760 Unit 9 Multiplication and Division

Teaching the Lesson materials

Key ActivitiesChildren explore lattice multiplication as an alternative method for multiplying multidigit numbers.

Key Concepts and Skills• Use addition facts to solve lattice multiplication problems.

[Operations and Computation Goal 1]• Use multiplication facts to solve lattice multiplication problems.

[Operations and Computation Goal 3]• Explore a strategy for solving problems involving multiplication of 1-digit by multidigit numbers.

[Operations and Computation Goal 4]

Key Vocabulary lattice multiplication

Ongoing Assessment: Informing Instruction See pages 762 and 763.

Ongoing Learning & Practice materialsChildren play Factor Bingo.

Children practice and maintain skills through Math Boxes and Home Link activities.

Ongoing Assessment: Recognizing Student Achievement Use journal page 228.[Geometry Goal 2]

Differentiation Options materials

Children multiply and divide multiples of 10 using time intervals in the musical composition Vexations.

Children practice multiplication using the partial-products algorithm.

� Math Journal 2, p. 227� Teaching Master (Math Masters,

p. 294)� lined paper� dictionary

EXTRA PRACTICEENRICHMENT

3

� Math Journal 2, p. 228� Student Reference Book, pp. 285

and 286� Home Link Master (Math Masters,

p. 293� Game Master (Math Masters, p. 448)� counters� number cards 2–9 (4 of each)

2

� Math Journal 2, pp. 226 and 227� Student Reference Book, pp. 70–72� Home Link 9�8� calculator� blank paper� counters (optional)� index cards (optional)

1

Objective To introduce the lattice method of multiplication.

Technology Assessment Management SystemMath Boxes, Problem 5See the iTLG.

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� Math Message Follow-UpQuickly review the answers. 192; 3,565; 2,632 Have children savetheir work for reference in the following activity.

� Exploring the Lattice Methodof Multiplication(Math Journal 2, p. 226; Student Reference Book, pp. 70–72)

This activity exposes children to an alternate algorithm formultiplication. It also provides an opportunity for cooperativeproblem solving.

Divide the class into groups of two or three, and call children’sattention to the problems in Column A on journal page 226. Pointout that these problems are the same ones they solved in the MathMessage but that the method used to solve them is one thatchildren might not have seen before. Ask groups to try to figureout how this method works. Once children think they understandhow to use it, have them try to solve the problems in Column Busing that method.

After everyone has had time to work the problems, bring the classtogether to share their discoveries. Note that Problem 3 involvesrenaming. Ask: Can someone explain what to do if a diagonal sumis a 2-digit number? Write the ones digit of the sum, and then addthe tens digit to the sum in the next diagonal.

WHOLE-CLASS ACTIVITY

WHOLE-CLASSDISCUSSION

1 Teaching the Lesson

Lattice MultiplicationLESSON

9� 9

Date Time

Megan has a special way of doing multiplication problems. She calls itlattice multiplication. Can you figure out how she does it?

Study the problems and solutions in Column A. Then try to use latticemultiplication to solve the problems in Column B.

Column A

3 � 64 �

5 � 713 �

7 � 376 �

Column B

1. 4 � 65 �

2. 6 � 815 �

3. 9 � 634 � 5,706

4,890

260

2,632

3,565

192

3

6 4

12

181

9 2

4

6 5

242

6 0

20

5

7 1

353

5 6

05

15

5

3

6

8 1

484

8 9

06

30

0

5

7

3 7

212

6 3

41

942

2

6

9

6 3

545

7 021

73

66

4

Math Journal 2, p. 226

Student Page

Lesson 9�9 761

Getting Started

Math MessageSolve without a calculator. Show your work on paper.

3 � 64

5 � 713

7 � 376

Home Link 9�8 Follow-Up Have children share their solution strategies. Theymay include modeling the problems with picturesor counters.

Mental Math and Reflexes Pose calculator puzzles such as the following:

Enter Change to How?

8 32 � 4

20 4 � 5

12 48 � 4

72 9 � 8

35 140 � 4

224 28 � 8

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762 Unit 9 Multiplication and Division

Explain to the class that this method of finding products is calledlattice multiplication. To support English language learners,discuss the meanings of the word lattice and write latticemultiplication on the board. A lattice is a structure that hascrossed strips that are used as a screen. In math, a lattice is a boxwith squares and diagonals that is used for multiplication.

