content math

Julie brings and eats one-third of a sandwich every day for lunch. If she made 11 sandwiches this month, how many lunches did she bring? Which of the following expressions would be a correct computation for the answer to the problem above?

A. 1/3 divided by 11 B. 11 multiplied by 1/3 C. 11 divided by 1/3 D. 1/3 times 11 (C) this expression would equal 11 multiplied by 3/1, which equals 33, the correct amount of lunches she is able to make from 11 sandwiches.

Matthias, a fourth-grader, wants to find 20% of 70, using mental math. Which of the following numbers is best for Matthias to use to multiply by 70 to find the correct answer?

A. 1/7 B. 40/200 C. ⅕ D. 0.2 (D) Most students at this level will know 7 x 2 = 14, and they will be able to move the decimal mentally.

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?

A. 10 ft B. 5ft C. 30 ft D. 15ft (D) 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, \frac{5}{10} = \frac{x}{30}105​=30x​. Rearranging, x = \frac{5}{10}(30) = 15x=105​(30)=15.

Student groups are given a six-sided die, with each side labeled a number 1 through 6. Each student group rolls the die 75 times and records the number that is rolled. If there are 8 groups of students participating in this activity, which of the following is most likely the total number of times a 4 was rolled?

A. 13 B. 78 C. 98 D. 154 (C) There are a total of 600 rolls for the class as each group records 75 rolls. The theoretical probability of rolling any number is 1/6 or about 16.7%, and one-sixth of 600 is 100. So, the students will roll a 4 about 100 times.

What is the perimeter of a square with an area of 81 cm2?

A. 18 cm B. 36 cm C. 81 cm D. 9 cm (B) A square has congruent sides, so if the area is 81 cm2, then one side is 9 cm. Since a square has four sides, 9 cm x 4 = 36 cm.

A pool empties at a rate of 12 quarts every 2 minutes. How many hours and minutes will it take to completely empty the pool which contains 12,000 gallons? (1 gallon = 4 quarts)

A. 33 hours and 20 minutes B. 66 hours and 40 minutes C. 133 hours and 20 minutes D. 16 hours and 40 minutes (C) Both quarts and minutes needs to be converted. 12 quarts = 3 gallons. 12,000/3 = 4,000 x 2 minutes = 8,000 minutes/60 minutes = 133 hours and 20 minutes

simplify 82−100÷4+6×12

A. 588 B. 129 C. 18 D. 102 (B) 82-100 divided by 4+6x12 82-25+6x12 82-25+72=129

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?

A. 60 B. 55 C. 180 D. 165 (D) The ratio 60/240 = ¼ so ¾ of students are not athletes. Since this can be applied to the sophomores, ¾ × 220 = 165 sophomores.

What is the mode of the following data set? 98, 93, 64, 88, 91, 102, 93, 76, 99, 93, 87

A. 64 B. 93 C. 38 D. 89 (B) The mode is the number that shows up most often in the data set.

Whitney is packing for a week-long trip. She fills her suitcase with 5 shirts, 3 pairs of pants, 2 skirts, and 2 dresses. If an outfit consists of 1 shirt and 1 bottom (pant or skirt) or 1 dress, how many different outfits can Whitney create?

A. 7 B. 12 C. 32 D. 27 (D) This is a permutation problem. How many unique lists can be made? She has 5 top choices and 5 bottom choices for a total of 25 outfits; she also has 2 dresses. 25 + 2 = 27

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

A. 7,500 cm B. 0.75 cm C. 750 cm D. 75 cm (C) Remember that Centi- means 1/100. 1 m = 100 cm therefore, 7.5 m = 750 cm.

This equation demonstrates which of the following properties? (4 × 7) × 8 = 4 × (7 × 8)(4×7)×8=4×(7×8)

A. The multiplicative inverse property B. The commutative property of multiplication C. The associative property of multiplication D. The distributive property of multiplication (C) Multiplication can be done in any order so the numbers can be associated in any way without changing the outcome.

Miss Osborn gives her class graph paper with the x and y axes labeled. She asks the students to draw a three-sided shape of their choice in one quadrant on the x-y plane. She then asks students to change the sign of each x value and regraph the shape. Which of the following concepts is Miss Osborn working on with her students?

