1 teaching the lesson materials - everyday math · pdf fileteaching the lesson materials ......

Technology Assessment Management SystemMath Boxes, Problem 2See the iTLG.

Teaching the Lesson materials

Key ActivitiesStudents practice the lattice method of multiplication, which has been modified to find products of decimals. They also discuss a traditional method for locating the decimal point in a product.

Key Concepts and Skills• Use place-value concepts to place the decimal point in products.

[Number and Numeration Goal 1]• Multiply decimals using the lattice and traditional methods.

[Operations and Computation Goal 2]• Make reasonable estimates for products of decimal factors.

[Operations and Computation Goal 5]

Ongoing Learning & Practice materials

Students practice rules of divisibility by playing Divisibility Dash.

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

Ongoing Assessment: Recognizing Student Achievement Use journal page 64. [Operations and Computation Goal 2]

Differentiation Options materials

Students use an area model to visualize decimalmultiplication.

Students use doubling and halving strategies tomentally multiply decimals.

Students display a methodfor multiplying decimals.

� Teaching Masters (Math Masters,pp. 55 and 56)

� calculator� markers; posterboard

ELL SUPPORTENRICHMENTREADINESS

3

� Math Journal 1, p. 64� Student Reference Book,

pp. 309 and 11� Study Link Master (Math Masters, p. 54)� Game Master (Math Masters, p. 432)Per partnership:� 4 each of number cards 0–9 (from the

Everything Math Deck, if available)� 2 each of number cards 2, 3, 5, 6, 9, and

10 (from another Everything Math Deck, ifavailable)

See Advance Preparation

2

� Math Journal 1, pp. 62 and 63� Student Reference Book,

pp. 20 and 39� Study Link 2�5� Teaching Aid Masters (Math Masters,

pp. 414 and 415; optional)

See Advance Preparation

1

Additional InformationAdvance Preparation Consider making at least one copy of Math Masters, pages 414 and415 for each student.

For Part 2, familiarize yourself with the directions for Divisibility Dash on page 309 of theStudent Reference Book.

Lesson 2�6 129

Objective To develop strategies for multiplying decimals.

EM07TLG1_G6_U02_LOP06.qxd 2/3/06 1:51 PM 29

130 Unit 2 Operations with Whole Numbers and Decimals

62

More Multiplying DecimalsLESSON

2� 6

Date Time

Math Message

Estimate each product. Then use the lattice method to solve the problem.

1. 28 � 13 Estimate

28 � 13 �

2. 2.8 � 1.3 Estimate

2.8 � 1.3 �

Use the product of 456 and 78 to solve the following problems.

3. 45.6 � 7.8 �

4. 456 � 0.78 �

5. 4.56 � 78 �

6. 0.456 � 7.8 � 3.5568355.68355.68355.68

3.64

3

364

3001

2 8

3

7

4 5

21

83

5 6

31

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32405

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42

48

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8

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2 8

3

39Sample estimates given.

Math Journal 1, p. 62

Student Page

Adjusting the Activity

� Math Message Follow-Up(Math Journal 1, p. 62; Student Reference Book,p. 20)

Students used lattice multiplication in Fifth Grade EverydayMathematics to find products of whole numbers. With somereview, most students should be able to use the lattice method. If necessary, refer them to page 20 of the Student Reference Book,and have them solve several of the Check Your Understandingproblems.

Ask volunteers to show how they found the product 28 � 13 usinglattice multiplication.

Use 2.8 � 1.3 to show the lattice method using decimal factors.Ask students to explain how they located the decimal point in theanswer. Answers vary. Draw attention to the arrows on the latticegrid and how students can use them to help locate the decimalpoint in the product. Demonstrate the procedure at the board oroverhead projector. See procedure on the following page.

Use one color to write the original factors and another color to write thepartial products inside the lattice.

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

WHOLE-CLASSDISCUSSION

1 Teaching the Lesson

Getting Started

Study Link 2�5Follow-Up Briefly go over the answers.Draw attention to the factors in problems wheremultiplication makes smaller(4b and 5c). If time permits,ask students to convert theiranswer for 6b to centimeters.

Mental Math and ReflexesStudents signal thumbs-up for products greater than the first factor and thumbs-down forproducts less than the first factor.

Suggestions:

2.03 � 10 thumbs-up 1,538 � 0.19 thumbs-down 849 � 0.993 thumbs-down62.3 � 0.1 thumbs-down 0.506 � 1.03 thumbs-up 704 � 1.005 thumbs-up

Math Message Complete Problems 1 and 2 at the top of journal page 62.

