Math Practice Test (7813)
A chef at a restaurant uses 1/5 liter of lemon juice and 3/10 liter of teriyaki sauce to make a marinade for 2 kilograms of salmon. How many liters of marinade does the chef use per kilogram of salmon? Give your answer as a fraction.
1/4
0.2 is equivalent to
2/10 and 20/100
0.02 is equivalent to
2/100
2 is equivalent to
200/100 and 20/10
Joshua walks the length of each of three trails on a hike. The first trail is 3.6 kilometers long. The second trail is 3.7 kilometers long. The third trail is 600 meters shorter than the sum of the lengths of the first two trails. Joshua walks at an average speed of 3 kilometers per hour over the course of the entire hike. How many minutes does it take Joshua to complete his hike?
280 minutes
1/4 of Anne's hot chocolate is made of milk. What is the amount of milk in 8 cups of Anne's hot chocolate? Devon explained how he found the answer to the problem shown, saying, "If 1/4 is milk, it's like the hot chocolate is 4 cups and 1 of them is the milk. Then if you double the hot chocolate you have to double the milk, so in 8 cups there are 2 cups of milk." Devon's partner, Milena, represented Devon's strategy using cubes as represented in the figure shown. Which of the following statements best characterizes how Milena's work represents Devon's strategy? A. Milena's work accurately represents Devon's strategy because it shows 1/4 of 4 and how that result was doubled. B. Milena's work accurately represents Devon's strategy, but an area model for multiplication would better represent the different units of measure involved in the problem. C. Milena's work does not accurately represent Devon's strategy because unit cubes cannot be used to represent parts of a whole. D. Milena's work does not accurately represent Devon's strategy because Devon's strategy used a different whole than the whole Milena used in her work.
A
A rectangular message board in Aleyah's dormitory room has a length of 30 inches and a perimeter of 108 inches. A rectangular bulletin board in the hallway outside Aleyah's room is twice as long and twice as wide as the message board. Which of the following statements about the bulletin board is true? A. The bulletin board has a width of 48 inches. B. The bulletin board has a length of 96 inches. C. The area of the bulletin board is twice the area of the message board. D. The perimeter of the bulletin board is four times the perimeter of the message board.
A
Ms. Garrett has been working on verbal counting with her students. She wants them to be more aware of patterns in the way number names are typically constructed. Which of the following number names LEAST reflects the typical pattern in the way number names are constructed in the base ten system? A. Eleven B. Sixteen C. Twenty-five D. Ninety
A
Which of the following word problems can be represented by the equation 4 × n + 8 = 16? A. A set of 5 baskets holds a total of 16 apples. The first basket has 8 apples and the other baskets each hold an equal number of apples. How many apples are in each of the other baskets? B. There are 12 baskets, 8 of which are empty. There are 16 apples, with an equal number of apples in each of the other 4 baskets. How many apples are in each of the 4 baskets? C. There are 16 baskets, 8 of which are empty. Each of the other baskets contains 4 apples. How many apples are there in all? D. There are 8 baskets with 4 apples in each basket and 16 apples that are not in a basket. How many apples are there in all?
A
In the partitive model of division, the quotient is the size of each group. In the measurement model of division, the quotient is the number of groups. Which of the following problems illustrates the measurement model of division? Select all that apply. A. Joe is making chocolate fudge and the recipe calls for 3 1/4 cups of sugar. Joe uses a 1/4-cup measuring cup to measure the sugar. How many times does Joe need to fill the measuring cup to measure the sugar needed for the recipe? B. 3 1/4 cups of soup fills 1/4 of a container. How many cups of soup will it take to fill the whole container? C. A trail is 3 1/4 miles long and trail markers are placed at 1/4-mile intervals along the trail. How many trail markers are placed along the trail?
