geometric figures are a part of most buildings. Geometry is often used by architects and this is the right choice.

A sixth-grade teacher is beginning a unit on probability. She utilizes the following steps in planning her unit: Determine the necessary prerequisite skills. Begin planning probability activities that involve the collection of data. Determine what the students already know by using a KWL chart. Plan the final assessment for the unit. What is the best order for the teacher to organize these steps?

IV, I, III, II The teacher should begin by planning the final assessment. This serves as her destination goal, where she wants her students to be at the end of the unit. Once the assessment is developed, the teacher needs to determine what prerequisite skills are necessary for successful mastery. The third step would be to assess what the students already know about probability. The teacher should follow the steps: assess, determine prerequisite skills, determine what students already know, and plan activities to get to the destination.

A teacher prompted her class to write an expression that matches the phrase "3 less than 2x." One student wrote the expression 3-2x3−2x on his paper. What suggestion should be given to the student to help him realize his mistake?

Identify key phrases and write the math symbols above the words. Writing the math symbols above the phrases will help the student connect the words to the symbols. "3 less than" means -3. Writing -3 above this phrase should help the student recognize their mistake of misplacing the subtraction/negative sign.

What type of sequence is the following number sequence? 4, 12, 20, 28, 36, 44...

It is an arithmetic sequence; you add 8 every time to get the next term. Arithmetic sequences have a common difference. This sequence has a common difference of 8 (12-4=8; 30-12=8; 28-20=8;36-28=8; 44-36=8).

A first-grade teacher wants to encourage her students to use addition and subtraction skills in their daily lives. Which of the following would be the most effective way to do this?

Look for opportunities during the day to ask students an addition or subtraction problem. For example, "We have 18 students in our class, but I only see 15 in line. How many students must still be getting water?" This is a good way for the teacher to point out real-world applications of addition and subtraction while having students practice the skill in context.

Ms. Lemmons' class is about to carry out a lab experiment over plant growth. Which of the following would be the most effective way to carry out the experiment?

Ms. Lemmons can help the students form a hypothesis, identify their variables, and design an experiment before starting the experiment. By guiding the students in preparing for the lab, Ms. Lemmons will make the students feel more comfortable during the lab. Since students are writing their own labs, this will be more engaging.

Mr. Howard would like to create a short freewriting activity to determine whether his students are using critical-thinking skills on their current topic. Which Bloom's verb would be the best for him to use to start his prompt?

Predict Predicting is a higher level Bloom's verb which indicates critical thinking ability.

Mrs. Luna tried flipping her classroom to teach common denominators, having students watch a lecture at home and then doing the homework practice during class. Many students did not watch the entire video because they thought they had the concept down after the first example. If she tries this again, how should she change her approach?

Provide a notes outline that needs to be filled in as they watch the video. This approach helps them stay engaged while watching.

Miss Kelly has been teaching fractions and believes her students understand composing and decomposing fractions through the activities they have done. What activity would be best to informally assess their knowledge before moving on to the next lesson?

Provide a warm-up question that asks them to write one way to decompose 3/4 This is a quick and informal assessment of knowledge.

Mrs. Nadir's students are great at determining the surface area of cubes. They struggle with determining the surface area of rectangular prisms. What should she do to help her students be successful?

Reinforce how to determine the area of rectangles and then procedurally add the areas of the faces of a block. This will ensure students know both how to determine the area of rectangles, and also shows the students where the surface area is coming from.

Ms. Smith gives a unit exam on transformations of geometric figures. It is a 20-question multiple-choice exam. All but one student gets a 100 percent on the exam. What can be said about her assessment? Select all answers that apply.

She probably should have added some open ended questions to give her students more opportunity to demonstrate mastery. Students should have to perform the transformations themselves to demonstrate deep understanding of the material. Her students are very good at answering multiple choice questions pertaining to transformations. This is true, since many students got 100 percent they are obviously good at answering those types of questions.

Which of the following activities is the best way for elementary students to learn how to write an equation for a line of best fit on a scatter plot?

Students create a scatter plot of data from a simple experiment where they compare the height to the arm span of various students in class. Students then answer guided questions about the correlation between arm span and height, make predictions, create a line a best fit, and write an equation for the line. This activity shows students the practical application of lines of best fit. Students see the relationship between an experiment, a scatter plot, a line of best fit, and the equation of the line. Students are guided through all aspects of creating the line and using the equation to make predictions.

