EC-6 Practice Questions 2
Sam and Jody are learning about money in their third-grade class. Sam tosses four coins on the table. What is the probability that all four coins will land on heads?
1 / 16 There are four coins and each has two sides, so there are 2 possible outcomes for each coin. To calculate the number of possible outcomes: 2 X 2 X 2 X 2 (or 2^4) = 16.
What is the probability that a couple's first or second child will be a boy?
1 / 2 The probability of couple's first child being a boy and the second child being a girl is ¼. The probability of the couple's first child being a girl and the second child being a boy is ¼ also. The probability that a couple's first or second child will be a boy is calculated by adding the two fractions together (¼ + ¼ = ½).
Given two even integers, a and b, determine what could be the least common multiple (LCM)?
(ab) ⁄ 2
The phrase "add the two like terms and keep the sign of the largest" is a step in the algorithm of calculating ______________________.
- ax + bx
Find -9^0.
-1
What is the probability that both a couple's last two children will be
1 / 4
What is the probability that both a couple's first two children will be boys?
1 / 4 The probability of the first child being a boy is ½. The probability of the second child being a boy is ½ as well. Multiply these two together to calculate the correct answer (½ x ½ = ¼).
Which of the following expresses the commutativity of -3^0 + ( a + 4 ) = ?
-3^0 + ( 4 + a )
How many natural numbers lie between the numbers 3^0 and 7^0?
0 Both equal 0 so no numbers lie between them.
At Leslie's beauty shop, she has found that a customer will want a color with a probability of 0.53, a haircut with a probability of 0.4, and both with a probability of 0.17. What is the probability that a customer will require a color and not a hair cut?
0.36 0.17 is included in the 0.53 so subtract 0.53 - 0.17 = 0.36
What is the probability of getting at least two tails in tossing three coins?
0.5
Which choice is a real number?
0^1 0 raised to any non-zero real number is 1.
The least common factor of any two numbers is...
1
What is the solution, if any, to the expression: 1n = ?
1 1 raised to any power is always 1.
Which of the following is not a prime number?
1 The number one is neither a composite number nor a prime number.
Carolyn wants to purchase a lot in Canada to build a house. She finds a lot that is 0.25 km2 with a creek running through the back of it. She wants to tell her family about her findings who live in New York. She needs to be able to convert the 0.25 km2 to ft2. Convert 0.25 km2 to ft2 using (1 square foot = 0.09 square meters).
2,777,778 square feet
Which is a factor of 125?
25
Arrange the following from smallest to largest. 14 inches, 1 foot, 0.4 yard, 15 cm
15 cm, 1 foot, 14 inches, 0.4 yard
Find 1^3 * 1 + 2 ^3 * 2
17
What is the greatest common divisor (GCD) of the following numbers? 630 and 36
18
What is the multiplicative inverse of 0.5?
2 multiplicative inverses are reciprocals of each other. 0.5 = 1/2 the reciprocal is 2/1 or 2
Which of the following is an example of the additive inverse element?
3 + (-3) = 0 A number added to the original number resulting in a sum of 0.
In converting 5 in3 to cm3 using the basic unit of (1 in = 2.54 cm), how many times should 5 be multiplied by 2.54.
3 times A good way to think about this conversion is to break the cubed inches into factors of inches. 5in X in X in = _______cm3 1 1 1 Notice how it will take 3 units of (1 inch = 2.54 cm) to cancel the three units of an inch in the numerator. 5in X in X in X 2.54cm X 2.54cm X 2.54cm = _______cm3 1 1 1 1in 1in 1in
What is the missing number? 4, 12, 36, 108, _____, 972
324 4 x 3 = 12 12 x 3 = 36 36 x 3 = 108 108 x 3 = 324 <= Answer 324 x 3 = 972
Christmas gift giving for a family of 15 is typically handled where each family member brings a gift with no name tag. Two labels are made for each number of 1-15. One label is folded and put in a hat, while the other label is taped to one of the gifts. Each family member draws a number from the hat. They receive the corresponding numbered gift. How many different ways are possible among the first 5 people who draw
360,360 Use permutation to find the answer.
Three times the width of a rectangle plus five is the same as seven more than four times the width. If W is used to represent the width of the rectangle, which of the following expresses this relationship?
3w + 5 = 4w+ 7
If an investment is compounded monthly, the rate (r) is divided by 12 (the n in this formula). Also, for an investment compounded semiannually, the rate is divided by 2. What would the rate be divided by if the investment was compounded quarterly?
4
Express 4 3/8 as a decimal number.