ELL

EM07TLG1_G6_U02_L06.qxd 2/3/06 1:44 PM Page 130

Adjusting the Activity

1. Record the factors on a lattice grid. Mark the decimal pointfor each factor above or beside the appropriate grid line.

2. Follow the grid lines below and beside the two decimalpoints to the point at which they meet on the lattice grid.Then follow the diagonal down to the end of the grid andplace a decimal point there. This procedure locates the decimal point in the answer.

Have students use a computation grid (Math Masters, p. 414) or a lattice multiplication grid (Math Masters, p. 415). If they need to use a facts table,refer them to page 370 of the Student Reference Book.

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

Continue with related examples, such as the following:

0.28 � 1.3 � 0.364 0.28 � 13 � 3.64

28 � 1.3 � 36.4 0.28 � 0.13 � 0.0364

Lesson 2�6 131

1

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0063

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0063

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80063

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801

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[show mini of SRB, p.6U02L06SRB01: Student Page]

[show mini of SRB, p.6U02L06SRB02: Student Page]

Lattice MethodThe lattice method for multiplying has been used forhundreds of years. It is very easy to use if you know the basicmultiplication facts.

Whole Numbers

Check Your UnderstandingCheck Your Understanding

Check your answers on page 415.

Draw a lattice for each problem. Then multiply.

1. 6 * 59 2. 77 * 86 3. 76 * 98 4. 7 * 648 5. 879 * 4

ExampleExample 4 * 915 � ?The box with cells and diagonals is called a lattice.Write 915 above the lattice. Write 4 on the right side of the lattice.

Multiply 4 * 5. Then multiply 4 * 1. Then multiply 4 * 9.Write the answers as shown.

Add the numbers along each diagonal, starting at the right.

Read the answer. 4 * 915 � 3,660

ExampleExample 86 * 37 � ?Write 37 above the lattice.Write 86 on the right side of the lattice.

Multiply 8 * 7. Then multiply 8 * 3.Multiply 6 * 7. Then multiply 6 * 3.Write the answers as shown.

Add the numbers along each diagonal, starting at the right.

When the numbers along a diagonal add up to 10 or more:

• record the ones digit in the sum.• add the tens digit to the sum along the next diagonal above.

Read the answer. 86 * 37 � 3,182

4

9 1 5

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9 13

60

42

0

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9 13

66 6

04

20

0

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3 721

43

8 2

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61

84

216

8

3 72

45

61

84

26

Student Reference Book, p. 20

Student Page

Check Your UnderstandingCheck Your Understanding

Check your answers on page 416.

Draw a lattice for each problem and multiply.1. 16.5 * 4.5 2. 4.03 * 17 3. 8.3 * 34.1

Decimals and Percents

Lattice Multiplication with Decimals

Lattice multiplication can be used to multiply decimals.

Did You Know?The lattice method ofmultiplication was usedby Persian scholars aslong ago as the year1010. It was often calledthe “grating” method.

ExampleExample Find 45.5 * 3.06 using lattice multiplication.

Step 1: Estimate the answer. 45.5 * 3.06 � 45 * 3 � 135(The symbol � means is about equal to.)

Step 2: Draw the lattice and write the factors, including the decimalpoints, at the top and right side. In the factor above thegrid, the decimal point should be above a column line. Inthe factor on the right side of the grid, the decimal pointshould be to the right of a row line.

Step 3: Find the products inside the lattice.

Step 4: Add along the diagonals, moving from right to left.

Step 5: Locate the decimal point in the answer as follows. Slide thedecimal point in the factor above the grid down along thecolumn line. Slide the decimal point in the factor on theright side of the grid across the row line. When the decimalpoints meet, slide the decimal point down along thediagonal line. Write a decimal point at the end of thediagonal line.

Step 6: Compare the result with the estimate from Step 1.

The product, 139.230, is very close to the estimate of 135.

ExampleExample Find 84.5 * 11.6 using lattice multiplication.

A good magnitude estimate is 84.5 * 11.6 � 85 * 10 � 850.

The answer to 84.5 * 11.6 should be near 850 (in the hundreds).

The product, 980.20, and the magnitude estimate, 850 are both in the hundreds.

Steps 1–3

Steps 4 –6

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Student Reference Book, p. 39

Student Page



Name Date Time

Divisibility Dash 132

4

Name Date Time

Divisibility Dash 132

4

Round Cards in your hand Divisor 2-digit or 3-digit multiples

1

2

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Player 2Record Sheet

Round Cards in your hand Divisor 2-digit or 3-digit multiples

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Player 1Record Sheet

309

309

Math Masters, p. 432

Game Master

63

More Multiplying Decimals continuedLESSON

2�6

Date Time

Use any multiplication algorithm you choose to solve the following problems. Show your work.

7. 8. 9. 10.