To multiply using the lattice method:

1. Write the factors on the outside of the grid, one across the topand one down the right side.

2. Multiply each digit in one factor by each digit in the other factor.

3. Add the numbers inside the lattice within each diagonal. If thesum on a diagonal exceeds 9, the excess 10s are added in thenext diagonal.

Ongoing Assessment: Informing InstructionWatch for children who confuse the numbers in the lattice. Have them use oneor more of the following strategies:• Use an index card to mark their place as they add

along each diagonal.

• Cross out the factors of the problem before adding so those numbers are not accidentally added along with the numbers within the grid.

• Try this alternative:

Children should not be required to learn this method, but theyshould try it. If they like it, they should not be discouraged fromusing it. Having choices among algorithms is important. Giventhose choices, most children will choose the ones that work best forthem. Have children read more about the lattice multiplicationmethod on pages 70–72 in the Student Reference Book.

2

3

5 408

122

4 2

10

15

thou

sand

shu

ndre

dste

nson

es

5 4

2

3

01

112

242

1

5

801

5 4

2

3

01

112

242

1

5

801

5 4

2

3

01

112

24

5

80

21

1

NOTE Many people view lattice multiplicationas a trick. However, if you look carefully,place value is evident within the lattice.

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� Practicing Lattice Multiplication(Math Journal 2, p. 227)

Children work with a partner to complete journal page 227.Circulate and assist as necessary.

Ongoing Assessment: Informing InstructionWatch for children who make mistakes as they work their way through the latticemethod. Check to see whether their mistakes are a result of incorrect fact recallor confusion about the steps.

� Playing Factor Bingo(Math Masters, p. 448; Student Reference Book,pp. 285 and 286)

Children play Factor Bingo to practice identifying factors. Thisgame was introduced in Lesson 9-6. If necessary, review the rules for the game on pages 285 and 286 in the Student Reference Book.

PARTNER ACTIVITY

2 Ongoing Learning & Practice

PARTNER ACTIVITY

Lesson 9�9 763

Lattice Multiplication PracticeLESSON

9� 9

Date Time

1. 8 � 45 �

3. 5 � 23 �

5. 6 � 431 �

2. 9 � 37 �

4. 3 � 124 �

6. 7 � 209 � 1,463

372

333

2,586

115

360

8

4 5

323

6 0

40 9

3 721

733 3

63

52 3

101

1 5

15 3

1 20

303 7

06

12

2

4

64 3

242

5 8

18

06

6

17

2 01

414 6

00

63

3

9

Math Journal 2, p. 227

Student Page

Factor BingoMaterials � number cards 2–9 (4 of each)

� 1 Factor Bingo game mat for each player (Math Masters, p. 448)

� 12 counters for each playerPlayers 2 to 4Skill Finding factors of a numberObject of the game To get 5 counters in a row, column, ordiagonal; or to get 12 counters anywhere on the game mat.Directions

1. Fill in your own game mat. Choose 25 different numbersfrom the numbers 2 through 90.

2. Write each number you choose in exactly 1 square onyour game mat grid. Be sure to mix the numbers up asyou write them on the grid; they should not all be inorder. To help you keep track of the numbers you use,circle them in the list below the game mat.

3. Shuffle the number cards and place them number-sidedown on the table. Any player can turn over the top card.This top card is the “factor.”

4. Players check their grids for a number that has the cardnumber as a factor. Players who find such a number coverthe number with a counter. A player may place only 1counter on the grid for each card that is turned over.

5. Turn over the next top card and continue in the same way.You call out “Bingo!” and win the game if you are the firstplayer to get 5 counters in a row, column, or diagonal. Youalso win if you get 12 counters anywhere on the game mat.

6. If all the cards are used before someone wins, shuffle thecards again and continue playing.

Games

Student Reference Book, p. 285

Student Page Factor Bingo Game Mat

448

Name Date Time

2 3 4 5 6 7 8 9 1011 12 13 14 15 16 17 18 19 2021 22 23 24 25 26 27 28 29 3031 32 33 34 35 36 37 38 39 4041 42 43 44 45 46 47 48 49 5051 52 53 54 55 56 57 58 59 6061 62 63 64 65 66 67 68 69 7071 72 73 74 75 76 77 78 79 8081 82 83 84 85 86 87 88 89 90

Write any of the numbers 2 through 90 on the gridabove.