A and C
Ms. Vargas asked her students to write an expression equivalent to 4(x−y)4(x−y). After substituting some values for x and y, a student named Andrew rewrote the expression as 4x−y4x−y. Andrew's expression is not equivalent to 4(x−y)4(x−y), but he thought his work was correct based on the substitutions he tried. For which of the following integer values of x and y would Andrew's expression appear to be correct? Select two choices. A. x=0 and y=0 B. x=0 and y≠0 C. x≠0 and y=0 D. x≠0 and x=y E. x≠0 and x=−y
A and C
Mr. Varela asked his students to define a square in terms of other two-dimensional geometric figures. Which two of the following student definitions precisely define a square? A. A square is a rectangle that has 4 sides of equal length. B. A square is a parallelogram that has 4 angles of equal measure. C. A square is a parallelogram that has 4 sides of equal length. D. A square is a rhombus that is also a rectangle. E. A square is a rectangle that is not a rhombus.
A and D
Ms. Stockton and her students are working on naming different polygons using their geometric attributes. She finds a suggestion online to use pattern blocks for this work. A set of pattern blocks is shown. Which two of the following statements describe limitations of using pattern blocks for the purpose of naming polygons based on their attributes? A. The blocks could support the conclusion that all polygons are convex. B. The blocks do not clearly show how polygons can be composed of other polygons. C. The blocks could support the conclusion that all polygons can be composed of equilateral triangles. D. The blocks do not show which polygons have the defining attribute of having at least one set of parallel lines. E. The blocks could support the conclusion that an attribute of polygons is that they must have at least two sides of equal length.
A and E
Which three of the following word problems can be represented by a division equation that has an unknown quotient? A.Ms. Bronson works the same number of hours each day. After 8 days of work, she had worked 32 hours. How many hours does Ms. Bronson work each day? B. Mr. Kanagaki put tape around 6 windows before painting a room. He used 7 feet of tape for each window. How many feet of tape did he use? C. Micah used the same number of sheets of paper in each of 5 notebooks. He used 45 sheets of paper in all. How many sheets of paper did Micah use in each notebook? D. Each shelf in a school supply store has 8 packs of markers on it. Each pack has 12 markers in it. How many markers are on each shelf in the store? E. Trina gave each of 7 friends an equal number of beads to use to make a bracelet. She gave the friends a total of 63 beads. How many beads did she give to each friend?
A, C, and E
36=6×6 6×5=30 6×30=180
Associative Property
36÷2=18 5×2=10 18×10=180
Associative Property
1/3 = 3/9 = 6/18 1/4 = 4/16 = 3/12 Ms. White's students are working on generating equivalent fractions like the ones shown. She asks her students to write a set of instructions for how to generate equivalent fractions. One student writes, "You have to multiply the bottom and the top of the fraction by a number." Which of the following revisions most improves the student statement in terms of validity and generalizability? A. You have to multiply both denominator and numerator by the same number. B. You have to multiply both denominator and numerator by the same nonzero number. C. You have to multiply both denominator and numerator by the same whole number. D. You have to multiply both denominator and numerator by the same positive whole
B
During a lesson in her second-grade class, Ms. Costa draws two squares of the same size, each representing the same whole. She then divides and shades the squares as represented in the figure. Her students consistently identify the area of each shaded region as one-fourth, but when they are asked if the areas are equal, some students say no. Which of the following statements most likely explains why the students see the areas as not being equal? A. The students think that the areas are not equal because the wholes are different sizes. B. The students think that the areas are not equal because the shaded regions are different shapes. C. The students have difficulty determining the size of geometric figures that include diagonal lines. D. The students have difficulty determining the part-to-whole relationship when working with visual models of fractions.
B
In word problems that have a multiplicative comparison problem structure, two different sets are compared, and one of the sets consists of multiple copies of the other set. Which of the following best illustrates a word problem that has a multiplicative comparison problem structure? A. There are 4 shelves in Joaquin's bookcase, and there are 28 books on each shelf. How many books are in Joaquin's bookcase? B. Marcus drives 3 times as many miles to get to work as Hannah does. Hannah drives 16 miles to get to work. How many miles does Marcus drive to get to work? C. A football field is 360 feet long and 160 feet wide. A soccer field is 300 feet long and 150 feet wide. The area of the football field is how many square feet greater than the area of the soccer field? D. An ice cream parlor sells 29 different flavors of ice cream and 4 different types of cones. How many different combinations consisting of an ice cream flavor and a type of cone are available at the ice cream parlor?