11. 12. 13. 14.

Solve the following problems mentally.

15. 1.5 � 10 � 16. 0.25 � 6 �

17. � 1.2 � 0.5 18. 0.03 � 6.2 �

19. 5.1 � 0.4 � 20. � 0.07 � 0.6

21. � 3.42 � 0.2 22. � 4 � 9.136.40.6840.0422.04

0.1860.61.515

1.52� 0.3

4.8� 15

0.21� 26

0.48� 25.4

23.65� 8

19.6� 4

0.46� 0.83

3.4� 7.9

26.86

12.192 5.46 72 0.456

0.3818 78.4 189.2

37 39


Student Page

� Locating Decimal Points in ProductsSome students may propose the following traditional method, or you may want to teach it as an alternative. For example, 2.8 � 1.3 � ?

1. Count the number of decimal 1 decimal place in 2.8places in each factor. 1 decimal place in 1.3

2. Add the number of decimal places. 1 � 1 � 2

3. Multiply the factors as ifthey were whole numbers. 28 � 13 � 364

4. To place the decimal point,start at the right of the productand move left the number ofdecimal places determined in Step 2. 3.64

Students know from a previous lesson that tenths times tenthsequals hundredths (0.1 � 0.1 � 0.01). Ask students how thisrelates to moving two decimal places in Step 4. Sample answer:When you multiply a number by 0.01 (or 10–2) you move thedecimal point 2 places to the left.

� Multiplying Decimals (Math Journal 1, pp. 62 and 63; Student Reference Book,p. 39)

Students work in pairs to complete journal pages 62 and 63.When most students have completed the pages, briefly go over the answers.

� Playing Divisibility Dash(Student Reference Book, pp. 309 and 11; Math Masters, p. 432)

Distribute four each of the number cards 0–9 from 1 deck and twoeach of the number cards 2, 3, 5, 6, 9, and 10 from a second deckto each group of two or three players, as well as a game recordsheet (Math Masters, p. 432). If necessary, have students readpage 11 of the Student Reference Book to review divisibility rules.

PARTNER ACTIVITY

2 Ongoing Learning & Practice

PARTNER ACTIVITY

WHOLE-CLASSDISCUSSION


� Math Boxes 2�6(Math Journal 1, p. 64)

Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lessons 2-8 and 2-10. The skill inProblem 5 previews Unit 3 content.

Writing/Reasoning Have students write a response to the following: When you multiply two factors, each of which is lessthan 1, the product is always less than either of the factors.Explain why, using two examples from Problem 3. Sample answer:In Problem 3a and 3c, you are taking a part of a number that isless than 1. Therefore, the product will be less than 1.

Ongoing Assessment:Recognizing Student Achievement

Use Math Boxes, Problem 2 to assess students’ abilities to estimate a productand to use an algorithm to multiply decimal numbers. Students are making adequate progress if they are able to make a reasonable estimate and choose a reliable algorithm to solve Problem 2. Some students may recognize that theproduct 0.53 � 29.6 will be close to �

12� of 30, or 15.

[Operations and Computation Goal 2]

� Study Link 2�6(Math Masters, p. 54)

Home Connection Students use estimation to multiply decimals and place decimal points. They also use “easy” fraction-decimal conversions to solve decimal-multiplication number stories.

INDEPENDENTACTIVITY

INDEPENDENTACTIVITY Math Boxes

LESSON

2�6

Date Time

4. Which landmark do you think is generallyused in each situation?

a. A teacher reports class scores on amath test.

Landmark

b. The owner of a small grocery storedecides which brand of cereal to stock.

Landmark mode

mean

1. Estimate each sum or difference.Then solve.

a. 35 � 18.23 Estimate

35 � 18.23 �

b. 674.92 � 0.843 Estimate

674.92 � 0.843 � 675.763

67516.77

152. 0.53 � 29.6 Estimate

Use any multiplication algorithm to solve0.53 � 29.6. Show your work.

0.53 � 29.6 � 15.688

3. Multiply mentally.

a. 0.93 � 10�1 �

b. 4.73 � 102 �

c. 0.05 � 10�2 �

d. 0.08 � 104 � 800.00.0005473.00.093

31 32 37 39

35 36 136 137

5. Plot and label the following points on the coordinate grid.

A: (4,5) B: (�3,6)

C: (2,�2) D: (0,4)

E: (�6,�3) F: (1,0)�1�2�3�4�5�7 �6 1 2 3 4 5 6 7 x

y

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64

Sample estimatesgiven.

Sample estimate: 15


Student Page

STUDY LINK

2�6

37–39

Name Date Time

Place a decimal point in each problem.