A. dilation B. Reflection C. Traslation D. Rotation (B) Changing the sign of one or both values reflects the shape across the opposite axis.

Students are separating costs of running a concession stand into expenses that depend on sales volume and those that do not. What concept does the teacher want students to understand through this activity?

A. fixed and variable income B. Supply and demand C. Sales tax D. Fixed and variable expenses (D) Fixed and variable expenses are best taught with real-world scenarios. The expenses that depend on sales such as inventory will vary, but expenses such as hourly wages are fixed.

Jason solved the equation 3x-2=13+1x-73x−2=13+1x−7 below: 3x-2-13+1x-7 +2 +2 +2 3x=15+1x-5 3x=10+1x -1x. -1x 2x=10 divide by 2 both sides x=5

What property of equality was misused in Jason's work? A. Multication property of equality B. Division property of equality C. Additive propert of 0 D. Addition property of equality (D) 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.

Chelsea made a quick trip to the store to pick up 6 items. The costs of the items are listed below. What is the range of the prices for this trip? $2.31, $1.97, $2.58, $2.87, $1.54, $2.86

A. $1.54 B. $2.87 C. $0.55 D. $1.33 (D) The range is the difference between the largest and smallest number: 2.87 - 1.54 = 1.33.

Stuart needs to run by the store on his way to school. He begins at home, which on a coordinate plane is represented by the point (0,4). He walks to the store, which is the equivalent of walking 2 units right and 4 units down. After grabbing something to eat for lunch, he walks 3 units to the left and 5 units up to school. What point represents the school?

A. (5, 1) B. (-1, 5) C. (3, 9) D. (3, 1) (B) From (0, 4), he ends up at the store which is at (2, 0). From there, he heads to school which is located at (-1, 5)

Which number is not natural?

A. 0 B. 1 C. 2 D. 3 (A) Natural numbers are whole counting numbers that begin with 1. Zero is not a natural number.

Julian rolled a normal 6-sided die 12 times. His rolls were as follows: 2, 4, 3, 3, 5, 1, 2, 6, 3, 1, 3, 5, 4. What is the probability that he will roll a 3 on the next roll?

A. 1/3 B. 1/6 C. 1/4 D. 1/12 (B) Rolling a die is an independent event meaning that none of the previous rolls affect his next one. There are 6 equal sides so the probability of rolling a 3 is ⅙.

Only a handful of birdseed is left in a birdfeeder. Each time a bird lands on the feeder, one seed randomly falls from the feeder. If the feeder has only 40 sunflower seeds, 65 millet seeds, 60 rye seeds, and 35 corn seeds left, what is the probability that a millet seed will fall next?

A. 7/40 B. 1/5 C. 13/40 D. 3/10 (C) The probability that a millet seed will fall is the number of millet seeds divided by the total number of seeds. The total number of seeds is 200 and there are 65 millet seeds. The probability is: \frac{65}{200} = \frac{13}{40}20065​=4013​.

The scores of the top quartile of students in a math class were 95, 86, 87, 91, 94, and 87 on the last test. What is the average score of these top students?

A. 89 B. 87 C. 90 D. 91 (C) The average is the sum divided by the number of entries: (95 + 86 + 87 + 91 + 94 + 87)/6 = 90.

Which symbol most accurately reflects the relationship between the two numbers below? 5.287 ______________. 5.29

A. > B. ≥ C. = D. < (D) To compare, expand 5.287 into 5 ones + 2 tenths + 87 thousandths. Expand 5.29 into 5 ones + 2 tenths + 90 thousandths. The number 5.29 is greater than 5.287 by 3 thousandths which is 0.003.

During the week, the teacher has students use a ruler to measure various objects. They begin with measuring straight lines and then move on to shapes and 3-D figures. At the end of the week, students are asked to research careers in which the mathematical ideas explored during the week could be used. Which of the following scenarios best demonstrates how the math concept explored in class is applied to a career context?

A. A police officer determining car speed B. A doctor measuring a babies weight C. An accountant calculating the taxes owned by a client D. An architect drawing plans for a new house (D) An architect uses measurements and scale, which mimics the skills learned in class.

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?

A. Ask students to practice skip counting at home with a parent or sibling. B. Practice skip counting daily with a quick video. C. Give students a set of nickels and have them count by fives to find the total value. D. Count students by twos when they are lined up in the hallway. (C) 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.