B
Mr. Walters asked his students to order 89, 708, 37, and 93 from least to greatest, and to be ready to explain the process they used to order the numbers. One student, Brianna, ordered the numbers correctly, and when Mr. Walters asked her to explain her process, she said, "The numbers 89, 37, and 93 are less than 100, so they are all less than 708, since that is greater than 100. Also, 37 is the least because it comes before 50 and the other two numbers are close to 100. Then 89 is less than 90, but 93 is greater than 90." Which of the following best describes the strategy on which Brianna's explanation is based? A. A counting strategy B. A benchmarking strategy C. An estimation strategy D. A place-value strategy
B
Ms. Roderick asked her lunch helper in her kindergarten class to get one paper plate for each student in the class. Which of the following counting tasks assesses the same mathematical counting work as this task? A. Having students line up according to the number of the day of the month in which they were born B. Showing students 10 pencils and asking them to get enough erasers for all the pencils C. Showing students a row of 12 buttons and asking them to make a pile of 8 buttons D. Asking students to count the number of triangles printed on the classroom rug
B
Ms. Simeone is working with her first-grade students on writing two-digit numerals. She wants to use an activity to assess whether her students are attending to the left-to-right directionality of the number system. Which of the following activities is best aligned with Ms. Simeone's purpose? A. Asking students to read the numbers 20 through 29 B. Asking students to represent the numbers 35 and 53 using base-ten blocks C. Asking students how many tens and how many ones are in the number 33 D. Showing students 23 cubes and 32 cubes and asking them which quantity is greater
B
The scenario in a word problem states that an office supply store sells pens in packages of 12 and pencils in packages of 20. Which of the following questions about the scenario involves finding a common multiple of 12 and 20 ? A. In one package each of pens and pencils, what is the ratio of pens to pencils? B. How many packages of pens and how many packages of pencils are needed to have the same number of pens as pencils? C. If the store sells 4 packages each of pens and pencils, what is the total number of pens and pencils sold in the packages altogether? D. How many gift sets can be made from one package each of pens and pencils if there are the same number of pens in each set, the same number of pencils in each set, and all the pens and pencils are used?
B
Mr. French's students are working on finding numbers less than 100 that are multiples of given one-digit numbers. When Mr. French asks them how they know when a number is a multiple of 6, one student, Crystal, says, "Even numbers are multiples of 6!" Mr. French wants to use two numbers to show Crystal that her description of multiples of 6 is incomplete and needs to be refined. Which of the following numbers are best for Mr. French to use for this purpose? Select two numbers. A. 15 B. 16 C. 20 D. 24 E. 27 F. 30
B and C
Recognize that in a multidigit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Mr. Johansen and his class are working on the mathematical objective shown. To assess what his students understand about the objective, Mr. Johansen plans to use base-ten blocks in a nonconventional way. He plans to first tell students which block will represent the unit and then ask students to determine what number is represented with the given base-ten blocks. Mr. Johansen wants to identify numbers that can be represented using only little cubes, rods, flats, and big cubes. If Mr. Johansen wants students to identify the number 32.6 from his representation, which two of the following base-ten blocks can he choose to represent the unit? A. Little cube B. Rod C. Flat D. Big cube
B and C
Marina explained how she found the difference 35−1835−18, saying, "I knew that 18 plus 2 is 20, and 35 plus 2 is 37, so 35 minus 18 is the same as 37 minus 20, which is 17. So 35 minus 18 is 17." Marina's partner, Jeremy, represented Marina's strategy using a number line, as shown in the figure. Which of the following statements best characterizes how Jeremy's work represents Marina's strategy? A. Jeremy's work accurately represents Marina's strategy because it shows that she correctly found the difference between 35 and 18. B. Jeremy's work accurately represents the part of Marina's strategy in which she considered 20 instead of 18 as the subtrahend, but it does not accurately represent how she took 20 away from 37. C. Jeremy's work does not accurately represent Marina's strategy because Marina's strategy involved shifting the problem, but Jeremy's work shows a counting-up strategy. D. Jeremy's work does not accurately represent Marina's strategy because Marina used a comparison interpretation of subtraction, but Jeremy's work shows a takeaway interpretation of subtraction.
