Objectives To review and provide practice with the partialproducts algorithm for 1-digit multipliers.

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1 Objectives To review and provide practice with the partialproducts algorithm for -digit multipliers. Teaching the Lesson materials Key Activities Students review the partial-products algorithm. They practice this method for -digit multipliers, using mental and paper-and-pencil procedures. Key Concepts and Skills Write numbers in expanded notation. [Number and Numeration Goal ] Add multidigit numbers. [Operations and Computation Goal ] Use basic facts to compute extended facts. [Operations and Computation Goal ] Use the partial-products algorithm to solve multiplication problems with -digit multipliers. [Operations and Computation Goal ] Estimate whether a product is in the tens, hundreds, thousands, or more. [Operations and Computation Goal ] Apply the Distributive Property of Multiplication over Addition. [Patterns, Functions, and Algebra Goal ] Math Journal, pp.8 and 9 Study Link 5 Teaching Aid Master (Math Masters, p. or ) slate Key Vocabulary partial-products method partial product Ongoing Assessment: Informing Instruction See page 9. Ongoing Assessment: Recognizing Student Achievement Use journal page 8. [Operations and Computation Goal ] Ongoing Learning & Practice materials Students use personal references for customary units of length to estimate lengths of objects. Students practice and maintain skills through Math Boxes and Study Link activities. Differentiation Options Math Journal, pp. 98, 7, and Study Link Master (Math Masters, p. 5) tape measure or ruler materials READINESS Students model -digit times -digit multiplication problems with base- blocks. READINESS Students explore patterns in extended facts. ENRICHMENT Students use multiplication to solve an old puzzle about houses, cats, whiskers, and fleas. Teaching Masters (Math Masters, pp. 5 and 5) Transparencies (Math Masters, pp. and ) base- blocks; erasable marker; transparent tape See Advance Preparation Additional Information Advance Preparation For the optional Readiness activity in Part, make transparencies of Math Masters, pages and, cut them apart, and tape them together with transparent tape. Technology Assessment Management System Journal page 8, Problems and See the itlg. Lesson 5 5 7

2 Getting Started Mental Math and Reflexes Pose extended multiplication facts problems. Suggestions: 5 = 7 = = = =, 7 =, 5 = 5, 8 7 = 5, 9 = 5, Math Message Paul s new baby sister sleeps about hours per day. About how many hours does she sleep in one week? Study Link 5 Follow-Up Partners compare answers. Students should focus on the number models they wrote for their estimates. Teaching the Lesson Math Message Follow-Up WHOLE-CLASS DISCUSSION Have students share solution strategies. Students may have tried either of these written strategies: Use an algorithm to find the product of 7 and. Use repeated addition: Add seven times. Or, they may have used one of these mental strategies: Multiply Double the result. 5 5 Multiply 7. Subtract 7 from the result. 8 If no one shares it, suggest the following strategy: Multiply 7. 7 Multiply 7. Add the results. 7 Tell the class that this last strategy makes use of the place value of each digit. It is the strategy on which the partial-products method, the multiplication method students will review in this lesson, is based. Finding Products Mentally WHOLE-CLASS Pose easy multiplication problems involving -digit times -digit numbers. Have students solve them mentally, write the answers on their slates, and at a signal, display the answers. Emphasize to students that they may write partial answers on their slates, but not the original problem. Ask them to circle the final answer. 8 Unit 5 Big Numbers, Estimation, and Computation