The fourth-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?

A. Because of the real-world context, the solution must belong to all the set of all natural numbers. Therefore the solution is acceptable. B. Because of the real-world context, the solution must belong to all the set of all natural numbers. Therefore the solution is unacceptable. C. Because this problem requires 20 ⅘ people to ride the bus, the solution is unacceptable. D. Because of the real-world context, the solution must belong to all the set of all rational numbers. Therefore the solution is unacceptable. (B) Natural numbers are whole counting numbers beginning with 1. They are often used in real-world problems. In this problem, 26 people from 4 classes → 104 people equally distributed on 5 buses. However, 104 ÷ 5 = 20 ⅘

Task A: You have 24 meters of fence to build a rectangular area for a garden. How many different sized gardens can you create if each side is a whole number? Task B: The length and width of a rectangle adds up to 20 inches. What is the range of areas that the rectangle can have if each side is a whole number? Both Task A and Task B shown above meet the goal of students exploring the relationship between area and perimeter. Which additional TEKS goal can be met through each of the tasks?

A. Finding multiple solutions B. Providing opportunities to write mathmatically C. Connecting math to real world D. Sparking interest (A) These tasks require students to find multiple solutions in order to reach a correct final answer.

A teacher is introducing a new concept to her class. She explains the concept and then does one example problem. Next, she writes a problem on the board for the students to try. What is the best next step for the teacher to take?

A. Give students the opportunity to discuss their thoughts with a neighbor, then allow them time to formulate and answer. B. Give the students 5 minutes to complete the problem, then collect and grade as a quiz. C. Immediately call on a student at random to work the problem. D. Provide the answer to the questions and ask students for a thumbs up if they agree. (A) t is appropriate to give students time to discuss their thoughts and work through the problem with feedback from peers before giving the answer or discussing the solution.

A teacher has presented adding fractions to her class and they have used manipulatives to gain a basic understanding. What is the next step in the learning process?

A. Give the student's fraction addition problems using numbers instead of manipulatives. B. Give the students problems with one variable to solve. C. Give homework with 10-15 problems to reinforce the concept. D. Give the student's word problems with at least one fraction. (A) This is the next step in the learning process. Students should remain within the same concept but move from concrete to abstract or symbolic representation.

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?

A. Give the students an online quiz with multiple answers B. Have students type a short paragraph explaining how they solved the problem. C. Show students a word problem from an online video that includes both words and pictures. D. Use a website that allows students to record themselves explaining the steps they took to solve the problem. (D) 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.

This equation demonstrates which of the following properties? (4 × 7) × 8 = 4 × (7 × 8)(4×7)×8=4×(7×8)

A. The distributive property of multiplication B. The multiplicitive inverse C. The commutitaive property of multiplication D. The associative property of multiplication (D) Multiplication can be done in any order so the numbers can be associated in any way without changing the outcome.

A first-grade class has been working on analyzing data using a bar graph. The majority of students are able to correctly answer questions related to the graph. What would be an appropriate extension activity for students to complete next to encourage higher-order thinking?

A. Have students work with a partner to come up with their own question that could be answered using the graph. B. Have students start working on line graphs now that they have mastered bar graphs. C. Give students a bar graph with larger numbers as a challenge. D. Give students a homework assignment related to bar graphs. (A) This allows students to think at a higher level because they are generating their own questions about the data.

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?

A. Have students write down what they think is the purpose of decimals and fractions. B. Repeat the lesson until students have committed the lesson to memory. C. Have students complete a pre-instructional worksheet on the topic. D. Highlight examples of decimal and fraction use from the students' lives. (D) 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.

Which culture is credited with developing the use of negative numbers?

A. Hindu- Arebic B. Babalonian C. Chinease D. Roman (C) Chinese culture is credited with using negative numbers first.

A third-grade class has been working on equivalent fractions. The teacher wants to use an "exit ticket" to assess students' understanding of equivalent fractions. Which of the following questions would allow the teacher to assess students' understanding while also encouraging higher-order thinking?

