Purpose: To illustrate multiplication of decimals by decimals Materials: Blank Decimal Squares for Multiplying Decimals by Decimals

(attached), Decimal Squares, and Dice

Activity 1 Multiplying by Decimals Blank Decimal Squares Multiply Decimals by Decimals

1. Shade blank tenths square #1 for .1, split the shaded amount into 10 equal parts, and double-shade one of these parts. What part of a whole square is double-shaded? (one hundredth) This activity illustrates .1 × .1 (taking 1 tenth of 1 tenth). Write a multiplication equation for this product. (.1 × .1 = .01)

Note: If a transparent Decimal Square for .1 is used, lines can be drawn on the shaded part of the square. 2. Shade blank square #2 for .3, split the shaded amount into 10 equal parts, and double-shade one of these 10 parts. What part of a whole square is double-shaded. (3 hundredths) This activity illustrates .1 × .3 (taking 1 tenth of 3 tenths). Write the multiplication equation for this product. (.1 × .3 = .03) 3. Shade blank square #3 for .3, divide it into 10 equal parts, and this time double-shade 2 of these 10 parts. What part of a whole square is double-shaded? (6 hundredths) This result illustrates .2 × .3 (taking 2 tenths of 3 tenths). Write the multiplication equation for this product. (.2 × .3 = .06)

Note: The illustrations in this lesson will help dispel the common student misbelief that "multiplication makes bigger." It will help students see that when multiplying by decimals less than 1, we are taking part of some amount, and this decreases the amount.

4. Shade blank square #4 for .8, split the shaded amount into 10 equal parts, and double-shade 3 of these parts. What does this illustrates? (.3 × .8 or taking 3 tenths of 8 tenths) Write a multiplication equation for this product. (.3 × .8 = .24)

TEACHER MODELING/STUDENT COMMUNICATION

MULTIPLICATION 6.NS.3 MULTIPLYING DECIMALS BY DECIMALS

Activity 2 Summarizing to See Patterns and Relationships

List the equations on the board from the preceding activities. Look for patterns in these multiplication equations and write a rule for multiplying two decimals. (The product is computed as if multiplying two whole numbers, and the total number of decimal places in the two numbers is the number of decimal places in the product.)

Activity 3 Approximating Products by Rounding Approximate the product by rounding each decimal to the

nearest tenth and then compute the product. a. .32 × .78 ≈ .3 × .8 = .24 b. .09 × .33 ≈ .1 × .3 = .03 c. .516 × .308 ≈ .5 × .3 = .15 d. .7 × .218 ≈ .7 × .2 = .14.

Activity 4 Student Activity with Decimal Squares Decimal Squares and dice

Select two Decimal Squares, roll a die to obtain a whole number, and compute the product of the whole number times each decimal from the squares. Then compute the product of the two decimals from the squares. One example is shown here. .3 .45 .45 × 4 × 4 × .3

Game: In the RED and GREEN GAME, each player in turn takes a red square and a green square and computes the product of their two decimals. The player with the greater product wins one point. If the two products are equal, both players win one point. The first player to win three points wins the game. Second Draw Option: After selecting two Decimal Squares, the player may discard one and select another. If this is done, the new square must be used in computing the product. Worksheets 6.NS.3 #19, #20 and #21

INDEPENDENT PRACTICE AND ASSESSMENT

Multiplying and dividing fractions and decimals can be challenging for many students because of problems that are primarily conceptual rather than procedural. From their experience with whole numbers, many students appear to develop a belief that "multiplication makes bigger and division makes smaller." When students solve problems in which they need to decide whether to multiply or divide fractions or decimals, this belief has negative consequences that have been well researched (Greer 1992).

NCTM Standards 2000, page 218

Name: _______ ____________________ Date: ______ ___ .

Blank Decimal Squares for Multiplying Decimals by Decimals 1. Shade .1 and divide it into 10 equal parts to show .1 of .1 2. Shade .3 and divide it into 10 equal parts to show .1 of .3

.1 x .1 = ______ .1 x .3 = ______

3. Shade .3 and divide it into 10 equal parts to show .2 of .3 4. Shade .8 and divide it into 10 equal parts to show .3 of .8

.2 x .3 = ______ .3 x .8 = ______