4.375 Answer B is correct. Find 3 ÷ 8 = 0.375. Add this to the whole number 4 as it is in the original problem
Express 4 3⁄8 as a decimal number.
4.375 3 / 8 = .375 .375 + 4 = 4.375
A recent survey reveals that 40% of young people between 15 and 25 years of age will buy an iPod this year. Of those who buy iPods 35% enjoy listening to country music. If N is the number of young people between 15 and 25 how many people between 15 and 25 this year will enjoy listening to country music on their iPods?
40% x 35% = .14N .40 x .35 = .1400
Which of the following approaches and initiatives used by a math teacher will best assist with planning, delivery, and reevaluating instruction to ensure that every student is learning sound and significant mathematics and is developing a positive disposition toward mathematics?
Observing, listening to and gathering other information about the students to assess what they are learning.
Is the graph of a circle a function? Describe why or why not.
No. It does not pass the vertical line test.
Is the graph of a circle a function? Describe why or why not.
No. It does not pass the vertical line test. Answer B is correct. There are multiple vertical lines that can be drawn over the graph that will touch the graph in more than one place (two places to be exact), so the graph is not a function.
having young children place similar shapes in columns is laying the foundation for which of the following?
bar graphs
Which set(s) does the number 3 belong to?
whole numbers integers rational numbers
proper way to denote multiplication?
xy 9x (a)(b) NOT x9
If 3y + 4x = 12, then what is the value of y in terms of x?
y = (12 - 4x) / 3
Since the area of a rectangle is A = L X W, what is the area of a triangle?
(LW) ⁄ 2
A shirt costs $49.99 plus 8.25% sales tax. What is the total cost of the shirt?
$54.11 To convert percent to decimal move the decimal two places to the left and drop the percentage sign. So, the decimal form of 8.25% is 0.0825. Multiple the cost of the product by the decimal representation of the percent: 49.99 X 0.0825=4.12. The tax for the shirt is $4.12. Add the tax and the cost of the shirt: 4.12 + 49.99=54.11. The total cost of the shirt is $54.11.
A store is having an end-of-the-year computer sale. What is the total cost of a discounted computer system (i.e., computer, monitor, and printer)?
(1) First you need to know the amount that is being discounted off the regular price for each of the items. (2) Next, you need to subtract the discounts from the regular prices to know the discounted sale price for each item. (3) Add the results of step (2) to calculate the total cost of the discounted computer system. Percentage Decimal format 33.3 % = .333 25% = .25 20% = .20 Computer: .333 x $1800.00 = $599.40 → 1,800 - 599.40 = 1200.60 Monitor: .25 x $360.00 = $90.00 → 360.00 - 90.00 = 270.00 Printer: .20 x $100.00 = $20.00 → 100.00 - 20.00 = 80.00 Total Cost: $1,550.60
area of a triangle
1/2 bh
What is the probability that both a couple's last two children will be girls?
1/4
A popcorn company needs to have a new side label printed for their large popcorn holiday can. The side label will cover the entire surface area of the cylinder part from top to bottom. The diameter of the can is 16 inches and the height is 20 in. How much area does the new label cover?
1005.31 in2 Given the diameter is 16, the radius is half of that. The circumference is C = 2πR = 2πR(8) = 50.265. The surface area is the product of the circumference and the height: 50.2655 X 20 = 1005.31 in2.
Jill's current salary is $53,241. She learns the school board has approved a 5% raise for the coming school year. Which is a method that Jill can use to determine her new salary?
105% x 53241 1 / 53241 = 1.05 / x 53241 + (.05)(53241)
What is the probability of being dealt 4 hearts from a standard 52-card deck if only 4 cards are to be dealt?
11 / 4165
Tymon is building a bookshelf. He has the entire outside completed. He must purchase wood to make the 5 shelves. Each shelf needs to be 26 3/4 inches long. He can purchase wood up to 16 feet long. He needs to allow 1/8 in for each saw cut, how many feet of wood does he need?
11 3/16
Walter looks forward to Fridays because his teacher plays his favorite math game during the math period. She gives the class a number, and the students write an expression to equal that number. The object is to use some unusual methods to calculate the number because the class wants to get as many different answers as possible. Today the teacher gives the number 24. Which of the following is the correct expression to equal 24?
60 ÷ 3 + 6 - 2 * (-1^0 )
An individual from Texas is interested in purchasing land in Canada. The realtor informs him that there is a piece of land that is 1.8 km2. The individual is lost as to the size of the piece of land. He needs to be able to convert the 1.8 km2 to square miles. Convert 1.8 km2 to square miles for the Texan (using 1 square mile = 2.6 square kilometers).