1. 2 4.3 º 7.06 � 171.558 2. 16.4 º 0.7 � 1 1.4 8

3. .8 2 7 º 9.5 � 7.8565 4. 7 5 6.3 º 5.1 � 3,857.13

Multiply. Show your work on a separate sheet of paper or on the back of this page.

5. � 2.28 º 7.9 6. � 49.7 º 0.6

7. � 3.84 º 13 8. � 0.19 º 53.9

Solve each problem. Then write a number model. (Hint: Change fractions to decimals.)

9. Janine rides her bike at an average speed of 11.8 miles per hour. At that speed, about how many miles can she ride in 6�

12� hours?

Number Model

10. Kate types at an average rate of 1.25 pages per quarter hour. If she types for 2�

34� hours,

about how many pages can she type?

Number Model

11. Find the area in square meters of arectangle with length 1.4 m and width 2.9 m.

Number Model

4.06 sq m

13.75 pages

76.7 miles

10.24149.9229.8218.012

Multiplying Decimals: Part 2

Multiply mentally by 0.10 to find 10%. Then mentally calculate the percent that has been assigned to each number.

12. 20% of $80.00 � 13. 5% of $220.00 �

14. 15% of 640 � 15. 30% of 80 = 2496$11.00$16.00

Practice

11.8 º 6.5 � 76.7

(1.25 º 4) º 2.75 � 13.75

1.4 º 2.9 � 4.06

Math Masters, p. 54

Study Link Master

Lesson 2�6 133

Math Boxes Problem 2 �



LESSON

2�6

Name Date Time

A Mental Multiplication Strategy

The same strategy was used to solve both example problems below. This strategy can also be used to multiply numbers mentally.

1. Explain the strategy. Sample answer:Divide the whole number by 2 and multiply thedecimal by 2 until you can multiply mentally.

2. Use the strategy to solve the problems below. Show your work.

a. 16 º 1.5 � b. 18 º 3.5 �

c. 20 º 0.75 � d. 0.125 º 16 �

3. Solve these problems mentally.

a. 8 º 7.5 � b. 24 º 1.25 �

4. Make up two problems that can be solved using a mental multiplication strategy.

a. b.Answers vary.

3060

215

6324

➤ ➤

➤ ➤

16 º 2.5

16 / 2 2.5 º 2

8 º 5

➤ ➤

72 º 0.125

72 / 2 0.125 º 2

36 º 0.25

36 / 2 0.25 º 2

18 º 0.50

Example 1: Example 2:

16 º 2.5 � 8 º 5 � 40

72 º 0.125 � 18 º 0.50 � 9

Math Masters, p. 55

Teaching Master

LESSON

2�6

Name Date Time

Modeling Decimal Multiplication

56

You can use an area model to find a product.

Example: 0.3 º 0.5Shade 0.3 of Next, shade 0.5 of The product is the area that isthe grid this way: the grid this way: double-shaded this way:

Since 0.15 of the grid is double-shaded,

0.3 º 0.5 � 0.15.

0.3 0.3

0.5

Shade each factor. Then find the product.

1. 0.9 º 0.4 2. 0.7 º 0.6

0.9 º 0.4 � 0.7 º 0.6 �

3. 0.5 º 0.5 4. Write your own problem.

0.5 º 0.5 � º �0.25

0.420.36

Answersvary.

Math Masters, p. 56

Teaching Master

� Modeling Decimal-Number Multiplication(Math Masters, p. 56)

Students shade grids to provide a visual model of decimal-numbermultiplication. They begin by reviewing the example on MathMasters, page 56. Students use different-colored pencils ormarkers, such as red and blue, to shade the areas representingfactors and then find the intersection of those shaded areas. Havestudents compare the sizes of factor and product areas to betterunderstand how multiplication can make smaller.

� A Mental Multiplication Strategy(Math Masters, p. 55)

To further explore multiplying decimals, students reviewexamples of a halving-and-doubling strategy and use thisstrategy to mentally compute products. They check theiranswers with a calculator.

� Creating Decimal Multiplication PostersTo provide language support for multiplication algorithms, havestudents create a poster that features their preferred method formultiplying decimals. Posters should include labeled factors andproducts, as well as brief descriptions of the steps involved.

Some students from other countries may have learned algorithmsthat involve unusual steps or procedures. Encourage volunteers to present these algorithms to the class. Work with students toidentify similarities and differences between algorithms.

15–30 Min

INDEPENDENTACTIVITY

ELL SUPPORT

5–15 Min

INDEPENDENTACTIVITY

ENRICHMENT

15–30 Min

INDEPENDENTACTIVITY

READINESS

3 Differentiation Options


1 teaching the lesson materials - everyday math · pdf fileteaching the lesson materials ......

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