Teaching the Lesson materials

Key ActivitiesStudents review the lattice method for multiplication with 1- and 2-digit multipliers. They practice using this multiplication algorithm.

Key Concepts and Skills• Add single-digit numbers. [Operations and Computation Goal 2]• Solve basic multiplication facts. [Operations and Computation Goal 3]• Use the lattice method to solve multiplication problems with 1- and 2-digit multipliers.

[Operations and Computation Goal 4]

Key Vocabularylattice • lattice method (for multiplication)

Ongoing Learning & Practice materialsStudents play Multiplication Top-It to practice basic multiplication facts.

Students practice and maintain skills through Math Boxes and Study Link activities.

Ongoing Assessment: Recognizing Student Achievement Use Math Masters,page 506. [Operations and Computation Goal 3]

Differentiation Options materials

Students explore patterns inthe Fact Lattice.

Students investigate Napier’sRods, a seventeenth-centurymultiplication method.

Students make posters to display multiplication algorithms.

� Teaching Masters (Math Masters,pp. 158–161)

� Teaching Aid Master (MathMasters, p. 435)

� Multiplication/Division Facts Table� scissors; chart paper� colored pencils and markers

ELL SUPPORTENRICHMENTREADINESS

3

� Math Journal 1, p. 125� Student Reference Book, p. 264 � Study Link Master (Math Masters,

p. 157)� Game Master (Math Masters,

p. 506)� per partnership: 4 each of number

cards 1–10 (from the EverythingMath Deck, if available)

2

� Math Journal 1, p. 124� Study Link 5�6� Teaching Aid Master (Math

Masters, p. 434)� Transparency (Math Masters,

p. 434; optional)� º, / Fact Triangles� index cards (optional)� dictionary (optional)

1

Lesson 5�7 349

Objectives To review and provide practice with the latticemethod for multiplication.

Technology Assessment Management SystemMath Masters, page 506See the iTLG.

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350 Unit 5 Big Numbers, Estimation, and Computation

19

Name Date Time

Lattice Multiplication Computation Grids

Math Masters, p. 434

Teaching Aid Master

� Math Message Follow-UpStudents share answers. The pair of digits in each cell names theproduct of two digits outside the lattice—one above the cell of thelattice and the other to the right of the cell of the lattice. Thus, themissing digits in the first lattice form the product of 6 and 4 (24).The missing digits in the second lattice form the product of 6 and 5 (30).

Tell students that in this lesson they will review the latticemethod for multiplication. Introduced in Third Grade EverydayMathematics, this algorithm relies almost entirely on the recall of basic multiplication facts. If students do not yet have a favoritemultiplication algorithm, the lattice method is a good one to suggest.

� Demonstrating the Lattice Method for 1-Digit Multipliers(Math Masters, p. 434)

Demonstrate the lattice method using the following examples.Students should show their work using the computation grids onMath Masters, page 434.

WHOLE-CLASS ACTIVITY

WHOLE-CLASSDISCUSSION

1 Teaching the Lesson

Getting Started

Math MessageWhat do you think the missing digits are?

Study Link 5�6 Follow-Up Ask volunteers to write solutions on the board. Students indicate thumbs-upif they agree with the solution. Challenge students to find a way to solve 340 � 50 mentally. Sample answer: Multiply 340 by 100. The answer is halfof this product, or 17,000.

Mental Math andReflexes Students use their Multiplication/DivisionFact Triangles to practice the facts in theTry Again pile. They transfer appropriatetriangles to the OK pile and color the OKfacts in the table on journal page 56, fasten their new piles with paper clips,and store them.

5

6 105

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Example: Use the lattice method to multiply 3 � 45.

A lattice ususally consists of two or more cellswith diagonals. Write 4 and 5 above the cells ofthe lattice. Write 3 on the right side.

Multiply 3 � 5. Write the answer as shown.

Multiply 3 � 4. Write the answer as shown.

Starting at the right, add the numbers insidethe lattice along each diagonal. Read the answerstarting on the left side of the lattice and continuing across the bottom. 3 � 45 � 135.

The sum of the numbers along a diagonal may be a 2-digitnumber. When this happens, write the ones digit in the answerspace and the tens digit at the top of the next diagonal.

Example: Use the lattice method to multiply 7 � 89.

The sum of the numbers in the middle diagonalis 12. Write 2 in the answer space and 1 at thetop of the next diagonal. Then add the numbersin that diagonal.

Read the answer: 7 � 89 � 623.

� Practicing the Lattice Method for 1-Digit Multipliers(Math Journal 1, p. 124)

Students complete Problems 1–5 independently. Partners checkeach other’s work.