C
Mr. Poynter asked his students to calculate the product 0.6×0.050.6×0.05 by converting the decimals into base-ten fractions. One student, Larissa, answered the problem as represented in the work shown. When Mr. Poynter asked Larissa to explain her strategy, she said, "I wrote the decimals 6 tenths and 5 hundredths as fractions and multiplied them. 6 times 5 is 30 and 10 times 100 is 1,000, so I got 30 thousandths. I cancelled out a zero on the numerator and a zero on the denominator and got 3 hundredths." Which of the following changes to Larissa's explanation is best for clarifying the mathematics that underlie her strategy? A. She should indicate why 0.6=6/10.6 and why 0.05=5/100. B. She should indicate why 6/10×5/100= 30/1000. C. She should point out that 30÷10/1000÷10= 3/100. D. She should point out that 0.03= 3/100
C
Ms. Chamberlain's students are discussing the following quadrilaterals and their diagonals. Ms. Chamberlain asks her students what they notice about the diagonals in the quadrilaterals. One student says, "I noticed that the diagonals of the quadrilaterals always cross at a right angle." Of the following sets of quadrilaterals, for which set is the student's conjecture always true? A. Quadrilaterals with one pair of congruent opposite angles B. Quadrilaterals with one pair of parallel opposite sides C. Quadrilaterals with two pairs of congruent adjacent sides D. Quadrilaterals with two pairs of parallel opposite sides
C
Ms. Cook's class was discussing strategies to compare two fractions. One student, Levi, said, "When the top numbers are the same, you know that the one with the smaller number on bottom is bigger." Ms. Cook asked her students to explain why Levi's claim is true. After giving the class time to work, she asked another student, Maria, to present her explanation. Maria said, "It's just like Levi said. For 1/4 and 1/2, they both have ones on top, and 4 is greater than 2, so 1/4 is less, just like 1/4 of a pizza is less than 1/2 of a pizza." Which of the following statements best characterizes Maria's explanation? A. It clearly explains why Levi's claim is true. B. It clearly explains why the converse of Levi's claim is true, but it does not explain why his actual claim is true. C. It shows that Levi's claim is true for one example, but it does not establish why his claim is true in general. D. It assumes that Levi's claim is true, but it does not establish why his claim is true in general.
C
Ms. Duchamp asked her students to write explanations of how they found the answer to the problem 24×15 One student, Sergio, wrote, "I did 24 times 10 and got 240, then I did 24 times 5 and that's the same as 12 times 10 or 120, and then I put together 240 and 120 and got 360." Ms. Duchamp noticed that four other students found the same answer to the problem but explained their strategies differently. Which of the following student explanations uses reasoning that is most mathematically similar to Sergio's reasoning? A. Since 24 is the same as 12 times 2 and 15 is the same as 5 times 3, I did 12 times 5 and got 60, then I did 2 times 3 and got 6, and 60 times 6 is 360. B. To get 24 times 5, I did 20 times 5 and 4 times 5, which is 120 altogether, and then I needed 3 of that, and 120 times 3 is 360. C. 15 times 20 is the same as 30 times 10, and that gave me 300, and then I did 15 times 4 to get 60, and 300 plus 60 is 360. D. 24 divided by 2 is 12, and 15 times 2 is 30, so 24 times 15 is the same as 12 times 30, and so my answer is 360.
C
Ms. Giansante asked her students to compare 3/4 and 5/7 and show their work. A student named Timothy compared the fractions as represented in the work shown. Ms. Giansante wants to provide a counterexample for Timothy to help him realize his method is not valid and will not always give the correct comparison. Which of the following pairs of fractions provides a counterexample to Timothy's method? A.2/3 and 3/5 B.4/7and 5/9 C.3/7 and 2/5 D.2/3 and 4/7
C
Ms. Rodriguez is working with her kindergarten students to develop the skill of counting on. Which of the following tasks is best aligned with the goal of having students count on? A. The teacher gives each student a number book with a different number on each page. The students must count out and glue the same number of pictures to match the given number on each page. B. The teacher gives each student a 10-piece puzzle, disassembled with a single number written on each piece. The students must put the puzzle together with the numbers in order. C. The teacher gives each student a shuffled deck of 10 cards, each with a single number from 1 to 10. When the students draw a number card, they must count to 20, starting from the number on the card they drew. D. The teacher gives each student 8 blocks and a number cube, with the sides of the number cube numbered from 3 to 8. When the students roll the number cube, they must count out the same number of blocks as the number rolled and create a tower with that number of blocks.