Which of the following situations might require the use of a common denominator? Select all answers that apply.

Subtraction of fractions Unless fractions have like denominators, you must always find a common denominator before you can add or subtract. Finding a common denominator requires finding a common multiple of the two (or more) denominators. It is important to note that you do not have to find the LCM or lowest common multiple; any common multiple will work. However, if the LCM is found and used, there will be considerably less simplifying to do in order to reduce to the lowest terms. Multiplication and division never require finding a common denominator. Addition of fractions Unless fractions have like denominators, you must always find a common denominator before you can add or subtract. Finding a common denominator requires finding a common multiple of the two (or more) denominators. It is important to note that you do not have to find the LCM or lowest common multiple; any common multiple will work. However, if the LCM is found and used, there will be considerably less simplifying to do in order to reduce to the lowest terms. Multiplication and division never require finding a common denominator.

Mr. Barrios is teaching a unit on multiplication to his fifth-grade class. On the very first day he gives an exit slip with the following problem on it: 123.456 x 789 = _______ Every single student gets the question correct. How should he adjust his teaching?

Teach more advanced multiplication content to challenge his students. This is the best answer. While every student getting the answer to the exit correct could indicate stellar teaching, it could also indicate that students had previously mastered the material. He should consider adding more advanced content to his lessons to keep his students challenged and engaged.

Students in Ms. Weikel's class are having difficulty remembering the metric unit prefixes. What should she do to help them remember the prefixes?

Teach students a helpful mnemonic device. Mnemonic devices can help students memorize essential information.

When considering the addition problem 1/3 + 3/8, which of the following statements is true? Select all answers that apply.

The Least Common Denominator = 24 Because 3 and 8 are relatively prime their least common denominator (LCD) can be found using the formula 3 • 8 = 24. Therefore, 24 is the LCD. 3 and 8 are relatively prime Two numbers are relatively prime if they have no common factors except 1. Because 3 and 8 are relatively prime, there is no whole number, other than 1, that will divide both 3 and 8 evenly without a remainder.

As Kate runs more miles per week, her time per mile improves steadily. She begins running 4 miles per week and it takes her more than 8 minutes to complete each mile. On the graph above, where would the line begin and what direction would it travel?

The line would begin in the top left and move towards the bottom right. The mile time would be the slowest when she is running the least. The line would start at the top left and move towards the bottom right.

Use the figure below to answer the following question. Which of the following triangles is congruent with the triangle shown above

The three sides and the three angles of congruent triangles are exactly the same, although the triangles may have different orientations. In this case, the triangle has been rotated counterclockwise.

If the measure of angle x is 60 degrees and the measure of angle z is 30 degrees, what can be said about angles x and z?

They are complementary angles. Two angles whose sum is 90 degrees are complementary. Since 60 and 30 equals 90, they are complementary.

Which of the triangles below is the best example of an obtuse triangle?

This triangle has one angle larger than 90\degree90°, making it an obtuse triangle.

Mr. Miller has taught addition with two-digit numbers and rounding. His students are beginning to use this concept in word problems. He teaches them 3 methods to simplify the process: guess and check, make a list, and draw a picture. Is teaching 3 different strategies a good practice?

Yes, because this allows students to develop a strategy that works for them. Students can use different strategies and teaching 3 is not too overwhelming.

The Parent Teacher Organization at Douglass Elementary baked cookies. The ingredients to make each batch of cookies cost $3. Each batch made 20 cookies. The PTO sold each cookie for $0.50. They produced b batches of cookies, and sold every single one of them. What is a valid expression, in terms of b, for the profit that the PTO made for their cookie sale?

[(0.5)(20) -3]b In general, Profit = Revenue - Expenses. The revenue that the PTO brought in from their bake sale was $0.50 for every cookie sold. There were 20 cookies in each of b batches of cookies made and sold. Therefore, there were a total of 20b cookies produced and sold. With each cookie selling for $0.50, the total revenue from the sale was 0.50 × 20b, which can also be expressed as (0.5)(20b) or (0.5)(20)b. The expense to produce the cookies was $3 for every batch. Therefore, expenses = 3b. Profit can now be expressed as the difference between revenue and expenses: (0.5)(20)b - 3b. The answer choices show b factored out, and so the answer [(0.5)(20) -3]b can be selected.