3 Discuss solution strategies after each problem. Do not insist that students use the last strategy mentioned in the Math Message Follow-Up, but encourage its use. Keep this activity brief, especially if students can solve the problems with ease. Suggestions: 5 = 8 7 = 9 = 9 8 = 98 7 = 5 9 = 5 Demonstrating the Partial- Products Algorithm for -Digit Multipliers (Math Masters, p. or ) Give each student a sheet of computation grid paper (Math Masters, page or ). Write the following problem on the board. If you think your class is not ready to start with a -digit factor, start with a -digit times -digit problem instead. 89 WHOLE-CLASS NOTE Like the addition and subtraction algorithms in Unit, the partial-products algorithm is a low-stress algorithm. Even if students have used a standard multiplication algorithm or some other multiplication method in the past, ask them to use the partial-products algorithm to solve the problems in this lesson. Ask the class to estimate whether the answer will be in the tens, hundreds, thousands, or more. thousands About how many thousands? About 5 thousands, but less than thousands. 89 is close to, but less than,,. Next, have students find the exact product on their grid paper. Ask a volunteer to demonstrate a solution method on the board. If others used different methods, ask them to demonstrate them. If no one used the partial-products method for multiplying, demonstrate it on the board. (See margin.) In this method, multiplication is usually done from left to right. This ensures that the most important products the largest ones are calculated first. But it is not incorrect for a student to multiply from right to left. Each part of the calculation, that is, each partial product, is written on a separate line. Then the partial products are added. This is usually very simple and has the benefit of providing practice with column addition.,s + 5, s 8 8 s 5 s 9 Ò [8s] or 8 Ò [s] or Ò [9s] or 9 Pose a few more multiplication problems until most students seem to understand the partial-products method. Ongoing Assessment: Informing Instruction When students are explaining the steps in the partial-products algorithm, watch for those who say 8 : the 8 in the problem to the right, for example, is in the hundreds place and has a value of 8, not 8. Encourage students to think and say [8s] or 8. The notation [8s], introduced in Third Grade Everyday Mathematics, is read as eight-hundreds. Lesson 5 5 9

4 Date 5 5 Time The Partial-Products Method Multiply using the partial-products method. Show your work in the computation grid on page ,. 7 5.,5.,7 Estimate whether your answer will be in the tens, hundreds, thousands, or more. Write a number model to show how you estimated. Circle the correct box. Then calculate the answer. Show your work on page China has the world s longest school year at 5 days. How many school days are in 7 years? a. Number model: b. Calculate the answer. days of school 8. People living in the United States eat about pounds of fresh fruit in one year. About how many pounds of fresh fruit would a family of eat in one year? a. Number model: s s,s,757 Sample answer: 78 s s,s Student Page 75 8, Sample answer: 5,5,s,s,s,,s,s,,s b. Calculate the answer. About pounds of fresh fruit,87, 8 Using the Partial-Products Algorithm with -Digit Multipliers (Math Journal, pp. 8 and 9) Adjusting the Activity Students complete journal page 8 independently. Partners compare their answers. Encourage students to write the number model for the partial products if they are not using mental math to solve the extended facts. For example: [s] or, A U D I T O R Y K I N E S T H E T I C T A C T I L E V I S U A L 9. Explain how estimation can help you decide whether an answer to a multiplication problem makes sense. Sample answer: By estimating, I can quickly get an answer that should be close to the exact answer. Math Journal, p. 8 Ongoing Assessment: Recognizing Student Achievement Journal page 8 Problems and Use journal page 8, Problems and to assess students ability to use the partial-products algorithm to multiply a -digit number by a -digit number. Students are making adequate progress if they can correctly calculate and then add the partial products. Some students may be able to solve Problems, which involve the multiplication of a -digit number by a - or -digit number. [Operations and Computation Goal ] Ongoing Learning & Practice Date 5 5 Student Page Time My Measurement Collection for Units of Length Use your personal references on journal page 98 to estimate the length or height of an object or distance in inches, feet, or yards. Describe the object or distance, and record your estimate in the table below. Then measure the object or distance, and record the actual measurement in the table. Object or Distance Estimated Length Actual Length Answers vary. 8 Estimating Lengths Using Personal References (Math Journal, pp. 98 and ) Students use their personal references for customary units of length to help them estimate the lengths of various classroom objects in inches, feet, and yards. Then they measure these objects with rulers or tape measures to check the accuracy of their estimates. Math Boxes 5 5 (Math Journal, p. 7) Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 5-7. The skill in Problem 5 previews Unit content. Math Journal, p. Unit 5 Big Numbers, Estimation, and Computation

