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 Model 0.2 on the grid. Model 0.6 on the grid. 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 Model 3.2 as the length of your rectangle. 3.2 Model 2.4 as the width of your rectangle. 2.4 Use blocks to fill in the rectangle. 3.2 x 2.4 = 7.68

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 Find 2.8 x 2.3 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 = 20 You will have 40 hundredths pieces. Model 0.4 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.