Art with Factors and Multiples

Multiplication is the root of most all the Math you will encounter through 4th and 5th Grade. Knowing what factors pair up to get a product (answer to a multiplication problem) is a great way to make your work more efficient. Factors are the numbers being multiplied, and the multiple is the answer. For example, 5 x 6 = 30, 5 and 6 are the factors, and 30 is the multiple.

If I look at the multiple 16, I know that one of the factor pairs is going to be 1 x 16. Since 16 is an EVEN number, it can be cut in half, or divided by two: 2 x 8. Should I stop there? Well, when I see patterns in numbers (which are everywhere in Math!), I can try to see what happens when I double one of the factors, 2, and then divide of halve the other factor, 8:

  • 2 x 2 = 4
  • 8 ÷ 2 = 4
  • 4 x 4 = 16

You can always head to your multiplication chart and find all the places where 16 shows up, then scroll with your finger up and to the left to find the factor pair. This strategy only works with factor pairs up to 12.

Let’s look at a larger number, like 48. We can find the places it falls on the chart, and we can also use doubling and halving to find ALL the factors.

Factors of 48 = 1, 2, 3, 4, 6, 8, 12, 24, 48

Go to your “Math and Art” section of your Math Journal. Your task is to make t-charts of the multiples: 16, 30, 33, 42, 36, 48, 25, 28, 24, 10, 12, 50, 56, 60. Then find all the factors of those multiples. The picture below shows how to set up the t-charts.

Pick 3-5 of those multiples, and create art from them. You can explore any and all options. You can use planes or cars, you can make robots to represent factors and multiples. You could draw trees or houses. It could be animals or basketballs. You can even draw a landscape and plop in the factors and multiples in the clouds, or the grass, or a Minecraft field. Whatever calls to you.

I chose to make a Garden of Factors by making the “roots” the multiple, and all the flowers sprouting out the factor pairs.

Have fun! I look forward to seeing your work.

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