5 Writing/Reasoning Have students write a response to the following: Donato said that there is more than one correct answer for each of the estimates in Problem. Do you agree or disagree? Explain. Sample answer: Yes. There can be more than one correct answer because it depends on the place value to which students round. For example, the following are both reasonable estimates for Problem b: +,8 +, =,8 and +, +, =,. Study Link 5 5 (Math Masters, p. 5) Date 5 5 Math Boxes Time. In, about,5, people living in the United States had been born in other countries. The circle graph shows where these people were born. a. Where were most of these people born? Latin America b. About what fraction of the people were born in Asia?. Estimate the sum. Write a number model to show how you estimated. a , Number model: b. 58,79, Student Page Sample answers:,,, Number model:,,,. Complete. Immigration Statistics Other Europe Rule: Multiply by 7. in out , Latin America Asia 5,, 8 Home Connection Students practice using the partial-products algorithm to find products with -digit multipliers.. Write two hundred million, three thousand, eighty-eight using digits. Fill in the circle next to the best answer. A.,,88 B.,,88 C.,,88 D.,,88 5. Look at the grid below. a. In which column is the circle located? C b. In which row is the circle located? A B C Differentiation Options Math Journal, p. 7 READINESS Modeling Multiplication with Base- Blocks (Math Masters, pp. and ) SMALL-GROUP 5 Min To explore the partial-products algorithm using a concrete model, have students model -digit times -digit multiplication problems with base- blocks. Place taped transparencies of Math Masters, pages and on a table. To model 8, use an erasable marker to mark off a portion of the grid that is squares high and 8 squares wide ( by 8). Study Link Master Name Date Time STUDY LINK 5 5 Multiplication Multiply using the partial-product method. Show your work in the grid below. 9,,9. 5 º 7. 8 º 75., Maya goes to school for 7 hours each day. If she does not miss any of the 8 school days, how many hours will Maya spend in school this year? a. Estimate whether the answer will be in the tens, hundreds, thousands, or more. Write a number model to show how you estimated. Circle the box that shows your estimate. Number model: 7, s s,s,7 b. Exact answer: hours,s,s,,s 5. The average eye blinks once every 5 seconds. Is that more than or less than a hundred thousand times per day? Explain your answer. Sample answer: Less; / 5 blinks per minute; º 7 blinks per hour; 7 º 7,8 blinks per day Start here. Array model of 8 Practice 7, , ,8 5,798,58,89, 8.,7, ,5,87 Math Masters, p. 5 5 Lesson 5 5

6 5 5 Teaching Master Name Date Time Patterns in Extended Facts. Use base- blocks to help you solve the problems in the first columns. Use the patterns to help you solve the problems in the third column. Use a calculator to check your work. º º º º º º, º º, º, Ask students to cover the array using as few base- blocks as possible.. Use what you learned in Problem to help you solve the problems in the table below. Use a calculator to check your work. º 8 º 8 º 8 º 8 º 8 º 8, º 8 º 8, º 8,. Explain how knowing º can help you find the answer to º. Sample answer: I know 8, so is just 8 with two zeros added on, or 8. I added on two zeros because there is a total of two zeros in the numerals and.. Make up and solve some problems of your own that use this pattern. Answers vary. Start here. Base- block model of 8 Math Masters, p. 5 Now match each part of the -by-8 array with a partial product. There are longs in each of rows. These cover 8 squares. There are 8 cubes in each of rows. These cover 8 squares. The longs and cubes cover 8 squares in all. Erase the transparencies. Use the transparencies and base- blocks to solve additional -digit times -digit problems. READINESS Exploring Patterns in Extended Facts (Math Masters, p. 5) PARTNER 5 5 Min To explore patterns in extended facts, have students use base- blocks to model the problems on Math Masters, page 5. Have students describe the patterns they see in Problem. Name Date Time 5 5 An Old Puzzle An old puzzle begins like this: A man has houses. In each house, he keeps cats. Each cat has whiskers. On each whisker sit fleas.. Answer the last line of the puzzle: Houses, cats, whiskers, fleas how many are there in all?,55. Use number models or illustrations to explain how you solved the puzzle. Sample answer: There are houses, cats, whiskers,,9 fleas. The total is,9,55. ENRICHMENT Solving an Old Puzzle (Math Masters, p. 5) PARTNER 5 5 Min To apply students multiplication skills, have them solve an old puzzle involving numbers of houses, cats, whiskers, and fleas. Math Masters, page 5 Unit 5 Big Numbers, Estimation, and Computation