A good way to convert between units is to follow this example. 1.8km2 * 1 = ________mi2 1 Replace the 1 with a unit fraction (or fractions) that will give the units you need. So in this case 1 mi2 = 2.6 km2 and we need the km2 units in the denominator of the fraction to cancel the km2 in 1.8 km2. 1.8km2 * 1mi2 = _________mi2 1 2.6km2 Notice how the km2 units cancel now. Replace the 1 with a unit fraction (or fractions) that will give the units you need. So in this case 1 mi2 = 2.6 km2 and we need the km2 units in the denominator of the fraction to cancel the km2 in 1.8 km2. 1.8km2 * 1mi2 = _________mi2 1 2.6km2 Simply divide 1.8 by 2.6 to get 0.69.
Students in the second grade class at Lovett Elementary are exploring properties of U.S. coins and bills. The teacher knows to help students make clear connections with the play money in class and real money they would use at a store that the lessons and activities need to be applicable to a real world situation. Which of the following situations would be the most applicable for the students? A. For students to shop in the "class store" and count out the money needed to make the pretend purchases B. For the teacher to assign the students to go to the grocery store and buy three items to bring back to a class store C. For the students to write down the cost of three items then add them to find the total cost of the three items D. For students to solve problems with money on a worksheet
A. For students to shop in the "class store" and count out the money needed to make the pretend purchases The use of play money gives students a concrete example of the coins. This hands-on experience with money allows the students to explore with the value of coins and bills. Shopping in a class store provides the students a real world experience in a controlled environment.
The 1st grade students, including ELL students, at Rice Elementary will be assessed over their understanding of U.S. coins and the value of each coin. During class instruction, all students were able to concretely work with play money to make connections with coins and values. The teacher must determine the best way to assess students over the values of the U.S. coins. Which would be an appropriate method to do so?
A. Provide pictures of each U.S. coin and have students match the picture with the value of the coin. Answer A is correct. English-language learners may particularly need modifications with mathematics assessments and instruction. Teachers should have visual models of strategies and structures used with related mathematics vocabulary identified.
First graders are applying skip counting as they count to 100. The teacher wants to explore common items for the students to use with skip counting. For skip counting by 5s, the teacher will have the students trace their hands and number their fingers then glue the hands on a large poster board to display the number of hands with five fingers it would take to reach 100. What are some things the teacher could use to teach skip counting by 2s?
A. Socks, shoes, feet Answer A is correct. Each of these examples (socks, shoes, feet) come in pairs or groups of two. By using concrete everyday objects which students use, the concept becomes more personal for the students to think through how to count by 2s and to see that it is really just counting in pairs.
A teacher has students working in groups of three to solve the following equation. She provides each group with two quarters, two dimes, and two nickels. Also, she explains that negative amounts would mean you owe the amount. -0.25 + ? = -0.15 The teacher is trying to get students to understand the concept of _________________.
Adding a positive and negative.
In the slope-intercept form of the equation of a line (y = mx + b), the m represents the slope of the line and the b represents the y-intercept. What does the x and y represent?
An infinite number of ordered pairs on the line.
Students in a fourth-grade class are working with geoboards. Each geoboard has a grid drawn on it and a peg at each intersection of the grid. Students stretch rubber bands around the pegs to create shapes. The teacher shows the student how to add the squares and fractions of squares enclosed by the rubber band to count the total number of squares within the triangle. This activity would best promote the student's understanding of which of the following geometry concepts?
Area
The students in a kindergarten class will vote between the zoo and the space center for the destination of their next field trip. The teacher has placed two bowls at the front of the room and given each student one marble to place in the bowl with the label of the destination he or she will choose. Students may only vote once. Which TEK would be best supported by this activity? A. use data to create real-object and picture graphs. B. collect, sort, and organize data into two or three categories C. draw conclusions from real-object and picture graphs D. compare two objects with a common measurable attribute
B. collect, sort, and organize data into two or three categories In this activity, the students are actively participating in the collecting, sorting and organizing data by placing their marbles in the bowl of their destination choice.
Third grade students will be learning about fractions to the ¼, 1/3, ½, 2/3, ¾, and whole. The teacher knows to use concrete objects to teach mathematical concepts is best practices for the students. In order to teach the fraction concept, which common tools would be best for the teacher to use to demonstrate fractions with items found in the classroom?
B. ruler, clock, counters Answer B is correct. Rulers can be used to show parts of a whole and fractional parts in fourths, eighths, and sixteenths. Clocks can be used to show fractional parts in fourths by quarter of the hour, half hour, etc. Counters can be used to show parts of a set and set models.
