Week 2 - Whole Numbers Part 1 Test Preparation Questions

Week 2 - Whole Numbers Part 1 Test Preparation Questions 1. Josh is a third-grade student in Ms. Carter’s classroom. Josh’s answer to three addition problems are shown. He incorrectly answered the first two problems but correctly answered the third problem. If Josh uses the same strategy to answer the following problem, what will his answer be? 2. Mr. Khan’s students are discussing the problems shown. Mr. Khan asks his students what relationships they notice in the problems. One student responds with the following conjecture. I noticed that when you divide by a number and then multiply the result by the same number, you always get back the first number. Provided that division by zero is excluded, for which of the following sets of numbers is the student’s conjecture true? Select all that apply. a. Whole Numbers b. Integers c. Fractions and Decimals 3. Rosana had a total of 9 shirts. She gave 2 to Emily. How many shirts does Rosana have now? Which of the following problems has the same mathematical structure as the problem above? a. Rosana used 7 paint colors for her project. Emily used 2 different paint colors for her project. How many paint colors did Rosana and Emily use together? b. Rosana has some books. She bought 1 more book. Now she has 8 books. How many books did Rosana start with? c. Rosana has a total of 3 stickers. Emily has 6 more stickers than Rosana. How many stickers does Emily have? d. Rosana brought 5 cookies for lunch. How many cookies did she have after she ate 4 of the cookies? 4. 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. Triana 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 gave to each friend? 5. 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? 6. One of Mr. Spilker’s students, Vanessa, incorrectly answered the addition problem 457 + 138 as represented in the work shown. 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 7. Mr. Rasche wants his students to understand that, depending on the context of a division word problem that has a remainder, the answer to the word problem will be found by ignoring the remainder, dividing the remainder into equal shares, or using the least whole number that is greater than the quotient. Mr. Rasche wants to illustrate these cases with word problems that involve the quotient 15 ÷ 2. Indicate whether the answer to each of the following word problems is found by ignoring the remainder, dividing the remainder into equal shares, or using the least whole number that is greater than the quotient. Word Problem Ignore the Remainder Divide the Remainder into Equal Shares Use the Least Whole Number That Is Greater Than the Quotient 15 chocolate chip cookies will be evenly divided between 2 children. How many cookies will each child get? A group of 15 people booked rooms in a hotel, and up to 2 people stayed in each

Student Explanation Provides Evidence Does Not Provide 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 2. 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. 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 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. 11. Ms. Duchamp asked her students to write explanations of how they found the answer to the problem 24 x 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 210 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. 12. 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 ¼ cups of sugar. Joe uses a ¼ 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 ¼ cups of soup fills ¼ of a container. How many cups of soup will it take to fill the whole container? c. A trail is 3 ¼ miles long and trail markers are placed at ¼ mile intervals along the trail. How many trail markers are placed along the trail. 13. Marina explained how she found the difference 35 - 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. 14. Mr. Schroeder asked his students to find the product 36 x 5. Four students shared their strategies with the class, and Mr. Schroeder recorded their methods on the board. Indicate whether each of the following representations of student methods demonstrates that the student used reasoning based on the distributive property or reasoning based on the associative property. Representation of Student Method Distributive Property Associative Property 36 ÷ 2 = 18 5 x 2 = 10 18 x 10 = 180 36 = 30 + 6 30 x 5 = 150 6 x 5 = 30 150 + 30 = 180 36 = 6 x 6 6 x 5 = 30 6 x 30 = 180 36 = 40 - 4 40 x 5 = 200 4 x 5 = 20 200 - 20 = 180 15. 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?