7 Objectives To introduce and provide practice with the partial-products algorithm for -digit multipliers. Teaching the Lesson materials Key Activities Students learn how to extend the partial-products algorithm to -digit multipliers. They make rough estimates and then use the partial-products method. Key Concepts and Skills Write numbers in expanded notation. [Number and Numeration Goal ] Use the partial-products algorithm to solve multiplication problems with -digit multipliers. [Operations and Computation Goal ] Estimate whether a product is in the tens, hundreds, thousands, or more. [Operations and Computation Goal ] Apply the Distributive Property of Multiplication over Addition. [Patterns, Functions, and Algebra Goal ] Math Journal, pp. and Study Link 5 5 Teaching Aid Masters (Math Masters, p. or ; p. 88 or 89; optional) slate See Advance Preparation Ongoing Assessment: Recognizing Student Achievement Use Mental Math and Reflexes. [Operations and Computation Goal ] Ongoing Assessment: Informing Instruction See page 5. Ongoing Learning & Practice materials Students play Name That Number to practice representing numbers in different ways. Students practice and maintain skills through Math Boxes and Study Link activities. Differentiation Options Math Journal, p. Student Reference Book, p. 5 Study Link Master (Math Masters, p. 5) Game Master (Math Masters, p. 89; optional) per partnership: deck of number cards " by 5" index cards (optional); calculator (optional) materials READINESS Students model multiplication problems with base- blocks. ENRICHMENT Students solve a multistep number story involving a dart game. ENRICHMENT Students complete Venn diagrams. Teaching Masters (Math Masters, pp. 55 and 5) Transparencies (Math Masters, pp. and ) base- blocks erasable marker; transparent tape See Advance Preparation Additional Information Advance Preparation For Part, place copies of Math Masters, page or near the Math Message. For the optional Readiness activity in Part, make transparencies of Math Masters, pages and ; cut them apart, and tape them together with transparent tape. Technology Assessment Management System Mental Math and Reflexes See the itlg. Lesson 5

8 Getting Started Mental Math and Reflexes Write multiplication problems on the board. Have students write number models to show their estimates. Suggestions: Sample answers are given ,8 59, , 7,5 5, 5 8,99 5 8,, 7,7 7,, Math Message Solve the following problems on a computation grid: 9 = 8 =,88 = =,9 Study Link 5 5 Follow-Up Have students compare answers and share how they decided whether an average person blinks more than or fewer than, times per day. Ongoing Assessment: Recognizing Student Achievement Mental Math and Reflexes Use Mental Math and Reflexes to assess students ability to estimate reasonable solutions to whole-number multiplication problems. Students are making adequate progress if they can write appropriate number models for the and problems. Some students may be able to estimate products for the problems. [Operations and Computation Goal ] Date 5 Time Multiplication Number Stories Follow these steps for each problem. a. Decide which two numbers need to be multiplied to give the exact answer. Write the two numbers. b. Estimate whether the answer will be in the tens, hundreds, thousands, or more. Write a number model for the estimate. Circle the box to show your estimate. c. On the grid below, find the exact answer by multiplying the two numbers. Write the answer.. The average person in the United States drinks about cups of soda per month. About how many cups of soda is that per year? a. b. c. numbers that give number model for your estimate exact answer the exact answer. Eighteen newborn hummingbirds weigh about ounce. About how many of them does it take to make pound? ( pound ounces) 8 s s,s,s a. b. c. 7,s,,s 88 numbers that give number model for your estimate exact answer the exact answer s s,s Student Page,s,s,,s Teaching the Lesson Math Message Follow-Up Go over the answers. Ask: How would you solve 9 in your head? Sample answer: Multiply and then subtract from the product. How would you solve 8 in your head? Sample answer: Multiply 8 and and then add the two products. Estimating Products (Math Journal, pp. and ) Tell students that in this lesson they will apply the partialproducts algorithm to multiply a -digit number by a -digit number. WHOLE-CLASS DISCUSSION PARTNER Math Journal, p. Unit 5 Big Numbers, Estimation, and Computation

