Unit 2 Quick Quiz 1 Name Use mental math to find the product. 1. 7 8 = 56 7 80 = 560 70 80 = 5,600 7 800 = 5,600 7 8,000 = 56,000 2. 3 9 = 27 3 90 = 270 30 90 = 2,700 3 900 = 2,700 3 9,000 = 27,000 3. 60 30 = 1,800 Solve. Show your work. 4. Neil wants to put 1-foot square tiles in his kitchen. The floor is a rectangle. It is 40 feet long and 20 feet wide. How many square tiles does Neil need? 40 20 = 800; 800 1-foot square tiles 5. Draw an area model for 3 30. Then find the product. 30 = 10 + 10 + 10 Check students drawings. 3 3 3 30 = (3 10) + (3 10) + (3 10) = 30 + 30 + 30 = 90; 90 Math Expressions 29 Houghton Mifflin Harcourt Publishing Company Unit 2, Quick Quiz 1
Unit 2 Quick Quiz 2 Name Multiply using any method. Show your work. 1. 4 67 2. 5 94 268 470 Estimate the product. Solve to check your estimate. 3. 9 68 Possible estimate: 9 70 = 630 9 68 = 612 Solve. Show your work. 4. A school sweatshirt costs $9. If the principal orders 195 sweatshirts, how much will the order cost? $1,755 5. Annalise bought 10 items at a computer store. She bought 2 computer games for $25 each and 3 computer games for $30 each. She paid $8 for a new mouse. How much did the computer games cost? List any extra numerical information. $140; extra information: 10 items; $8 for a new mouse Math Expressions 30 Houghton Mifflin Harcourt Publishing Company Unit 2, Quick Quiz 2
Unit 2 Quick Quiz 3 Name Multiply using any method. Show your work. 1. 48 29 2. 64 37 1,392 2,368 Estimate the product. Solve to check your estimate. 3. 68 97 Possible estimate: 70 100 = 7,000 68 97 = 6,596 4. 58 86 Possible estimate: 60 90 = 5,400 58 86 = 4,988 Solve. 5. Draw an area model for 42 56. Then find the product. Check students' drawings. 56 = 50 + 6 42 = 40 40 + + 2 2 50 + 6 2,352; 42 56 = 150 402 + 150 22 + 16 402 + 16 22 2,000 + 240 + 100 + 12 = 2,352 Math Expressions 31 Houghton Mifflin Harcourt Publishing Company Unit 2, Quick Quiz 3
Unit 2 Quick Quiz 4 Name Multiply using any method. Show your work. 1. 4 3,819 2. 6,423 7 15,276 44,961 Estimate the product. Solve to check your estimate. 3. 3 4,756 Possible estimate: 13 4,0002 + 13 800) = 12,000 + 2,400 = 14,400 3 4,756 = 14,268 4. 6 5,939 Possible estimate: 16 5,0002 + 16 900) = 30,000 + 5,400 = 35,400 6 5,939 = 35,634 Solve. Show your work. 5. It costs 9,179 points to build each apartment building in the computer game Big City Building. What is the cost to build 6 apartment buildings? 55,074 points Math Expressions 32 Houghton Mifflin Harcourt Publishing Company Unit 2, Quick Quiz 4
Unit 2 Test Name 1. Use the numbers on the tiles to complete the steps to find 30 60 by factoring the tens. Tiles may be used more than once. 2 3 6 8 10 18 30 60 = ( 3 10) ( 6 10) = (3 6) ( 10 10 ) = 18 100 900 1,800 = 1,800 2. Select the expression that is equivalent to 42 68. Mark all that apply. A 40 (60 + 8) + 2 (60 + 8) B 40 2 + 60 8 C (40 60) + (40 8) + (2 60) + (2 8) D 32 + 24 + 12 + 16 E (8 2) + (8 4 tens) + (6 tens 2) + (6 tens 4 tens) 3. There are 18 eggs in a carton. If there are 70 cartons, how many eggs are there? 1,260 eggs 4. Sara bought 12 bags of large buttons with 15 buttons in each bag. She bought 17 bags of small buttons with 30 buttons in each bag. How many more small buttons are there than large buttons? Show your work. 330 small buttons; 1 12 15 60 + 120 180 2 17 30 00 + 510 510 411 5 1 0-1 8 0 3 3 0 Math Expressions 33 Houghton Mifflin Harcourt Publishing Company Unit 2 Test