PARTNER ACTIVITY 3

5 6

151

6 8

18 8

2 6

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620 8

48

124

Lattice MultiplicationLESSON

5 � 7

Date Time

Use the lattice method to find the products.

1. 3 � 56 � 2. 8 � 26 � 3. 7 � 74 �

4. 6 � 315 � 5. 9 � 284 �

6. 47 � 63 � 7. 26 � 26 �

8. 16 � 473 � 9. 46 � 805 � 37,0307,568

6762,961

2,5561,890

518208168

77 4

41

951 8

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825 5

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366

Math Journal 1, p. 124

Student Page

Lesson 5�7 351

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4 5NOTE The lattice method is a very efficientalgorithm, no matter how many digits are inthe factors. For problems with 1- and 2-digitmultipliers, the lattice method takes about thesame amount of time as the partial-productsalgorithm or the traditional multiplication algorithm. For problems with three or moredigits in the factors, the lattice method is muchfaster and much more likely to yield a correctanswer.

Adjusting the Activity

Have students look up the term lattice in the dictionary and think of places where they might see lattices, such as a gate, awindow, or a patio. Have students discusswhy this word is used to describe the multiplication algorithm.

AUDITORY � KINESTHETIC � TACTILE � VISUAL

ELL

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352 Unit 5 Big Numbers, Estimation, and Computation

� Demonstrating the Lattice Method for 2-Digit Multipliers(Math Masters, p. 434)

Demonstrate the lattice method for 2-digit multipliers using theexample below. Use a transparency of Math Masters, page 434 orcopy the lattices onto the board. Students should show their workon the lattice grids.

Example: Use the lattice method to multiply 34 � 26.

Write 26 above the lattice. Write 34 on the right side.

Multiply 3 � 6. Then multiply 3 � 2.

Multiply 4 � 6. Then multiply 4 � 2.

Write the answers as shown.

Starting at the right, add the numbers inside the lattice along each diagonal. The sum of the numbers along the second diagonal is 8 � 2 � 8 � 18. Write 8 in the answer space and 1 at the top of the next diagonal.

Read the answer: 34 � 26 � 884.

The lattice method of multiplication may seem like a trick. It is not, of course, and place value is evident within the lattice.

� Practicing the Lattice Method with 2-Digit Multipliers(Math Journal 1, p. 124)

Students complete Problems 6–9 independently. Partners checkeach other’s work.

PARTNER ACTIVITY

WHOLE-CLASS ACTIVITY

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Adjusting the Activity

� Use an index card to mark the place when adding along each diagonal.

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

� Extend the diagonal lines through the lattice as shown.

AUDITORY � KINESTHETIC � TACTILE � VISUAL

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Consider these suggestionsfor students who need help with thelattice method.

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Lesson 5�7 353

STUDY LINK

5�7 Lattice Multiplication

19

Name Date Time

Use the lattice method to find the following products.

1. 5 º 46 � 2. 8 º 67 �

3. 7 º 836 � 4. 4 º 329 �

5. 25 º 31 � 6. 49 º 52 �

7. Use the lattice method and the partial-products method to find the product. 84 º 78 � 6,552

2,548775

1,3165,852

536230

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4 6

202

3 0

30 8

6 741

853 6

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78 3

565

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01

83

66

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23 1

060

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02

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057 5

45 2

202

4 8

01

84

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85 9

8. � 33.67 � 5.9 9. 68.4 � 5.82 �

10. 71.44 � 37.67 � 11. � 101.06 � 29.9171.1533.7774.2239.57

Practice

Math Masters, p. 157

Study Link Master

Math Boxes LESSON

5 � 7

Date Time

1. This is a circle graph of what Seema does on a typical day.

a. What does she spend the least amount of time doing?

b. She spends about the same amount of time at school and doing homework as she does

.

c. About what fraction of the day does she spend doing chores, eating, and relaxing?

�15�

sleeping

Soccer practice

3. Complete.

Rule: � 80

4. Write each number using digits.

a. twenty-six million, nineteenthousand, eighteen

b. three hundred fifty-two million, eighthundred thousand, two hundred

352,800,200

26,019,018

5. Look at the grid below.a. In which column

is the triangle located?

b. In which row is the triangle located?