The teacher is gathering data on the students from the past three assessments given in her class. In order to analyze and draw conclusions on the data in the most efficient manner, the teacher has decided it would be best to plot the assessment scores for each student to determine the probability with which the students will pass future assessments. In looking for patterns and relationships within the data, for which variables will the teacher be looking? A. Patterns in each student's class attendance B. Patterns of increasing assessment grades C. Patterns in assessment grades over time and within similar concepts D. Patterns in similarity of concepts and how often a student studies
C. Patterns in assessment grades over time and within similar concepts Tracking data for assessment grades over time and within similar concepts will show the teacher if the student is performing better within those concepts, staying stagnant or decreasing in ability to answer questions correctly. The data can also show the teacher where the student needs extra help and more practice.
A $900 washer/dryer pair is on sale for 20% off. The department store offers a one day special on Memorial Day: take an additional 15% off. The application of which algebraic formula is needed to solve this common retail scenario?
Composition of functions
Which property is used in answering the following problem? Given the area of this rectangle is 56 in2, write the equation to solve for x.
Distributive property
Given the task of computing two consecutive even numbers whose sum is 50. Let x represent one number. Determine the choice below that should represent the second number.
Either (x+2) or (x-2)
Students normally receive either a 0 or 100 for an attendance grade each day based on whether they are present or not. This particular day the teacher decides to give the students a quiz after a lesson has been presented and all students who take the quiz receive a grade of 100 for participation that day. The teacher plans to look at the quizzes to determine the level of comprehension of the topics taught that day, mark corrections, hand back the quizzes to the students the next day, and adjust the contents taught the next day based on the results. What type of assessment techniques is the teacher utilizing?
Formative
A teacher decides to assign students a project where they will develop an amortization schedule of a purchase so they can apply a lesson using the future value formula and observe the details line by line as payments are made. What would be the best approach in assigning a purchase?
Have the class research products online such as stereos, game stations, and etc, and choose an item they would like to purchase Students can take ownership of the project and begin to understand how much extra the interest will cost them if they are to purchase the item they want on credit. English Language Learners could even research a product from their previous location.
How to find number of steps in a pattern.
In this pattern the order of the numbers that represent total cubes is ascending (getting larger in value) by increments of numbers that represent the steps. Following this pattern, it will take a total of 21 blocks to build 6 steps. Number of cubes: 1, 1+2=3 3+3=6 6+4=10 10+5=15 15+6=21 For Steps: 1, 2, 3, 4, 5, 6,
A third-grade class is using plaster of Paris to make impressions of their hands. Each student needs 12 ounces of plaster to make an impression of their hands. There are a total of 20 students in the class. How many pounds of plaster will the teacher need for the activity?
It takes 12 ounces of plaster per impression. Since there are 20 students, then it will take 20 * 12 = 240 ounces of plaster to make all the impressions. The answer choices are all given in pounds (lb) not ounces (oz). The next step is to convert 240 ounces to pounds. Using the conversion that 1 pound is equivalent to 16 ounces: 1 lb = 16 oz Convert ounces to pounds dividing 240 oz by 16 oz. 240 / 16 = 15 lb.
Mr. Grant wants his fourth-grade math students to learn to work collaboratively, to discuss alternative approaches to solving tasks, and to justify their solutions. Students are grouped in pairs and Mr. Grant gives his students the following task: Express the ratios below in the lowest forms: 15/25, 18/6, 9/36, 18/15 Which of the following best describes the level of student engagement expected with the given task?
It will not engage students in high level forms of thinking. This is a low-level task. It is not a cognitively challenging task that has the potential to engage students in complex forms of thinking if the goal is to increase students' ability to think, reason and solve problems. The task does not match with the teacher's goal for student learning.
Word problem: Troy and Walter are neighbors. They both have mowed their grass today. Troy mows his grass every 3 days. Walter mows his grass every 5 days. How many days will it be before they both mow their grass on the same day? Based on the word problem, the lesson will most likely cover which of the following?
Least common multiple
Students learning to solve for missing values through input/output tables which increase the output (or y value) by the same value are laying a foundation to be able to work with which kind of function as they mature in their mathematical knowledge?
Linear Functions Answer D is correct. As the x value changes, if the y value always changes by the same value, you are working with a linear function. The correct answer is D.
E T V D Students are classifying the letters of the alphabet according to the type of symmetry they have. Which of the following letters has the same kind of symmetry as the letters shown above?
M
In order to develop, justify and use conversions within a measurement system, the teacher will arrange the classroom in collaborative grouping so students are able to practice measuring mass then converting it within the system. Which measurement system will the students be working with in this collaborative setting?