Name 5. Draw an area model for 8 543. 543 = 500 + 40 + 3 8 8 Explain how you used the model to find the product. 4,344; (8 500) + (8 40) + (8 3) = 4,000 + 320 + 24 = 4,344; Possible explanation: The area model is divided into sections that show 543 as hundreds, tens, and ones, and the multiplication of each section. I multiplied each section by 8 and added the partial products. 6. For numbers 6a 6e, choose Yes or No to tell whether the equation is true. 6a. 6 7 = 42 Yes No 6b. 6 700 = 4,200 Yes No 6c. 60 70 = 42,000 Yes No 6d. 600 70 = 420,000 Yes No 6e. 6 7,000 = 42,000 Yes No 7. Find 3 67. 201 Math Expressions 34 Houghton Mifflin Harcourt Publishing Company Unit 2 Test
Name 8. Use the numbers on the tiles to complete the area model for 39 67. 67 = 39 = 60 + 7 7 30 30 9 + + 9 9 60 + 7 30 60 Show how to use the area model and expanded notation to find 29 48. 67 60 + 7 39 = 30 + 9 30 60 = 1,800 30 7 = 210 9 60 = 540 9 7 = 63 2,613 9. Estimate 19 43 by rounding each number to the nearest ten. 800 10. For numbers 10a 10d, choose True or False to describe the statement. 10a. 67 9 is greater than 60 9. True False 10b. An estimate of 67 9 is 7,000. True False 10c. 67 9 is less than 630. True False 10d. 67 9 = (6 9) + (7 9) True False Math Expressions 35 Houghton Mifflin Harcourt Publishing Company Unit 2 Test
Name 11. Find 3 6,251. 18,753 Use estimation to explain why your answer is reasonable. Possible explanation: The answer is reasonable because it is close to an estimate of 3 6,300 = (3 6,000) + (3 300) = 18,000 + 900 = 18,900. 12. For numbers 12a 12d, choose Yes or No to tell whether the equation is true. 12a. 50 400 = 20,000 Yes No 12b. 500 4 = 200 Yes No 12c. 5 40 = 20 Yes No 12d. 5 40,000 = 200,000 Yes No 13. The best estimate for 85 40 is that it must be greater than? but less than?. Select one number from each column to make the sentence true. Greater than Less than 2,400 2,400 3,200 3,200 3,600 3,600 4,000 4,000 14. Choose the number from the box to complete the statement. The product of 28 and 153 is closest to 3,000 3,200 4,500 4,800. Math Expressions 36 Houghton Mifflin Harcourt Publishing Company Unit 2 Test
Name 15. A concert costs $63 per person. A group of 8 people go to the concert. What is the cost for the group? Explain how found your answer. $504; Possible explanation: Multiply 8 63. Find the tens product, the ones product, and then add to find the total. 8 60 = 480 8 3 = 24 1 480 + 24 504 16. A school is holding a raffle as a fundraiser. The price for each raffle ticket is $5. If 324 tickets are sold, how much money will be raised? A $319 C $1,500 B $329 D $1,620 17. Each member of the band practices for 4 hours each week. There are 215 boys and 207 girls. How many hours of practice is this? Part A Identify any extra information given in the problem. Explain your reasoning. No extra information is given. To find the total number of hours practiced, you must know the number of band members (given as the number of boys and girls) and the hours that each practiced. Part B Solve the problem. Show your work. 1,688 hours; 1 215 + 207 422 422 4 1,688 Math Expressions 37 Houghton Mifflin Harcourt Publishing Company Unit 2 Test
Name 18. Select the expression that is equivalent to 4 600. Mark all that apply. A 6 + (100 4) + 10 C (6 + 4) (100 + 1) B (6 40) 10 D (6 4) (100 1) 19. Chen is making cards. He buys 50 blank cards. He uses 8 stickers on each of 16 cards and 7 stickers on each of 22 cards. He has 32 stickers left over. How many stickers are on the cards? Part A Identify any extra information given in the problem. 50 blank cards and 32 stickers left over Part B Solve the problem. Show your work. 282 stickers; 16 8 = 128; 22 7 = 154; 128 + 154 = 282 20. Draw an area model for 3 4,681. Then write an equation to match your model. 4,681 = 4,000 + 600 + 80 + 1 3 3 Equation: 3 4,681 = 14,043 21. Use the numbers on the tiles to complete the steps to find the solution to 3 55. Tiles may be used more than once. 3 55 = 3 (50 + 5 ) 3 5 8 = (3 50 ) + (3 5 ) = 150 + 15 50 53 68 150 165 = 165 Math Expressions 38 Houghton Mifflin Harcourt Publishing Company Unit 2 Test