You may use a numberonly once.

To help you keep track of the numbers you use,circle them in the list.

132

4

Math Masters, p. 448

Game Master

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764 Unit 9 Multiplication and Division

5. This shape is a .

It has sides and vertices.

1010decagon

3. 16 books in all. 3 books per shelf. How many shelves? How many books left over? 1 book

5 shelves

Date Time

2. Use the partial-products algorithmto solve. Show your work.

238 574� 6 � 5

2,8701,428

4. Draw an angle that measuresbetween 0° and 90°.

Sample answer:

6. What is the median number ofhours children sleep each night?

hours9

1. Name the eight factors of 24.

, , , ,

, , , 2412864321

Math BoxesLESSON

9� 9

37

74259 260

167 168

103

NumberHours of Children

8 ////

9 ////\ ////

10 ////

11 /

68 69

80

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Math Journal 2, p. 228

Student Page � Math Boxes 9�9(Math Journal 2, p. 228)

Mixed Practice Math Boxes in this lesson are linked withMath Boxes in Lessons 9-11 and 9-13. The skill inProblem 6 previews Unit 10 content.

Writing/Reasoning Have children write an answer to the following: Explain how you found all the factors for 24 inProblem 1. Sample answer: I drew all the arrays for 24

and wrote a number model for each array. The factors for thenumber models are all factors for 24.

Ongoing Assessment:Recognizing Student Achievement

Use Math Boxes, Problem 5 to assess children’s progress toward identifyingand describing plane and solid figures. Children are making adequate progress ifthey record the number of vertices and sides correctly. Some children may identify the shape correctly.

[Geometry Goal 2]

� Home Link 9�9(Math Masters, p. 293)

Home Connection Children show someone at home howto find products using the lattice method and partial-products algorithm. You might want to send home

the Student Reference Book, which includes descriptions of these methods.

INDEPENDENTACTIVITY

Math BoxesProblem 5 �

INDEPENDENTACTIVITY

Name Date Time

Multiplication Two Ways, Part 1HOME LINK

9�9

Observe as your child solves these problems. See if your child can use more than onemethod of multiplication, and find out which method your child prefers. Both methodsare discussed in the Student Reference Book on pages 68–72 and in the Unit 9Family Letter.

Please return this Home Link to school tomorrow.

FamilyNote

68–72

Use the lattice method and the partial-products algorithm.

1. 2 � 46 �

3. 3 � 274 �

2. 5 � 83 �

4. 8 � 906 � 7,248

415

822

92

46� 280

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274� 3600210

� 12822

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Math Masters, p. 293

Home Link Master

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� Multiplying and DividingMultiples of 10 In Music(Math Masters, p. 294)

To apply children’s understanding of multiplication, havethem solve problems related to the musical compositionVexations on Math Masters, page 294. When they have

finished the page have children share their strategies for solvingthe problem. Encourage them to discuss the computation as wellas the conversions between the units.

� Practicing Partial Products(Math Journal 2, p. 227)

To offer children more experience with the partial-products algorithm, have children solve the problems on journal page 227using the partial-products algorithm. They record their work on asheet of paper and check their answers with a partner.

Planning Ahead

For Exploration F in Lesson 9-10, you will need to gather smallobjects in varying weights (paper clips, rubber bands, straws,pencils, crayons, erasers, calculators, and so on).

15–30 Min

PARTNER ACTIVITYEXTRA PRACTICE

15–30 Min

INDEPENDENTACTIVITYENRICHMENT

3 Differentiation Options LESSON

9 � 9

Name Date Time

Mathematics in Music

The French composer Erik Satie lived from 1866 to 1925.He wrote a piece of music called Vexations, in which the same tune is played 840 times in a row without stopping. It takes about 30 seconds to play this tune once.

1. About how many minutes would it take to play all of Vexations without stopping? about minutes

2. How many hours is that? hours

3. Suppose someone played the whole piece 4 times without stopping.Could this be done in 1 day?

4. How many times a day could the whole piece be played without stopping?

5. Look up the meaning of vexation in a dictionary.Explain why you think Satie gave the piece of music that name.

Sample answer: It is probably an extremelyannoying piece to listen to.

3 times

No

7420

Math Masters, p. 294

Teaching Master

Lesson 9�9 765

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