Metric system Answer C is correct. Mass is measured in grams and kilograms, both of which are metric units of measurement. Mass is also measured on a different scale than weight, which is part of the U. S. customary system.
Average daily temperatures are most likely calculated using which method of central tendency?
Midrange Because the temperature fluctuates so much through the day, taking the average of the lowest and highest temperature for the day is the easiest method.
The probability of the union of any two events is the following. P(AÈ B) = P(A) +P (B) - P(AÇB) If A and B are mutually exclusive, determine the probability of a union of two events.
P(AÈ B) = P(A) + P(B) In the probability of a union of two events, there is a subset of two events that overlap and a subset of two events that do not overlap. In the group that overlaps, there is the need to subtract the intersection because it is included in the sum of the individual probabilities. In the group that is mutually exclusive (or does not overlap), there is not a need to subtract a non-exist intersection.
Which method below does not define a function?
Passes the horizontal line test.
Which methods define a function?
Passes the vertical line test. A correspondence assigning only one range value to each domain value. A set of ordered pairs where the first component is never repeated.
Three students are playing a game using the spinner above. Each student draws three boxes on a piece of paper. The spinner is spun, and each student writes the number in any one of the three boxes. The spinner is spun two more times, and each time the students write the number in a remaining empty box. The students then compare numbers, and whoever has the largest three-digit number wins the game. This game would be particularly useful in helping students' understanding of:
Place value. Place value refers to the value of a digit as determined by its position in a number. Practice of this activity enables students to explain that the value of a number increases when digits farthest to the left have greatest value.
The product of two rational numbers can belong to which of the following combinations of sets of numbers?
Rational numbers, integers, whole numbers, and natural numbers
The teacher tells the class to put the following numbers in order from smallest to largest. 8 -3.5 9⁄2 π 2.1 2.03 √ 2 Based on the exercise the teacher has given, the exercise is most likely trying to assess which of the following number concepts.
Relative magnitude
Alex makes the target board shown above and places it on the floor. Alex makes a conjecture that is possible to obtain any score from 0 to 15 by dropping exactly three coins on the board, assuming all the coins land somewhere inside the square. Which of the following statements best evaluates Alex's conjecture?
The conjecture is invalid, since it is impossible to obtain a score of 12 or 14. A conjecture is a mathematical statement which appears likely to be true, but has not been formally proven to be true. Investigating this conjecture further proves it to be invalid since it is impossible to obtain a score of 12 or 14: If all three coins fall inside the 3-point circle then the score is a 9. If, in another attempt, two of the coins fall inside the 5-point circle then 10 is the preliminary score. If the third coin falls inside the 3-point circle then the final score is 10+3 =13. If, on the other hand, the coin falls inside the 1-point circle then the final score is 10+1 =11. It is impossible to obtain a score of 12. The same argument can be made for a score of 14. The conjecture is invalid.
Given the assignment of converting 215oF to Celsius, a 6th grader comes up with an answer of 101.7oC. Evaluate the reasonableness of converting 215oF to 101.7oC.
Since the boiling point in Fahrenheit is 212o and the boiling point in Celsius is 100o, the answer seems reasonable.
Calculators, base-ten blocks, attribute blocks and cubes are some of the manipulatives a math teacher has available to teach several mathematical concepts to his class. Attribute blocks is a type of manipulative most effectively used to teach which of the following sets of concepts?
Sorting, classification, investigation of size, shape, color, logical reasoning, sequencing, patterns, symmetry, similarity, congruence, thinking skills, geometry, organization of data.
Base-ten blocks, attribute blocks, Cuisenaire rods and cubes are some of the manipulatives a math teacher has available to teach several mathematical concepts to his class. Cuisenaire rods is a type of manipulative most effectively used to teach which of the following concepts?
Sorting, ordering, counting, number concepts, comparisons, fractions, ratio, proportion, place value, patterns, even and odd numbers.
The teacher uses the smart board in his classroom to access a website with a large hill. He asks students, "What information would we need to know in order to be able to calculate the approximate distance of climbing to the top of the hill?" The teacher used ___________________ to assist students in developing, comprehending and applying mathematical concepts.
Technological Tools
Find the sum of the following: 2/9 + 1/4 + 1/6
The Least Common Denominator (LCD) is 36. 2/9 + 1/4 + 1/6 = 8/36 + 9/36 + 6/36 = 23/36 The key to finding the right answer here is in understanding that it is necessary to find the LCD and how to do that. The LCD is basically a number that is divisible by all three denominators. In this case 36 is the lowest number that is divisible by 9, 4, and 6. Finding the Lowest Common Denominator (LCD) is important because fractions cannot be compared or added/subtracted unless you have the same size and same number of parts in one whole. Circles divided into mini parts, four parts and six parts, can all be divided into 36 equal parts for comparison.