A. If ⅓ of the class is girls, can you draw a picture of what this might look like? B. Which fraction is equivalent to ¼: ⅝, 2/8, or 2/4? C. What is the first step for finding equivalent fractions? D. Is 2/4 equivalent to ⅝? (A) This question asks students to use higher-order thinking skills by applying what they know about equivalent fractions to a real-life scenario. Students will need to think about what a reasonable class size would be, and then use their knowledge of equivalent fractions to determine how many of the students are girls.

A teacher carries around a bag of marbles with 10 of each of the following colors: blue, white, and yellow. She asks students to draw one marble from the bag. Before they draw, they must state the probability of drawing a certain color. The first student says the probability of drawing a blue is 1 out of 3 because 10 out of 30 simplifies to 1:3. The student holds onto his blue marble. The next student says his probability of drawing yellow is 1:3. Evaluate his statement.

A. It is correct because a yellow marble has not been drawn. B. It is correct, however he should have clarified how he reduced the fraction. C. It is incorrect and a common misconception about independent events. D. It is incorrect and a common misconception about dependent events. (D) The correct answer would be 10:29 because one blue marble has been removed. These events are dependent because the second event is affected by the first event.

Mrs. Johnson lets her students choose between two different 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?

A. Problem B is harder than Problem A. B. Problem B is less interesting than Problem A. C. Problem A requires a lower mathematical knowledge. (B) 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.

During a unit on finances, a teacher begins an activity by randomly assigning a job and an hourly wage to each student in class. Which of the following real-life situations is best to help students understand gross income versus net income?

A. Students may purchase bonds. B. Students can choose to invest in the stock market. C. Students can have a portion of the earnings put into savings. D. Students must pay taxes on their earnings. (D) Gross income is the amount made before any deductions; requiring students to pay taxes shows them the difference between gross and net income.

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

A. Students will show what skills they have mastered and what skills still need to be practiced. B. Students will improve processing speeds. C. Students will show their levels of understanding on a unit of study. D. Students will all achieve grade level performance. (A) 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.

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?

A. Summative B. Formative C. Criterion D. Formal (B) 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.

Many students reach an incorrect answer when multiplying two-digit numbers, as shown in the work here. Which of the following is mostly likely the error made by students? 17 x13 321 +170 =491

A. The 20 composed from the multiplication of 3 ones and 7 ones was not carried and therefore caused the error in the final answer. B. The product of 1 ten and 1 ten was recorded as 1 one hundred, but should have been recorded as 1 ten. C. The 4 hundred should have been 5 hundred because the student forgot to carry a ten from the previous column. D. The product of 1 ten and 7 ones was written in the wrong location requiring the student to add a zero to the second row. (A) When 3 and 7 are multiplied, you get 21. This is decomposed to 20 and 1. The 20 needs to be carried, but the student did not write the 2 above the 1 in 17, causing an additional error.

Ginny and Carter are learning about probability and their teacher hands them a bag with 18 red marbles and 10 green marbles. Ginny draws 2 red marbles and keeps them on her desk. Carter wants to draw green marbles on his turn. How did the probability of drawing a green marble change from when Ginny drew her marbles to when Carter will draw?

A. The probability of drawing a green marble increased B. The probability of drawing a green marble decreased C. The probability of drawing a green marble did not change because the number of green marbles did not change. D. The probability of drawing a green marble did not change because the total number of marbles was not affected. (A) Since 2 red marbles have been removed, there is now a higher chance of a green marble being drawn. The probability changed from 10/28 or 36% to 10/26 or 38%, which is an increase.

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?

A. The student added the numbers first, then rounded the answer. B. The student rounded to the nearest hundred instead of the nearest ten. C. The student rounded all three numbers up. D. The student rounded all three numbers down. (A) 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.

Student work is shown below. Step 1: 6x-8=10x+46x−8=10x+4 Step 2: -8=4x+4−8=4x+4 Step 3: -12=4x−12=4x Step 4: -3=x−3=x What property could be used to justify the student work from Step 1 to Step 2?

A. Transitive property of equality B. Multiplication property of equality C. Addition property of equality D. Associative property of addition (C) The addition property of equality states that if you add the same number to both sides of an equation, then the equation stays balanced. Step 2 is obtained by adding -6x−6x to each side.

Jamie deposits $245 into her health club account at the beginning of the year. Each time she visits, $7 is deducted from her account. Which equation represents VV, the value in her account after xx visits?

