What Do You Notice? Array Model

# What Do You Notice? Array Model

What Do You Notice? is a super easy activity that lends itself well to a lot of great math thinking and conversation. These low floor, high ceiling posters are a great way to engage families during a Family Math Night event. That’s why we included them in our Virtual Family Math Night.

Skills

K-2: geometry, counting, repeated addition

3-5: geometry, single- and double-digit multiplication, distributive property of multiplication, array model of multiplication

Background Information

What’s really cool about multiplication is that no matter what two numbers are multiplied together, geometrically the result creates a rectangular array*. That’s because multiplication is simply repeated addition. The color coding of the poster array helps students visualize this repeated addition. For example, the pink rectangle represents 3 + 3 + 3 + 3 + 3 and so on. But equally clear is that the problem 14 x 13 is 14 rows of 13: 13 + 13 + 13 + 13 + 13…

The other really cool thing is that we can break that visual representation down into partial products. For example, the array on the poster represents the problem 14 x 13. Using partial products to solve the problem would look like:

Each one of the partial products is clearly visible in the array model. When we break apart the factors into addends (10 + 4 and 10 + 3) and then multiply, we’re using the distributive property of multiplication.  This array is a great example of how the different topics in math can help support each other…in our case how geometry can show how numbers work.

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