Activity 6.2b: Multiplication of Decimals

Purpose: Explore models for multiplication of decimals.

Materials: Base-ten blocks or app Links to an external site., paper, calculator.

Use base-ten blocks and the area model for multiplication to find the wholes and tenths. Neatly draw each area, labeling the base and height, and show the base-ten blocks that make up the area. Alternatively, use the Number Pieces app, to build each area, carefully annotating the illustrations to state the base and height.

Show the expanded and standard algorithms, using the illustrations to justify any carrying that happens.

Example: 2.3 x 1.2

If multiplication is an area, base x height, then what is the area 2.3 x 1.2?

Ideally we would use physical base-ten blocks with a flat as one whole square unit of area:

Let's draw this out on paper. First measure out the rectangle with the proper base and height.

Now show separate the ones and tenths in the base and height.

Given that 1 whole flat is one square unit, mark off the wholes, tenths, and hundredths in the area.

Label the wholes, tenths, and hundredths, then combine them for the total area.

We could also show this with the Number Pieces app Links to an external site.:

Here is another example built with the Math Learning Center number pieces app Links to an external site..

Now it is your turn.

Use base-ten blocks and the area model for multiplication to find the wholes and tenths. Neatly draw each area, labeling the base and height, and show the base-ten blocks that make up the area. Alternatively, use the Number Pieces app, to build each area, carefully annotating the illustrations to state the base and height.

Show the expanded and standard algorithms, using the illustrations to justify any carrying that happens.

1.  2.4 x 1.2
2.  1.4 x 1.3
3.  2.6 x 1.5
4.  3.5 x 2.7