A. V=245−7x B. V=245+7xV=245+7x C. V=245x-7V=245x−7 D. V=7x-245V=7x−245 (A) The $245 represents the y-intercept or starting point and $7 represents the slope. Here $7 is deducted from the account for each visit (xx), so the 7x7x is subtracted from the $245.

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?

A. What would you estimate the width of your desk to be? What would you estimate the height of your locker to be? B. Which is longer: one foot or one yard? C. What unit would you use to measure your pencil? D. How many inches are in a foot? How many feet are in a yard? (c) his 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.

Mrs. Spisak's goal in this lesson is to have her students use calculators to develop financial literacy. Which of the following activities best addresses this goal?

A. Write out fractions on paper with the amount of a monthly bill on top and monthly income on the bottom, which students then put in simplest form. B. Have students calculate sales tax and discounts on grocery store items. C. Give students a checkbook register and have a race to see how fast they can find the balance. D. Multiply a monthly salary by 12 using pencil and paper for an annual budget. (B) This gives students real world practice using a calculator for financial literacy.

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?

A. [3(n-4)]2 B. 3(n-4)2 C. 3(n2-16) D. 32(n-4)2 (B) The key steps are #3 and #4. Only (n-4) is squared and then multiplied by 3.

In which of the following situations is estimation least appropriate?

A. a meteorologist talking about the probability for rain tomorrow B. a father talking about the size of the fish he caught and released that morning at the lake C. a mother giving medication to her child with a cough D. a sports announcer reporting on the number of people expected to attend a playoff game (C) medicine should be given in the exact measurements

A second-grade class has created a pictograph of what type of shoe each person is wearing. What is the next visual representation students can make from the information given?

A. bargraph B. Circle graph C. a stem- and leaf plot D. A line graph (bar grap) A bar graph can easily be created from a pictograph and mimics the same shape. This is scaffolded for the children to learn how to create a bar graph.

Mrs. Wilhelm is teaching a lesson on surface area. Every time a student raises their hand to answer, Mrs. Wilhelm addresses them by name and says that she appreciates how they participate in class. She also offers small candies for challenge questions. Which learning theory best matches Mrs. Wilhelm's teaching method?

A. behaviorism learning theory B. social learning theory C. constructivist learning theory D. sociocultural learning theory (A) Behaviorism involves the teacher conditioning students to use the expected behavior in class. Mrs. Wilhelm is conditioning the students to participate with encouragement and positive reinforcement.

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

A. coloring in 100-blocks to represent percent B. using a variety of methods and scenarios to determine percentage C. comparing percentages from their test scores throughout the year D. writing percentages from decimal or fraction conversions (B) Presenting percentages in a variety of real-world scenarios helps students to review and fully grasp the concept as they practice using them.

A second-grade teacher is introducing the idea of adding different kinds of coins. Which would be the most effective beginning activity?

A. demonstrating how to add a nickel and a dime B. identifying a coin as a penny or not C. having the students use coins to represent a problem D. providing the problem using numbers and words (C) Since the students are just learning a skill for the first time, they are in the concrete learning progression stage and should use manipulatives.

A first-grade teacher is reviewing expanded form with her students and is using the number 74 as an example. She explains to students that since the value of the 7 is actually 70, the expanded form of 74 is 70 + 4. She notices that several students seem confused. What step could she take to improve students' understanding of expanded form?

A. having students model 74 using base ten blocks and asking them what the 7 tens are worth B. asking students to add 70 + 4 to see that it equals 74 C. playing an online interactive game that allows students to practice several examples of expanded form D. using an anchor chart or visual aid that shows the steps to writing a number in expanded form (A) using base ten blocks will allow students to visualize and understand that 7 tens is worth 70, which will deepen their understanding of the actual process of writing numbers in expanded form.

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

A. making cash available on short notice B. charging high interest rates C. supporting local economies in depressed cities D. increasing the credit scores of low-rated borrowers (B) 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.

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?

A. mnemonic device B. use of manipulatives C. reduced answer choices D. math drills (A) Teaching the student to use a mnemonic device such as "PEMDAS" will help the student to recall which operations to solve first.

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?

A. numberline B. an array C. fraction strip D. a drawing of 4 items with 4 of them shaded in (B) Arrays are used to represent multiplication or division problems, not as a way to represent fractions.

