Multiply and Multiply and Divide Divide

DecimalsDecimalsUsing ModelsUsing Models

Multiply Decimals Multiply Decimals The Area Model 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

0.2 x 0.6 =

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 Multiply Decimals The Area Model The Area Model

0.12

But what if we have whole numbers???But what if we have whole numbers???

Multiply Decimals Multiply Decimals The Area Model The Area Model

We could use a bigger grid!We could use a bigger grid!

1.4 x 0.5

OR…

= 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 Multiply Decimals by Building RectanglesBuilding Rectangles

Multiply Decimals by Multiply Decimals by Building RectanglesBuilding Rectangles

1. Model 3.2 as the length of your rectangle.

3.2

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

What Does This Method What Does This Method Do For Students?Do For Students?

Builds an understanding of the size of Builds an understanding of the size of numbers.numbers.

Relates the idea of place value to Relates the idea of place value to something tangible.something tangible.

Creates a deeper understanding of the Creates a deeper understanding of the multiplication algorithm.multiplication algorithm.

Enforces the concept of area.Enforces the concept of area.

Builds prior knowledge for the use of Builds prior knowledge for the use of algebra tiles with polynomials.algebra tiles with polynomials.

Your TurnYour Turn

1.1. Find 2.8 x 2.3 Find 2.8 x 2.3

2.2. Find 3.1 x 2.7Find 3.1 x 2.7

Work BackwardsWork Backwards

What multiplication problem is modeled by the blocks shown below?

2.4 x 2.4 = 5.76

What Are Some What Are Some Disadvantages To Using Disadvantages To Using

This Model?This Model? Students are used to relating the blocks to Students are used to relating the blocks to

different numbers.different numbers.

Modeling Decimal Modeling Decimal DivisionDivision

= 1 = 0.1 = 0.01

The blocks are still the same!

We can divide decimals by separating blocks into equal groups.

Let’s divide 0.4 by 0.02

Divide Decimals by Divide Decimals by GroupingGrouping

€

0.4 ÷ 0.02

1. Model 0.4You will have 40 hundredths pieces.

2. Divide the 40 pieces into groups of 0.02

How many equal groups are there?

= 20

Let’s Try AnotherLet’s Try Another

€

5.6 ÷1.4= 4

Drawing ConclusionsDrawing Conclusions

Find 36 divided by 12. How does this Find 36 divided by 12. How does this problem and its quotient compare to 3.6 problem and its quotient compare to 3.6 divided by 1.2?divided by 1.2?

Could you use base-ten pieces to find the Could you use base-ten pieces to find the quotient of 2.3 divided by 0.3? Justify your quotient of 2.3 divided by 0.3? Justify your answer.answer.