Multiply and Divide Decimals Using Models Multiply Decimals

Multiply and Divide Decimals Using Models

Multiply Decimals The Area Model =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. 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. 01 We can divide decimals by separating blocks into equal groups. Let’s divide 0. 4 by 0. 02

Divide Decimals by Grouping = 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 =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.