Which basic operation(s) has commutativity?
addition
Use the information below to answer the question that follows. Mark has been employed by the school district for 11 years. This year the school board approved a raise for faculty and staff. Mark's semi-monthly gross pay increased from $2,541.79 to $2,654.65. His net pay increased from $1,589.67 to $1,659.58. Mark's deductions include health insurance, life insurance, TRS, Medicare, taxes, a 3% deduction for stock, and etc. He notices that his health insurance and life insurance combined have increased about $16.00 from last year and both of these deductions are tax exempt. The other deductions that have changed are based on a percentage of his salary. Mark has the opportunity each month to work a few extra hours with detention, bus, or cafeteria duties. Mark wants to determine what percentage he will actually bring home of his extra earnings doing these odd duties. Which of the following is the best estimate Mark will bring home of any extra earning based on the information gathered from his pay increase this year provided he does not move into a higher tax bracket.
The difference in gross pay is $112.86. The difference in net pay is $69.91. Add the insurance deduction of $16 back to the $69.91, because this amount is deducted only one time will not effect future deductions when extra money is earned. The percentage of net pay is 85.91/112.86 = .76 or 76%.
What graphing technique is used to describe the difference in the graphs of y = x2 and y = -x2 ?
The graphs are reflected across the x-axis forming the mirror image of the other across a line.
Samantha works at a clothing store where she receives an employee discount of 20% on all clothing items. She wants to buy a sweater that usually sells for $90, but is on sale for 25% off. How much will the sweater cost Samantha if she applies both the 25% off sale price and her 20% employee discount?
The key to solving this problem is to remember that the entire price of the sweater is represented by 100%, so a 25% reduction leaves 75% and a 20% reduction leaves 80%. So, 100%-25% = 75%, and 75% of $90 = (.75)(90) = $67.50. Then, 100%-20% = 80%, and 80% of $67.50 = (.80)(67.50) = $54.00.
The teacher is introducing comparing whole numbers in terms of greater than and less than. The teacher brings to class ads from two different grocery stores. The teacher instructs the students to find three items that appear in each ad and compare their prices. What mathematical comparative language should the students use to compare prices?
The oranges at store A are less expensive than the oranges at store B. Answer D is correct. The formal mathematical language indicates to use the expressions of less than and greater than when comparing real numbers, whole numbers and fractions. The correct answer is D.
The width and length of a rectangle are whole numbers different from zero. Which of the following statements about the rectangle must always be true?
The perimeter is an even number. If the length and the width of a rectangle are whole numbers different from zero then the perimeter is an even number because the perimeter is the distance around an object.
Mary wants to put new floor covering in her living room. The room is 14ft x 15ft. She is debating whether to put carpet back in the room or put hardwood flooring in the room. The carpet she likes is $25.95/yd2. The hardwood floor she likes is $12.95/ft2. What is the total difference in price of the new carpet and the hardwood flooring including tax of 8.25%?
The room has 210ft2 (14ft x 15ft) or 23.3yd2 (210 / 9). The price of the carpet is $655.45 (23.3 x 25.95 x 1.0825). The price of the hardwood floor is $2,943.86 (210b x 12.95 x .0825). The difference is $2,288.41.
least common multiple
The smallest number that both numbers will divide into without a remainder There is no such greatest common multiple.
2(x + 2) = 2x + 4 from a rectangle made of algebra tiles
The width of the rectangle is 2 and the length is (x + 2). The area is 2x + 4.
Which could be used to find two consecutive even numbers whose sum is 80?
There is not a solution. Because 80 is the sum of doubles (40+40) there is not two consecutive even numbers that will equal 80.
Which choice best describes an explanation a teacher could give a student to help him/her judge the reasonableness of the solution in the following scenario. Evaluate: -7 - 12 The student gives an answer of 5.
Think of your checking account being overdrawn by $7 and you write another check for $12. How much would be in your checking account?
Mrs. Wilson is preparing her 4th graders for Mathematic TEKS. Four math problems similar to the one shown below fill up the blackboard. The cost of a sweater at Sears was $75.00. At the Back-to-School sale it was marked $13.50 off of the original price. What was the price of the sweater during the sale? Explain the process you used to find the sale price. A first-year math teacher visiting Mrs. Wilson's classroom quickly observes the tasks have "real world" context, require an explanation, involve multiple-steps, are "text-like" but require no manipulatives and show no connection to meaning. Which of the following best describe the reason Mrs. Wilson most likely chose the tasks for her students?