9 For each problem on pages and, students first decide which two numbers need to be multiplied to give the exact answer (Step a). In Step b, they make a rough estimate of that product and write a number model that shows how they made that estimate. They should not do Step c at this time. Do Problem as a class: Step a An average person drinks about cups of soda in month. In year, a person will drink times that amount. To find the amount of soda a person drinks in one year, you would multiply. Write, but do not calculate the exact answer at this time. Step b To estimate the answer, round to and write a number model for the rough estimate:. Or round to and write a number model for the rough estimate: 7. Looking at the number models, you can tell that the answer will be in the hundreds, so circle s. Have students work with a partner to complete Steps a and b for the rest of the problems. Date 5 Time Multiplication Number Stories continued. A test found that a lightbulb lasts an average of days after being turned on. About how many hours is that? a. b. c. numbers that give number model for your estimate exact answer the exact answer. A full-grown oak tree loses about 78 gallons of water through its leaves per day. About how many gallons of water is that per year? 78 s s,s 5,,s,s,,s 8,,5 8,7 a. b. c. numbers that give number model for your estimate exact answer the exact answer s s,s Student Page,s Math Journal, p.,s,,s Extending the Partial-Products Algorithm to -Digit Multipliers (Math Journal, pp. and ) Demonstrate how to use the partial-products algorithm to find the exact answer and check the estimate for Problem on journal page. (See margin.) Work from left to right. Point out that each part of one factor is multiplied by each part of the other factor. Ongoing Assessment: Informing Instruction WHOLE-CLASS As students say each step, watch for those who say, for example times instead of sixties or times. Remind students to consider the value of each digit. Problem :? s + 7 s s Ò [s] or Ò [s] or Ò [s] or Ò [s] or Do several more problems with the class. Suggestions: 8 5 = =,7 = 88 8 =,5 Adjusting the Activity Organize the multiplication problems as follows: ( ) ( ) Students then add the partial products in the table to find the total: 7. A U D I T O R Y K I N E S T H E T I C T A C T I L E V I S U A L Lesson 5 5