Unit 2 Multiplication with Whole Numbers What Is Assessed? 4.NBT.5 Multiply by one- and two-digit numbers, using place value. 4.NBT.3 Round multidigit whole numbers. 4.MD.2 Solve word problems involving money. Mathematical Practices K 12.MP.1 K 12.MP.2 K 12.MP.4 K 12.MP.6 K 12.MP.7 Materials one-, five-, and ten-dollar bills Explaining the Assessment 1. The assessment will require students to apply content learned in the unit involving multiplication using place value. 2. Read the task aloud with the class. 3. Discuss finding the total cost of several items. Ask students to explain whether or not they would use the same strategy if the costs of each item are the same or if they are different. 4. When working through some of the items in the Performance Assessment, students will have to consider what items and the number of these items that can be bought for a given total cost. Discuss strategies that can help with this task, such as using estimation and using guess and check. Math Expressions 39 Houghton Mifflin Harcourt Publishing Company Unit 2 Performance Assessment
Name ACTIVITY Shop for a Clothing Drive Mrs. Liston and 9 of her friends are shopping for clothes to donate to a winter clothing drive. The store has many clothing items for sale. The table shows the items Mrs. Liston and her friends can buy and the price for each item. Clothing for Sale Item Price Shirt $15 Jeans $25 Sweater $45 Boots $75 Coat $99 1. Mrs. Liston has $259. Is it possible for her to spend the whole amount by buying only one kind of item at the store? How do you know? No; Possible explanation: The prices of a shirt, jeans, a sweater, and boots each have 5 in the ones place. The product of any number and 5 has a 0 or 5 in the ones place, and $259 has a 9 in the ones place. So, if Mrs. Liston bought more than one of any of these items, she could not spend $259. The price of a coat has a 9 in the ones place. The product of 9 and any 1-digit number other than 1 does not have 9 in the ones place, as $259 does. So, Mrs. Liston could not spend $259 by buying a certain number of coats. 2. What are 2 different ways that Mrs. Liston can spend $259 at the store? Response should indicate that the student considered the amount Mrs. Liston could spend and the price of the items she could buy. Possible answer: She could buy 1 of each item, or 4 shirts, 4 pairs of jeans, and 1 coat. 3. If Mrs. Liston and her friends each spend $259 at the store, how much money do they spend in all? How do you know? $2,590; Possible explanation: First I added the number of people: 1 + 9 = 10. Then I multiplied $259 by 10. 4. Mrs. Liston collected $1,800 for the clothing drive. She buys 24 pairs of jeans and 24 sweaters. What could she buy with the money that is left? Response should indicate that the student considered the amount of money Mrs. Liston has left based on the amount of money she spent, as well as the price of the items she could buy with this money. Possible answers: 24($25) + $24($45) = $600 + $1,080 = $1,680. $1,800 - $1,680 = $120, so Mrs. Liston has $120 left. She could buy 8 shirts for 8($15) = $120; 1 pair of boots and 1 sweater for $75 + $45 = $120; 1 coat and 1 shirt for $99 + $15 = $114. Math Expressions 40 Houghton Mifflin Harcourt Publishing Company Unit 2 Performance Assessment