To increase students' speed and accuracy in solving problems. Not all tasks used by a teacher may engage students in a cognitively demanding activity. If the goal is to increase students' speed and accuracy in solving routine problems, then tasks that focus on procedures without connections to understanding, meaning or concepts may be appropriate. Use of these types of tasks may improve student performance on tests that consist of low-level items and may lead to greater efficiency of time and effort in solving routine aspects of problems that are embedded in more complex tasks.
Using the Present Value Formula, students have calculated a house payment for a loan set up on an annuity. The principal is $127,000 and the monthly payments are $583.56. The students want to know how much interest over the period of the note (30 years) will accrue. They decide the first step is to calculate the total amount to be invested in the house. For this, they determine the following equation should be used. Payment amount x Number of payments = Total amount invested What should the next step of the algorithm be?
Total amount invested - Principal
How long will it take for money to double in a savings account that is compounded continuously at 3.5% interest?
Using the formula A = Pert. A = Pert 2P = Pe .035t Let A = 2P and r = .035 2 = e.035t Divide by P Ln 2 = .035t Take the logarithms on both sides In 2 / .035 = t 19.8 = t
The teacher helps a student draw a horizontal line 3 inches with a straightedge and a perpendicular line 2 inches connecting the edge of these lines at a point. The teacher should use several questions to help the student critically think about this graph.
Will the length of the line connecting these two lines be longer or shorter than these lines? What kind of triangle does this form? You can use the scale on the straightedge to measure the length of the connecting line; however, is there another method to calculate the measurement of the connecting line?
Which of the following has an irrational rather than a rational solution?
Y^2 - 5 = 0
Popular toys for Christmas are on sale for 35% off. Early shoppers on December 20th can take an additional 25% off before 7 a.m. Let f(x) = price with 35% off and let g(x) = price with 25% off. Express the best concept or procedure in mathematical language that describes a method to find the price of the toy before 7 a.m. on December 20th.
[g(f(x))]. The composition of functions finds the sale price of the toy with the 35% discount [f(x)] and then finds the sale price of the toy with an additional 25% discount [g(f(x)].
Which of the following solves (5a) ⁄2 + 3b =7 for a.
a = (14 - 6b) / 5
Mr. Taylor wants to introduce his students to the concept of place value. Which of the following sets of manipulatives best describe those that can effectively be used to teach this concept?
base-ten materials, decimal squares, 10-frames, Cuisenaire rods, math balance, cubes, 2-color counters
Determine the choice that illustrates the commutative property for (a + b) + c =
c + (a + b)
The letters a, b, and c represent whole numbers greater than zero with a < b < c. Which of the following numbers is greatest?
c / a
Irrational number
can not be expressed as a fraction and decimals repeat forever.
prerequisites for children to recognize patterns.
classify objects exploration of many objects determine similarities and differences
Ms. Brown wants to introduce her students to the concept of ratio. Which of the following sets of manipulatives best describe those that can effectively be used to teach this concept?
color tiles, cubes, Cuisenaire rods, tangrams, pattern blocks, 2-color counters
Which counting technique method should be used to determine how many possibilities exist in forming a committee of six members in a high school that has 38 faculty members available to serve on this committee?
combinations
Mrs. Johnson teaches fourth graders with learning disabilities. She asks them to add the following numbers: 15 12 28 +45 Jamie responds very quickly with 100. When Mrs. Johnson asks him how he solved it he replies: "I added 15 and 45 and got 60 and then I added 12 and 28 and got 40. Next, I added 60 and 40 together and got 100." Which of the following two properties of numbers did Jamie use to solve this problem?
commutative and associative Jamie used the commutative property to change the order of the numbers to be added when he moved the 45 up with the 15. Then he used the associative property to group the 15 and 45 for a sum of 60 and the 12 and 28 together for a sum of 40.
Which of the following is NOT a prerequisite for children to recognize patterns?
compare sets. In the sequence of prenumeration steps, comparing sets is after recognizing patterns. Children have to be able to recognize patterns and be further able to tag items one to one in order to compare sets.
The teacher could best help the students understand that the triangle is equivalent to half a square by showing them how to:
create a reflection of the triangle along its longest side.
Tonya is trying to help her 3rd grade student understand how to check for mathematical reasonableness. The student has calculated 8 + 7 = 21. What is a technique she might suggest to help her student learn estimation?
doubling When numbers are consecutive, doubling can be very helpful in estimating the reasonableness of an answer. Informal counting techniques (e.g., double plus one and double minus one) can be used to correctly solve this problem.