10 Using the Partial-Products Algorithm (Math Journal, pp. and ) PARTNER Students complete the remaining problems on journal pages and in the same way. They check their estimates and complete Step c by finding the exact answer using the partialproducts algorithm. Adjusting the Activity Ask students to respond to the following question in a Math Log or on an Exit Slip (Math Masters, page 88 or 89): Explain how the partial-products algorithm is similar to finding a team s score in a game of Multiplication Wrestling. Look for students to note that every part of one factor is multiplied by every part of the other factor. A U D I T O R Y K I N E S T H E T I C T A C T I L E V I S U A L Links to the Future Do not expect all students to master the partial-products algorithm for two -digit multipliers at this time. This algorithm will be practiced and reinforced throughout Fourth Grade Everyday Mathematics. Lesson 9-8 introduces multiplication of decimals. This is a Grade 5 Goal. Date 5 Math Boxes Student Page Time Ongoing Learning & Practice Playing Name That Number (Student Reference Book, p. 5; Math Masters, p. 89) PARTNER. a. Measure the line segment to the nearest inch. About 5 inches b. Draw a line segment that is half as long as the one above. c. How long is the line segment you drew? About inches 8 Students play Name That Number to practice representing numbers in different ways. See Lesson - for additional information.. Estimate the product. Write a number model to show how you estimated. a. 8 Number model: b Number model: Sample answers: 5, 7 7,. Write each number using digits. a. three hundred forty-two thousandths. b. six and twenty-five hundredths.5. Multiply. Use the partial-products method., 5 º If you remove 7 gallons per day from a 5-gallon water tank, how many days will it take to empty the tank? About days Math Boxes 5 (Math Journal, p. ) Mixed Practice Math Boxes in this lesson are linked with Math Boxes in Lessons 5-8 and 5-. The skill in Problem 5 previews Unit content. Writing/Reasoning Have students write a response to the following: Devon wrote, for Problem a. Explain the error he might have made. Sample answer: He wrote thousands, not thousandths. Math Journal, p. Unit 5 Big Numbers, Estimation, and Computation

11 Study Link 5 (Math Masters, p. 5) READINESS Home Connection Students practice using the partial-products algorithm with -digit multipliers. Differentiation Options Modeling Multiplication with Base- Blocks (Math Masters, pp. and ) SMALL-GROUP 5 Min To explore the partial-products algorithm using a concrete model, have students use base- blocks to model multiplication problems involving two -digit numbers. Place taped transparencies of Math Masters, pages and on a table. To model 7 *, use an erasable marker to mark off a portion of the grid that is 7 squares high and squares wide (7 by ). Name Date Time STUDY LINK 5 More Multiplication Multiply using the partial-products algorithm. Show your work.,7,8. 58 º 7. 5 º, 8. º 5. 7 º 8 5.,. 7, º 7 º 5 Try This 7,7 Study Link Master 7, 7. º º 9 Practice 9. 5,7 8 5,9.,7,78 9,79. 5,58,7. 9,,7 Math Masters, p. 5,75 8 Start here. Array model of 7 Lesson 5 7

12 Name Date Time 5 A Dart Game Vanessa played a game of darts. She threw 9 darts. Each dart hit the target. She scored 55 points. Where might each of her 9 darts have hit? Use the table to show all possible solutions. 5 5 Ask students to cover the array using as few base- blocks (flats, longs, and cubes) as possible Math Masters, page 55 Start here. Base- block model of 7 Name Date Time 5 Sorting Numbers Study the Venn diagrams in Problems and. Label each circle and add at least one number to each section. Sample p answers:.. Try This 8 5, 7, 8,,, divisible by 8 5, 5 Teaching Master as a factor 75, 99,,,5,,5 5 7, multiples of 8,,5 77 build arrays with 5 rows multiples of 7 Sample answers: Sample answers: Now match each part of the 7-by- array with a partial product. Match the flats with. These cover squares. Match the vertical longs with. These cover squares. There are 7 rows with longs in each row. These cover 7 squares. There are 7 rows with cubes in each row. These cover 7 squares. There are 5 ( ) cubes in all. Erase the transparencies. Use the transparencies and base- blocks to model and solve other -digit-times--digit problems. ENRICHMENT Scoring a Dart Game (Math Masters, p. 55) To apply students multidigit multiplication skills, have them use various strategies to solve a multistep number story involving a dart game with more than one possible answer. Ask students to explain how they know they found all the solutions. ENRICHMENT Solving Venn Diagram Puzzles (Math Masters, p. 5) 5 5 Min To apply students understanding of extended multiplication and division facts, have them solve Venn diagram puzzles based on factors. PARTNER 5 5 Min Math Masters, p. 5 8 Unit 5 Big Numbers, Estimation, and Computation

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