Name The store puts some items on sale, as shown in the table. Clothing for Sale Item Original Price Sale Price Shirt $15 $12 Jeans $25 Sweater $45 $42 Boots $75 $56 Coat $99 5. How would these sale prices affect what Mrs. Liston could have bought with $1,800? Explain. Response should indicate that the student considered the amount Mrs. Liston saved as a result of the sale and used this savings to increase the items she could buy. Possible answer: The original price of jeans and a sweater is $25 + $45 = $70. The sale price is $25 + $42 = $67. $70 - $67 = $3, so Mrs. Liston saves $3 on each set of jeans and a sweater she buys. The savings on 24 sets is 24($3) = $72. Originally, Mrs. Liston had $120 left. $120 + $72 = $192, so now Mrs. Liston has $192 left to spend. She could buy 1 coat, 1 pair of boots, and 3 shirts for $99 + $56 + 3($12) = $191. 6. Mrs. Liston and her friends would like to buy a shirt, a pair of jeans, and a sweater for 32 people. They will hold a dinner to raise the money needed to buy these items on sale. They plan to estimate the money needed. Will this help them set an appropriate goal for their dinner? Explain your decision. Possible answer: No; Possible explanation: The estimated cost of a shirt, jeans, and a sweater is $10 + $30 + $40 = $80. The estimated cost of these items for 32 people is 30($80) = $2,400. The exact cost of a shirt, jeans, and a sweater is $12 + $25 + $42 = $79. The exact cost for 32 people is 32($79) = $2,528. $2,400 < $2,528, so $2,400 is not an appropriate goal. 7. Explain how to write a word problem that requires multiplication and addition to solve using the information in the table. Give a problem in your explanation. I would start by writing the answer first. To get an answer, I would multiply some prices by the number of items, so 3 pairs of boots on sale would be $3($56) = $168 and 1 pair of jeans would be $25. Then I would add the prices together to know the amount to use in my question; $168 + $25 = $193. I know that $193 is a little less than $200. Then I would write the question, such as Mrs. Liston s aunt sends her $200 for the clothing drive. What can Mrs. Liston buy with the money her aunt sent? Math Expressions 41 Houghton Mifflin Harcourt Publishing Company Unit 2 Performance Assessment
Performance Assessment Rubric An Exemplary Response (3 points) Correctly uses place-value understanding and multiplication concepts to determine the total cost of more than one of the same kind of item Correctly adds, subtracts, and multiplies whole number money amounts to find the total cost of different kinds of items Correctly estimates a product and is able to determine if the estimate is appropriate Uses strategies that exemplify the mathematical practices identified for this task A Proficient Response (2 points) Correctly uses place-value understanding and multiplication concepts to determine the total cost of more than one of the same kind of item Correctly adds, subtracts, and multiplies whole number money amounts to find the total cost of different kinds of items with minor errors Estimates a product and analyzes the appropriateness of the estimate Shows evidence of using strategies that are based in the mathematical practices identified for this task An Acceptable Response (1 point) Uses multiplication concepts to determine the total cost of more than one of the same kind of item making few or minor errors Adds, subtracts, and multiplies whole number money amounts to find the total cost of different kinds of items making some errors May have difficulty estimating and determining whether the estimate is appropriate Completes the task, but approach lacks a clear strategy and evidence of the mathematical practices identified for this task A Limited Response (0 points) Struggles with using multiplication concepts to determine the total cost of more than one of the same kind of item Makes multiple computational errors when adding, subtracting, and multiplying whole number money amounts to find the total cost of different kinds of items Does not make meaningful estimations Makes failed attempts to complete the task Math Expressions 42 Houghton Mifflin Harcourt Publishing Company Unit 2 Performance Assessment