According to the TEKS, which of the following is a developmentally appropriate activity for an average sixth grader to establish number sense?

A. placing positive and negative numbers on a number line B. graphing an ordered pair on the coordinate plane where x and y are both positive C. multiplying 2- and 3-digit numbers together D. using positive and negative numbers to represent financial situations (D) Students in sixth grade should be able to use positive and negative numbers in real-world scenarios such as money owed or money earned.

Ms. Yu brings several apples of different sizes to her third-grade class and asks each student to cut a piece of string to a length they think would wrap around the apple without overlapping. The students then measure their string length with a ruler and record their answers. Finally, students discuss the data they recorded and compare their predictions. What skill is the teacher introducing to the students with this activity?

A. relating the circumference of a circle to its radius B. applying relationships among similar figures to analyze how changes in scale affect area and volume C. estimating measurements and evaluating the reasonableness of the solution D. using concrete objects and pictorial models to create linear equations (C) The students are estimating the circumference of the apple and then comparing their results for reasonableness.

A teacher is planning a formative assessment to determine how well his students can differentiate between the concepts of area and volume. Which of the following formative assessments would be the most appropriate for this topic?

A. sorting drawings of shapes into area and volume categories B. writing a short essay describing areas and volumes in daily life C. calculating the areas and volumes of figures D. defining area and volume (A) Sorting drawings of different shapes according to area and volume will show whether students can differentiate between the two concepts. This assessment will be quick to perform and quick for the teacher to grade.

Ms. Valerie is teaching a unit on percentage and sets up a mock store in her classroom where all of the items are marked on sale. She marks each item with a discount of 15% off, 20% off, or 30% off and establishes a tax rate of 7%. Ms. Valerie then has each student choose three items and calculate the final price, including the discount and taxes. The teacher most likely planned this activity to demonstrate her understanding of how to do which of the following?

A. use visual media such as graphs, tables, diagrams, and animations to communicate mathematical information B.use questioning strategies to promote mathematical discourse in the classroom C. apply mathematics to real life and a variety of professions D. assist learning through the use of technological tools and mathematics manipulatives (C) Ms. Valerie's lesson shows students how to apply percentages to real life in the sales profession.

Anthony sold x boxes of popcorn for $6.00 per box for his Cub Scout troop. Which expression will help him determine the amount of money he earned for his troop?

A. x/6 B. x + 6 C. x - 6 D. 6x (D) He needs to multiply the number of boxes by the cost of each box to determine the total earned.

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

A. y = x + 2 B y = x2 C.y = 2x D. y = -x (B) This equation works for all sets of numbers. 1 = (-1)2 = 1 0 = (0)2 = 0 4 = (2)2 = 4

A teacher writes the problem shown below on the board for a warm-up. 7x + 4 - 3x + 2 = 127x+4−3x+2=12 She asks students to combine like terms as the first step in solving the problem. Which equation demonstrates an understanding of the first step?

A.4x−2=12 B. 10x + 2 = 1210x+2=12 C. x = 2x=2 D. 4x + 6 = 124x+6=12 (D) This correctly combines like terms, which should always be the first step.

Which of the following activities would best allow a teacher to demonstrate an appreciation for cultural diversity in a math class?

A.Comparing donations made to the Red Cross by different minority groups B. Graphing the Debts of of countries to the United States C. Discuss the average wage and cost of living for cities around the world D. Incourage students to donate towards international relief efforts in foreign countries (C) This allows students to discuss different things about a variety of cultures without it being competitive.

Students in Mrs. Wilson's class have mastered multiplication and have been introduced to division. Mrs. Wilson gave a test over introductory concepts in division and found that a number of students struggled. Which of the following strategies is best to help improve the students' understanding of division?

A.Use manipulatives to model division and connect it to multiplication. B. Teach that multiplication and division are opposites, and have students memorize times tables to make division easier. C. Provide a new study guide with division problems and give a new test again in two days. D. Separate the class into groups and have at least one student that understands division in each group. The higher-level students can reteach the struggling students the concept through peer tutoring. (A) Using manipulatives is the first stage of understanding in mathematics. Starting here allows the teacher to identify any misunderstandings before moving on and allows students to connect prior learning.

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:

A.formal non-standard measurement. B. informal non-standard measurement. C. informal standard measurement. D. formal standard measurement. (B) 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