3

B

162–166

2. Estimate the sum. Write a number model to show how you estimated.

a. 715 � 1,904 � 688

Number model:

b. 867 � 2,346 � 3,596

Number model:900 � 2,300 � 3,600 � 6,800

700 � 1,900 � 700 � 3,300Sample answers:

1

A B C

2

3

4 144

choreseating

relaxing

school andhomework

sleep

soccer practice

Seema’s 24-Hour Day

181

in out

50 4,000

70

90 7,200

100

45 3,6008,000

5,600

125

Math Journal 1, p. 125

Student Page

� Playing Multiplication Top-It(Student Reference Book, p. 264; Math Masters, p. 506)

Students play Multiplication Top-It to develop automaticity withmultiplication facts. See Lesson 3-3 for additional information.

Ongoing Assessment:Recognizing Student Achievement

Use Math Masters, page 506 to assess students’ automaticity with basic multiplication facts. Students are making adequate progress if they can name theproduct of the factors generated by the two cards. Some students may play avariation of the game and demonstrate the ability to mentally solve 2-digit by 1-digit multiplication problems.

[Operations and Computation Goal 3]

� Math Boxes 5�7(Math Journal 1, p. 125)

Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 5-5. The skill in Problem 5previews Unit 6 content.

� Study Link 5�7(Math Masters, p. 157)

Home Connection Students use the lattice method tosolve multiplication problems. Students are asked to solveProblem 7 by using both the lattice method and the partial-products method.

INDEPENDENTACTIVITY

INDEPENDENTACTIVITY

Math MastersPage 506 �

PARTNER ACTIVITY

2 Ongoing Learning & Practice

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354 Unit 5 Big Numbers, Estimation, and Computation

LESSON

5�7

Name Date Time

Napier’s Rods

Scottish mathematician John Napier (1550–1617) devised a multiplication method using rods made of bone, wood, or heavy paper. These rods were used to solve multiplication and division problems.

Example 1: Example 2:

4 º 67 � 268 8 º 5,239 � 41,912

Cut out the rods on Math Masters, page 159. Use the rods and the board onMath Masters, page 160 to solve the following problems and some of your own.Use another method to check your answers.

1. 5 º 79 � 2. 7 º 92 �

3. � 6 º 236 4. � 9 º 5,84152,5691,416644395

Try This

5. Show a friend how you would use Napier’s Rods to solve 3 º 407 or 9 º 5,038.

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Math Masters, p. 158

Teaching Master

LESSON

5�7

Name Date Time

Fact Lattice Patterns

1. Look at a Multiplication/Division Facts Table. Find the shaded diagonal showing the doubles facts.

2. Find the doubles facts on the Fact Lattice on Math Masters, page 435. Shade the doubles facts lightly with a colored pencil.

3. Compare the two fact tables. Sample answers:a. List 3 things the tables have in common.

Both show multiplication and division facts for the factors 1–9; both are a square shape; both show the square products along a diagonal; both show the factors along the top and one side.

b. List 3 things that are different on the Fact Lattice.Lists factors in reverse; shows factors from 0–9, not 1–10;shows zeros in 10s place for numbers � 10; has diagonallines between the 10s and 1s place for products; shows factors on the right; and does not shade square products.

4. Describe 2 patterns that you see on the Fact Lattice. Sample answers:a. Not counting zero as a factor, in the 9s columns and rows,

the digit of the 10s place goes up by 1 while the digit for the 1s place goes down by 1.

b. The bottom (1s) digits in the 2s column and rows repeat a pattern on 0, 2, 4, 6, 8.

5. Which of your Fact Lattice patterns is also in the Multiplication/Division Facts Tablein your journal?Sample answer: The 9s pattern is in the fact table.

Math Masters, p. 161

Teaching Master

� Exploring Fact Lattice Patterns(Math Masters, pp. 161 and 435)

To explore the use of the lattice grid for multiplication, havestudents find patterns in the Fact Lattice (Math Masters,page 435)

� Investigating Napier’s Rods(Math Masters, pp. 158–160)

To apply students’ understanding of lattice multiplication, havethem use Napier’s Rods to solve problems.

Discuss students’ responses to Problem 5. Students may note thatwhen solving a problem with 0 as a digit in one of the factors, aspace is left between the rods where the 0 rod would be.

� Creating Visuals for Multiplication AlgorithmsTo provide language support for multiplication, have studentsmake posters to illustrate the multiplication algorithms they havelearned. Display the posters for students to refer to during the restof the unit.

Planning Ahead

For use in Part 1 and the optional Enrichment activity in Part 3of Lesson 5-8, borrow a ream of copy paper and an empty cartonused to pack 10 reams of paper.

15–30 Min

SMALL-GROUP ACTIVITY

ELL SUPPORT

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INDEPENDENTACTIVITYENRICHMENT

5–15 Min

PARTNER ACTIVITYREADINESS

3 Differentiation Options

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