Partial-Products Multiplication (Part 2)

Transcription

1 Partial-Products Multiplication (Part ) Objectives To introduce and provide practice with the partial-products algorithm for -digit multipliers. epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment Management Common Core State Standards Curriculum Focal Points Interactive Teacher s Lesson Guide Teaching the Lesson Ongoing Learning & Practice Differentiation Options 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 ] Key Activities Students learn how to extend the partialproducts algorithm to -digit multipliers. They make rough estimates and then use the partial-products method. Ongoing Assessment: Recognizing Student Achievement Use Mental Math and Reflexes. [Operations and Computation Goal ] Ongoing Assessment: Informing Instruction See page 5. Playing Name That Number Student Reference Book, p. 5 Math Masters, p. 89 (optional) per partnership: deck of number cards (the Everything Math Deck, if available) Students practice representing numbers in different ways. Math Boxes 5 Math Journal, p. Students practice and maintain skills through Math Box problems. Study Link 5 Math Masters, p. 5 Students practice and maintain skills through Study Link activities. READINESS Modeling Multiplication with Base- Blocks transparencies of Math Masters, pp. and base- blocks erasable marker transparent tape Students explore the partial-products algorithm using a concrete model. Scoring a Dart Game Math Masters, p. 55 Students solve a multistep number story involving a dart game. Solving Venn Diagram Puzzles Math Masters, p. 5 Students apply their understanding of extended multiplication and division facts. Writing Multiplication Number Stories Students write and solve multiplication number stories. Materials Math Journal, pp. and Study Link 5 5 Math Masters, p. or ; p. 88 or 89 (optional) slate 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, and tape them together. Teacher s Reference Manual, Grades pp. 9,,,, Lesson 5

2 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. 5 5 = 5 = = =,8 59 =, 8 5 = 75 7, 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. NOTE For additional practice using a standard procedure for rounding whole numbers to the nearest ten and hundred, see 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 ] Teaching the Lesson Date Student Page Time Math Message Follow-Up WHOLE-CLASS DISCUSSION 5 Multiplication Number Stories Follow these steps for each problem. a. Decide which two numbers need to be multiplied to give. 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 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.. 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 s s,s,s,s,,s 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. Math Journal, p. Unit 5 Big Numbers, Estimation, and Computation

3 For each problem on pages and, students first decide which two numbers need to be multiplied to give (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.,5 s s,s,s,s,,s. 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? a b. 8 =, c. 8,7 s s,s Student Page,s Math Journal, p.,s,,s Extending the Partial-Products Algorithm to -Digit Multipliers (Math Journal, pp. and ) WHOLE-CLASS Demonstrate how to use the partial-products algorithm to find 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 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

4 Algorithm Project The focus of this lesson is partial products. To teach U.S. traditional multiplication, see Algorithm Project 5 on page A. Using the Partial-Products Algorithm (Math Journal, pp. and ) Students complete the remaining problems on journal pages and in the same way. They check their estimates and complete Step c by finding 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. 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. Fluently multiplying whole numbers using the standard algorithm is expected in Grade 5. Lesson 9-8 introduces multiplication of decimals. This is a Grade 5 Goal. 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 Ongoing Learning & Practice Playing Name That Number (Student Reference Book, p. 5; Math Masters, p. 89) Students play Name That Number to practice representing numbers in different ways. See Lesson - for additional information. Date 5 Math Boxes Student Page Time Math Boxes 5 (Math Journal, p. ) INDEPENDENT. 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. Estimate the product. Write a number model to show how you estimated. a. 8 Number model: b Sample answers: 5, Number model: 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 8 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. Study Link 5 (Math Masters, p. 5) Home Connection Students practice using the partial-products algorithm with -digit multipliers. INDEPENDENT Math Journal, p. Unit 5 Big Numbers, Estimation, and Computation

5 Study Link Master Differentiation Options READINESS Modeling Multiplication with Base- Blocks (Math Masters, pp. and ) SMALL-GROUP 5 Min 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 7, 7. º º 9 8 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 ). Practice 9. 5,7 8 5,9.,7,78 9,79,75. 5,58,7. 9,,7 Math Masters, p. 5 Start here. Array model of 7 Ask students to cover the array using as few base- blocks (flats, longs, and cubes) as possible. Start here. Base- block model of 7 Lesson 5 7

6 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 Math Masters, page 55 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. Scoring a Dart Game (Math Masters, p. 55) INDEPENDENT 5 5 Min 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. Solving Venn Diagram Puzzles (Math Masters, p. 5) 5 5 Min 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... Try This 8 5, 7, 8,,, divisible by 8 5, 5 Teaching Master as a factor 75, 99,,,5,,5 5 7, Sample p answers: multiples of 8,,5 77 build arrays with 5 rows Math Masters, p multiples of 7 Sample answers: Sample answers: To apply students understanding of extended multiplication and division facts, have them solve Venn diagram puzzles based on factors. Writing Multiplication Number Stories 5 5 Min To apply students understanding of multiplication algorithms, have them write and solve multistep multiplication number stories. Then have them record a number model using a letter for the unknown. Some students may be interested in writing and solving problems that involve distances, intervals of time, liquid volumes, masses of objects, or money. Stories may look similar to the following: Simon is filling the ketchup bottles at his restaurant. Each bottle holds ounces of ketchup. There are tables in each room and rooms in the restaurant. How many ounces of ketchup will he need to fill one bottle for each table? Answer: 57 oz; Number model with unknown: ( ) = n; Number model with answer: ( ) = 57 Provide opportunities for students to revise and share their writing. Then have partners solve each other s problems. 8 Unit 5 Big Numbers, Estimation, and Computation