C
One of Mr. Spilker's students, Vanessa, incorrectly answered the addition problem 457 + 138 as represented in the work shown. 457 + 138 = 585 Mr. Spilker wants to give Vanessa another problem to check whether she misunderstands the standard addition algorithm or whether she simply made a careless error. Which of the following problems will be most useful for Mr. Spilker's purpose? A. 784 + 214 B. 555 + 134 C. 394 + 182 D. 871 + 225
C
One of Mr. Terry's students, Yvonne, found the answer to the problem 3/8 × 2/9 as represented in the work shown. 3/8 x 2/9= 2/8 x 3/9= 1/4 x 1/3= 1/12 When Mr. Terry asked Yvonne to explain her work, she said, "It's easier to just switch the numerators to make simpler fractions." Which of the following statements is true of Yvonne's strategy? A. Yvonne's strategy can only be used to rewrite products of fractions where the difference between the numerators is 1 and the difference between the denominators is 1. B. Yvonne's strategy can only be used to rewrite products of fractions where both fractions are less than 1. C. Yvonne's strategy can be used to rewrite any product of two fractions, but it will not always result in fractions that can be simplified. D. Yvonne's strategy can be used to rewrite any product of two fractions, and it will always result in fractions that can be simplified.
C
Which of the following fractions has a value between the values of the fractions 7/9 and 8/11 ? A.1/2 B.2/3 C.3/4 D.4/5
C
Mr. Benner places a row of 5 cubes on a student's desk and asks the student, Chanel, how many cubes are on the desk. As Chanel points at the cubes one by one from left to right, she counts, saying, "One, two, three, four, five." Then she says, "There are five cubes!" Mr. Benner then asks Chanel to pick up the third cube in the row. As Chanel points at three cubes one by one from left to right, she counts, saying, "One, two, three." She stops, then picks up the three cubes, and gives them to Mr. Benner. Chanel has demonstrated evidence of understanding which two of the following mathematical ideas or skills? A. Using numerals to describe quantities B. Recognizing a small quantity by sight C. Counting out a particular quantity from a larger set D. Understanding that the last word count indicates the amount of objects in the set E. Understanding that ordinal numbers refer to the position of an object in an ordered
C and D
A student answered two elapsed-time problems using the same method, as represented in the work shown. The student's answer to the first problem was correct, but the student's answer to the second problem was incorrect. 1. 7:05am- 1:45pm 7-1=6 45-5=40 6hrs 40 mins passed 2. 11:45pm- 3:20am 11-3=8 45-20=25 8hrs 25 mins passed If the student continues to use the same method, for which two of the following time intervals will the student give the correct elapsed time? A. 6:45 A.M. to 9:15 A.M. B. 10:10 A.M. to 3:35 P.M. C. 2:30 P.M. to 7:50 P.M. D. 8:55 P.M. to 4:20 A.M. E. 11:25 P.M. to 5:30 A.M.
C and E
Which two of the following inequalities are true? A. 0.56 > 0.605 B. 0.065 > 0.56 C. 0.56 > 0.506 D. 0.605 < 0.056 E. 0.506 < 0.65 F. 0.65 < 0.605
C and E
Ms. Celantano found the following representation of the decimal multiplication problem 0.7×0.4=0.28 in her curricular materials. The representation uses a 10-by-10 grid of small squares. Which three of the following statements about the representation are true? A. The area of the four small gray squares in the top row represents 0.4, and the area of the seven small gray squares in the left column represents 0.7. B. The representation shows a repeated-addition interpretation of decimal multiplication. C. In the representation, each of the small squares represents one hundredth. D. In the representation, the outer square represents one. E. The representation can be used to show that 0.7×0.4=0.4×0.7
C, D, and E
3/4+ 5/6= 18/24 + 20/24= 38/24+ 1/10= 380/240+ 24/240= 404/240 A student adds the fractions 3/4, 5/6, and 1/10 as represented in the work shown. The teacher notices that there is an error in the student's work that keeps the work from being mathematically correct. Which of the following aspects of the work does the student need to revise for the work to be mathematically correct? A. The student needs to simplify answers to lowest terms. B. The student needs to use the least common denominator. C. The student needs to write the final answer as a mixed number. D. The student needs to use the equal sign properly.