Workers at a local factory make $8, $10, or $12.50 per hour. Each receives a $50 weekly gas allowance. Let h = hours and r= rate. Which expression can be used to represent the gross weekly pay of each individual?
hr + 50
Determine the linear inequality represented in a graph.
if the circle is open it does not include that number (ex. x<5). A closed circle includes that number (ex. x< or equal to 5)
Instant feedback
if the teacher had the students grade their quizzes and then turn them in to the teacher for her assessment. In this way, students would have received instant feedback and not have to wait until the next day to see the results of their work.
Mr. Jansen's second-grade students have been working on addition and are now ready to begin learning two-digit subtraction. To introduce this new unit of study he first has students work on addition problems they are familiar with and then follows up by demonstrating to them how those problems are related to subtraction. This approach best demonstrates Mr. Jansen's understanding that —
instruction in math should build on existing knowledge of math.
Summative assessment
is designed to allocate grades based on how a student proves their understanding of the subject.
Formative assessment
is embedded in the sequence of instruction and is designed to enhance learning with non-threatening results and adapt to student needs.
Learning to skip count forward in lower grades is preparation for which of the following mathematical operations?
multiplication Answer D is correct. Skip counting builds the foundation for learning multiples and how multiples applies with multiplication. A multiple is simply a number multiplied (or skip counted) by an integer. The correct answer is D.
The symbol Æ is often used in mathematics and represents...
null set empty set no solution also represented by using { } Does not represent 0. Only zero can represent 0.
Mr. Jansen has been debating whether or not he should allow his students to use calculators to do their math. Some of his students are learning disabled. When considering the use of calculators for math exercises Mr. Jansen should keep in mind that —
once students have demonstrated that they know the correct way to perform math calculations they should be allowed to use a calculator.
Which choice represents an element whose only factors are itself and 1?
prime numbers By definition, prime numbers are natural numbers greater than 1 that only have two factors, themselves and one.
expressing probability
probability is always between 0 and 1 inclusively. (represented as a decimal, not a percent)
The greatest benefit of providing elementary students with mathematical tools such as geoboards is that these tools:
provide students with visual representations that promote their conceptual understanding.
Which number system is a repeating decimal a member of?
rational
Simplify S^3 . t^4 . S^8 . t^6
s^11 . t^10 s^3+8 x t^4+6 = s^11 x t^10
Ms. Senath teaches math to a diverse group of students in her fourth-grade class, some of them with learning disabilities. It is important for her to remember when presenting math instruction to her students that —
she should teach math concepts from the concrete to the representational to the abstract.
Slope
slope (m) = rise / run
Determine the choice that does NOT relate to the following: 10x + 5
solve for the value of x A variable in an expression can never be solved for. It is independent. Any value may be substituted in for x.
The diagram shows the first two steps in modeling a computation involving numbers A and B using base-ten blocks. Which type of computation is being modeled with the blocks?
subtraction with regrouping Base ten blocks in picture Number A, Step 1 represent the number 42; that's four tens and two units. Base ten blocks in picture Number B, Step 1 represent the number 27; that's two tens and seven units. Next, notice that picture Number A, Step 2 shows twelve units and only three tens are left, while the presentation in Number B, Step 2 continues the same as in Number A, Step 1. One can infer from this observation that ten units were taken from one of the four tens to make 12 units so that 7 units can be taken away from it because otherwise there would not be enough. This computation illustrates subtraction with regrouping.
A teacher begins a new lesson on Trigonometry on Monday. She would like to identify which concepts of the new lesson are most difficult for students to comprehend, so that she can adjust her lesson plans for Tuesday as the lesson progresses. Which of the following assessment methods would be least appropriate for achieving this goal?
summative
Mrs. Johnson teaches fourth graders, some with learning disabilities. Many of them are having trouble with expressions similar to this one: 12 + (7 X 2) - 2(5 + 3). Students' trouble is most likely the result of misunderstanding —
the order of operations.
Which figure is two-dimensional?
triangle, square, circle, etc. NOT cone, pyramid, cylinder, etc.
A math tutor decides there is a demand for her services. She offers tutoring sessions 3 times a week in 2-hour blocks. She pays $30 per hour for the rent of a room which covers utilities. The packets she provides for each student for the week with study material and examples cost her $5. Write her cost equation for each week and identify the marginal cost and fixed cost.
y = 5x + 180, marginal cost $5, and fixed cost $180.
Solve for x. 4x + 6 / x - 3 = 6x / x - 3
Ø The solution for x is 0 so the solution must be discarded.