Which of the following best describes the polygon shown?

a convex pentagon A pentagon has 5 sides. A convex polygon has no angles greater than 180°. Another way to think of how to identify a convex pentagon is that it has no angles pointing inward.

A third-grade teacher is teaching a whole group lesson on counting money. After the lesson is complete, she asks students to form groups of four and find the total of different sets of bills and coins that she will display on the board. During the group activity, there is a lot of commotion and off-task behavior, and several students begin working independently instead of with their group. What could the teacher have done differently to improve the group activity?

assigned groups ahead of time and established clearer expectations for group members The most likely cause of the off-task behavior and lack of participation is that students were unable to form effective groups and were unsure of how they should contribute to the group. Carefully assigning group members and explaining how each student will contribute would likely have led to an improved outcome.

Which of the manipulative materials below would be most suitable for teaching decimal notation to the hundredths place? Select all answers that apply.

decimal squares Decimal squares are tag-board pictures of 10x10 grids that have portions of the 100 smaller squares shaded. Students are asked to name the decimal represented by the shaded or unshaded area. They see that the sum of the shaded and unshaded areas always equals 100 hundredths or 1. Base ten blocks are hands-on manipulatives consisting of a large cube (made up of 1000 smaller cubes), a flat (10 x 10 grid or a 100 square), a long (1 x 10), and a unit cube (1 x 1). Base ten blocks allow the representation of decimals from 0.001 (the smallest cube) to 1 whole (the largest cube). base ten blocks Base ten blocks are hands-on manipulatives consisting of a large cube (made up of 1000 smaller cubes), a flat (10 x 10 grid or a 100 square), a long (1 x 10), and a unit cube (1 x 1). Base ten blocks allow the representation of decimals from 0.001 (the smallest cube) to 1 whole (the largest cube).

Which of the following classroom activities is the best example of teaching inquiry-based science when learning basic anatomy?

dissection of a preserved frog in small groups Hands-on activities, which allow students to participate in the learning and apply acquired knowledge, have been proven to be the best method of science instruction.

Adam wants to determine how much to charge for an event. He looks through his records from old events to determine a reasonable price for the venue, the average price of catering, and thinks about other incidentals. He then solicits quotes from several people and places before setting a price for the event. What process is he using to create this budget?

formal reasoning Formal reasoning is used to answer questions and solve problems that have a single solution (a right answer) by using rules of logic and algorithms (systematic methods that always produce a correct solution to a problem) to reach a conclusion. This is what Adam did when planning the budget.

Malik set up a conversion: 3 gallons \times \frac{4 quarts}{1 gallon} \times \frac{2 pints}{1 quart} \times \frac{2 cups}{1 pint}×1gallon4quarts​×1quart2pints​×1pint2cups​ Which of the following conversions is he making?

gallons to cups The conversion begins with gallons and ends with cups. All of the other units will cancel out.

Students are asked to solve the word problem below. The school carnival is coming up and Jenny and Sarah plan to sell cupcakes. Since the school carnival is a fundraiser, Jenny and Sarah's parents make a donation to their cupcake booth to get them started. Jenny starts with a $5 donation and sells her cupcakes for $3 each. Sarah starts with a $10 donation and sells her cupcakes for $2 each. How many cupcakes do Jenny and Sarah have to sell for their profits to be equal? One student's response is "Zero, because if Jenny sells her cupcakes for more money, then she will always have more profit." Which of the following activities could help the student realize his misconception?

graphing the scenarios Graphing the two scenarios will help the student see where the graphs intersect and therefore are equal in profit.

Mrs. Cooper wants to reinforce a concept she is teaching her sixth-graders by having students use their calculators to solidify their conceptual understanding. In which of the following activities would the use of a calculator be most beneficial to conceptual understanding?

having students graph lines with different yy-intercepts then determine how bb changes the graph of y=mx+by=mx+b With this activity, students are gaining an understanding that when bb increases, the graph shifts up, and when bb decreases, the graph shifts down.

Which of the following activities best illustrates an activity related to using scientific inquiry in the classroom?

helping students identify a problem and develop testable questions that might lead to a solution An engaging part of scientific inquiry is allowing students to participate in the process of identifying problems to solve and asking questions that might lead to a solution.