D
A grocery store sells both green grapes and red grapes for a regular price of $2.89 per pound. Nelson buys 1.5 pounds of green grapes and 2.25 pounds of red grapes at the store on a day when the regular price is reduced by $0.75 per pound. Which of the following expressions represents the amount, in dollars, that Nelson will pay for the grapes? A. 1.5 + 2.25 × 2.89 − 0.75 B. (1.5 + 2.25) × 2.89 − 0.75 C. 1.5 + 2.25 × (2.89 − 0.75) D. (1.5 + 2.25) × (2.89 − 0.75)
D
A student found an incorrect answer to the problem 2/5 × 4/3. The student's answer is represented in the work shown. 2/5 x 4/3= 6/20= 3/10 Which of the following student work samples shows incorrect work that is most similar to the preceding work? A. 5/4x 1/2= 6/8=3/4 B. 5/3 x 12/15= 60/45=3/2 C. 7/4 x 7/3= 28/21=4/3 D. 1/2 x 9/10= 10/18= 5/9
D
A student incorrectly answered the problem 305.74 × 100. The student's answer is represented in the work shown. 305.74 x 100= 305.7400 Which of the following student work samples shows incorrect work that is most similar to the preceding work? A. 246.7 x 100= 2,467 B. 13.05 x 100= 13,500 C. 46.13 x 10= 460.130 D. 94.03 x 10= 94.030
D
Last Tuesday, a group of 5 researchers in a laboratory recorded observations during a 24-hour period. The day was broken into 5 nonoverlapping shifts of equal length, and each researcher recorded observations during one of the shifts. Which of the following best represents the amount of time each researcher spent recording observations last Tuesday? A. Between 4 and 4 1/4 hours B. Between 4 1/4 and 4 1/2 hours C. Between 4 1/2 and 4 3/4 hours D. Between 4 3/4 and 5 hours
D
Mr. Aronson noticed that one of his students, Wesley, incorrectly solved a multiplication problem, as represented in the work shown. Which of the following most likely describes the reason for Wesley's error? A. Wesley did not regroup correctly. B. Wesley did not add the regrouped 2 correctly. C. Wesley did not apply his multiplication facts correctly. D. Wesley did not attend to the place value of each digit in the factors correctly.
D
Ms. Carter shows one of her students, Brandon, a set of cubes. She tells Brandon that there are 13 cubes in the set and asks him to take 1 cube away from the set. Ms. Carter then asks Brandon, "How many cubes do you think are in the set now?" Brandon quickly answers, "Twelve." Brandon has demonstrated evidence of understanding which of the following mathematical ideas or skills? A. Using numerals to describe quantities B. Counting with one-to-one correspondence C. Recognizing a small quantity without counting D. Knowing that each previous number name refers to a quantity which is one less
D
Ms. Fisher's students are working on identifying like terms in algebraic expressions. When Ms. Fisher asks them how they know when terms are like terms, one student, Coleman, says, "Like terms have to have the same variable in them." Ms. Fisher wants to use a pair of terms to show Coleman that his description of like terms is incomplete and needs to be refined. Which of the following pairs of terms is best for Ms. Fisher to use for this purpose? A. 9d and 5 B. 8xy and xy C. 5a4 and 2a4 D. 4h2 and 7h3
D
Ms. Howe's students are learning how to use models to help them answer word problems. The models use bars to represent the relationships between the given quantities and the unknown quantity. In each model, the unknown quantity is represented with a question mark. The quantities given in the word problem occupy the other boxes. Ms. Howe shows the following model to her students. Which of the following word problems best corresponds to the model shown? A. Max had $24. He gave $18 to Olivia and the rest to Sarah. How much money did Max give to Sarah? B. Max had $24. He gave 1/3 of his money to Sarah and the rest to Olivia. How much money did Max give to Olivia? C. Max gave $24 to his friend Sarah and $18 to his friend Olivia. What is the total amount of money Max gave to his two friends? D. Max has $24 in his piggy bank, which is 2/3 of the amount of money that Max has altogether. How much money does Max have altogether?
