Activity 3.3

Math Activity 3.3: Multiplication as Area with Base-ten Blocks

Purpose: Explore the area model for multiplication of whole numbers with base-ten blocks.

Materials: Base-ten blocks, or Math Learning Center app Links to an external site., or Cool Math 4 Kids app Links to an external site. 

Example 1:

2 x 3 = 6

Using the area model for addition of whole numbers, along with base-ten blocks, we can help kids visualize math.

The illustration above is for 2 x 3. According to the area model, we draw or build a rectangular grid that has a base of 2 and a height of 3. Area is base x height. So in this case we can see that an area that is 2 by 3 has 6 squares with, that is, 2 x 3 = 6

Example 2:

Consider 23 x 12

Create an area with base-ten blocks with a base of 23 and a height of 12.

The image above shows 4 distinct regions:

In this case no trading in of ones for tens, nor tens for hundreds is necessary.

23 x 12 = 266

Instructions:

Create areas with base-ten blocks to show each of the following. Use the areas to show how to get the product. You have to do some trading on some of these problems.

1. 14 x 12
   
   
2. 15 x 13
   
   
3. 14 x 23
   
   
4. 26 x 14

On some of the problems above, you will have to trade ten ones for one ten. Be sure to show this trade in the illustration and state it in your explanation.

What to submit?

Complete your work on paper or a Google Doc or the text editor below. You can draw the rectangular arrays for each area on paper to take pictures of, or take screenshots of an online base-ten block app. Each multiplication problem will need at least one sketch, an explanation, the expanded form to match the 4 regions of the base-ten block array, and the final product.