A second-grade teacher is planning a group activity in which students will sort 3D shape models based on their defining attributes. How should the teacher plan on grouping students for this activity, and why?

heterogeneously, so that struggling students can learn from their peers and other students can benefit from explaining their reasoning Heterogeneous grouping is the best choice for this type of activity, because it allows students to learn from their peers and deepen their understanding by explaining the concept to others.

In a kindergarten class, two students have discovered that four butter tubs full of sand will fill a plastic pitcher. This learning is best described as:

informal non-standard measurement. Formal activities are generally teacher-developed and completed by all students. Informal activities are developed or discovered by the student, and with younger students this discovery often occurs during play. This "play" activity is informal and results in a discovery about the relationship between butter tubs and a pitcher; both are non-standard measuring tools. Therefore, this is the correct answer. D formal standard measurement.

Mr. Fielder has assigned students an open-ended research question for his fifth-grade science class. Which of the following should Mr. Fielder provide to ensure active engagement for his students in the activity?

inquiry-based instruction Inquiry-based instruction ensures students are active while learning.

Which activity would best support second-grade students in developing an understanding of the stages in the life cycles of insects?

making and recording observations of a butterfly as it progresses from the egg stage to an adult butterfly while also using a chart to identify, name, and explain the stages This inquiry-based activity is tied directly to the learning goal. Students would compare their observations with the existing scientific understanding of the life cycle.

After reviewing a student's math assessment, the student's teacher has determined that the student is not following the order of operations when solving problems. Which of the following is the most appropriate remedial intervention?

mnemonic device Teaching the student to use a mnemonic device such as "PEMDAS" will help the student to recall which operations to solve first.

Mr. Yoder gave each of his students some Starbursts and some Skittles. He instructed the students to use the candy to set-up and solve multi-step equations, using the Starbursts to represent the x's, the Skittles to represent the constants, and different colors to represent positives and negatives. To solve the equations, students must determine how many Skittles are equivalent to one Starburst. Which of the following concepts is Mr. Yoder most likely working on with his students?

order of operations when solving equations Suppose a student was solving 2x + 3 = 5, and had 2 Starbursts and 3 Skittles equal to 5 Skittles. Before they could figure out how many Skittles are equivalent to one Starburst, they first must take away 3 Skittles so the Starbursts are by themselves before determining how to divide the remaining Skittles evenly among the Starbursts. Students will realize that it is not possible to determine how many Skittles represent one Starburst without first getting the Starbursts by themselves on one side. This allows students to discover that you must add or subtract the constants first before using multiplication or division to isolate the variable.

Traditionally, most elementary questions asked during instruction and assessment are at the recall level. Which level of Bloom's Taxonomy encourages the learner to think at the highest level?

synthesis (creating) The highest level of the hierarchy is synthesis (creating).

Mr. Shields is teaching a unit on magnetism with his third-grade students. Many have a misconception that all metals are attracted to magnets. Which of the following activities would most effectively help his students think critically about this statement?

testing magnetic attraction with a variety of metals One of the best ways for students to explore science, especially to disprove their misconceptions, is hands-on investigations. By giving them a variety of metals, some that will attract (ferromagnetic like iron) and others that won't (non-magnetic like copper), they can experience this difference first hand.

Students were asked to draw a picture representation of adding 2 fractions. What equation is represented by the picture below?

⅔ + ½ = 1 ⅙ This is the equation represented. The boxes are drawn to show a common denominator between ⅔ and ½ of 6.

Based on the image below, if triangle DEF is congruent to triangle GHI, which of the statements is true?

∠G and ∠F are complementary If two triangles are congruent, then corresponding sides (sides that are in the same position) and corresponding angles (angles that are in the same position) are also congruent. In the figure, this means that DE = GH, DF = GI, and EF = IH and m∠D ≌ m∠G, m∠F ≌ m∠I, m∠E ≌ m∠H. The symbol in the corner of ∠E and ∠H tells us that E and H are right angles and are each equal to 90°. Since the sum of the angles in any triangle is 180°, this means that since m∠H = 90°, then m∠G + m∠I = 180 - 90 = 90° and would, therefore, be complementary. But what about ∠G and ∠F? Well, since ∠F and ∠I are corresponding angles, they are congruent and their measures can be substituted for each other. So, m∠G + m∠F = 90°. Therefore, this option is a true statement.