D
Ms. Shaughnessy is working with her class on measuring area using nonstandard units. While the students are finding the area of the surface of their desks using rectangular note cards, one student says, "I can just measure the long side of the desk with the long side of the card, then measure the short side of the desk with the short side of the card, and multiply them." Which of the following best describes the validity of the student's strategy? A. The strategy is not valid because the same unit must be used to measure each side of the desk. B. The strategy is valid only if the note cards are squares. C. The strategy is valid and the unit of measurement is square units. D. The strategy is valid and the unit of measurement is note cards.
D
36=30+6 30×5=150 6×5=30 150+30=180
Distributive Property
36=40−4 40×5=200 4×5=20 200−20=180
Distributive Property
15 chocolate chip cookies will be evenly divided between 2 children. How many cookies will each child get?
Divide the Remainder into Equal Shares
In Ayana's recipe the bananas are split between only 2 loaves, while in Natalie's recipe the bananas are split between 3 loaves. If I have to split a cookie, I would rather split it in two because I get more, so Ayana's loaves contain more bananas.
Does Not Provide Evidence
I started with 10 cubes and 5 cubes—that is 15 cubes—and then I took away the extra 2 cubes and got 13 cubes.
Does not use the Making-Ten Strategy
I started with 8. Then I counted 9, 10, 11, 12, 13.
Does not use the Making-Ten Strategy
A company wants to equip each new workstation with 2 computer monitors. The company has 15 monitors. How many new workstations can be equipped with 2 monitors?
Ignore the Remainder
Mr. Kirk asked his students to compare 0.196 and 0.15. Four of his students correctly answered that 0.196 is greater than 0.15, but they gave different explanations when asked to describe their strategies to the class. Indicate whether each of the following student explanations provides evidence of a mathematically valid strategy for comparing decimal numbers. Student Explanation 0.196 is larger because there is one in the tenths, and then nine hundredths is more than five hundredths. And then I'm done. 0.196 is greater because in the thousandths place six is greater than five, and in the hundredths place nine is greater than one. 0.196 is bigger than 0.15 because if it is three numbers long, it will always be bigger than if it is two numbers long. 0.196 is more than 0.15 because nineteen hundredths is bigger than fifteen hundredths.
Provides Does not Does not Provide
Ayana makes only 2 loaves and Natalie makes 3 loaves. If they made the same number of loaves, like 6, then Ayana would use 9 bananas and Natalie would use 8. So Ayana's loaves have more because 9 is more than 8.
Provides Evidence
In Ayana's recipe there are 3 bananas for 2 loaves, so there is a whole banana for each loaf and you split the last banana in half. In Natalie's recipe there is one banana for each loaf and the fourth banana is split in 3. So in Ayana's loaf there are 1 and a half bananas, and in Natalie's there are 1 and a third, and a half is more than a third.
Provides Evidence
A group of 15 people booked rooms in a hotel, and up to 2 people stayed in each room. What is the minimum number of rooms that the group could have booked?
Use the Least Whole Number That Is Greater Than the Quotient
John wants to buy a new toy car that costs $15, and he saves $2 at the end of each week for the car. At the end of how many weeks will John have enough money to buy the car?
Use the Least Whole Number That Is Greater Than the Quotient
I separated 3 cubes from the 8 so I have 5 and 5, which is 10, and 10 and 3 adds up to 13.
Uses the Making-Ten Strategy
I took 2 cubes from the 5 and put them with the 8, and then I knew 10 and 3 is 13.
Uses the Making-Ten Strategy
A student's incorrect solutions to two equations are represented in the work shown. 7x=70 x=0 4x=44 x=4 If the student continues to use the same strategy, what will be the student's solution to the equation 2x=24?
x=4
