MULTIPLICATION 5.NBT.7
MULTIPLICATION OF DECIMALS BY DECIMALS
Purpose: To illustrate multiplication of decimals by decimals
Materials: Blank Decimal Squares for Multiplying Decimals by Decimals
(attached), Decimal Squares, and Dice
TEACHER MODELING/STUDENT COMMUNICATION
Activity 1
Blank
Decimal
Squares
Multiply
Decimals
by
Decimals
Multiplying by Decimals
1. Shade blank 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 doubleshaded? (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 doubleshaded? (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)
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
Round each decimal to the nearest tenth to approximate the
product.
a. .32 × .78 ≈ .3 × .8 = .24
c. .51 × .34 ≈ .5 × .3 = .15
Activity 4
Decimal
Squares
and
dice
b. .09 × .33 ≈ .1 × .3 = .03
d. .7 × .23 ≈ .7 × .2 = .14.
Student Activity with Decimal Squares
Each student selects two Decimal Squares, rolls a die to obtain a whole
number, and computes the product of each decimal from the squares
with the whole number from the die and the product of the two decimals
from the squares. Have a few examples written on the board.
.3
× 4
1.2
.45
× 4
1.80
.45
× .3
.135
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. The new square must be used in computing the product.
INDEPENDENT PRACTICE AND ASSESSMENT
Worksheets 5.NBT.7 #19, #20 and #21
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
.1 x .1 = ______
3. Shade .3 and divide it into 10 equal parts to show .2 of .3
.2 x .3 = ______
2. Shade .3 and divide it into 10 equal parts to show .1 of .3
.1 x .3 = ______
4. Shade .8 and divide it into 10 equal parts to show .3 of .8
.3 x .8 = ______
.