Transcript Multiply and Divide Decimals - Math GR. 6-8

Multiply and
Divide Decimals
Using Models
Multiply Decimals
The Area Model
=1
= 0.1
= 0.01
You can model the multiplication of decimals by using an
area model.
Let’s try 0.2 x 0.6
Multiply Decimals
The Area Model
0.2 x 0.6 = 0.12
1. Model 0.2 on the grid.
2. Model 0.6 on the grid.
3. Your answer is the sum of
the overlapped squares.
Multiply Decimals
The Area Model
But what if we have whole numbers???
We could use a bigger grid!
1.4 x 0.5
OR…
Multiply Decimals by Building
Rectangles
=1
= 0.1
= 0.01
You can model the multiplication of decimals by building
a rectangle.
Let’s try 3.2 x 2.4
Multiply Decimals by Building
Rectangles
1.
Model 3.2 as the length of your
rectangle.
2. Model 2.4 as the width
of your rectangle.
2.4
3. Use blocks to fill in
the rectangle.
3.2 x 2.4 = 7.68
3.2
What Does This Method Do For
Students?
 Builds an understanding of the size of numbers.
 Relates the idea of place value to something tangible.
 Creates a deeper understanding of the multiplication
algorithm.
 Enforces the concept of area.
 Builds prior knowledge for the use of algebra tiles with
polynomials.
Your Turn
1. Find 2.8 x 2.3
2. Find 3.1 x 2.7
Work Backwards
What multiplication problem is modeled by the blocks shown below?
2.4 x 2.4 = 5.76
What Are Some Disadvantages To
Using This Model?
 Students are used to relating the blocks to different
numbers.
Modeling Decimal Division
The blocks are still the same!
=1
= 0.1
= 0.01
We can divide decimals by separating blocks into equal groups.
Let’s divide 0.4 by 0.02
Divide Decimals by Grouping
0.4 0.02 = 20
1. Model 0.4
You will have 40
hundredths pieces.
2. Divide the
40 pieces
into groups
of 0.02
How many
equal groups
are there?
Let’s Try Another
5.6 1.4 = 4

Drawing Conclusions
 Find 36 divided by 12. How does this problem and its
quotient compare to 3.6 divided by 1.2?
 Could you use base-ten pieces to find the quotient of 2.3
divided by 0.3? Justify your answer.