Hands-On Pre-Algebra Activity

Here's the pre algebra math challenge I gave my son. Given a cup which holds exactly 3 units and a cup that holds exactly 5 units, measure 4 units.

We still have a set of MEASURE UP!® Cups by Discovery Toys from when the kids were babies. They are each marked with a number and are proportional. I gave my son the 3 cup and 5 cup, some water and an empty glass.

At first he was a bit angry and asked repeatedly for the 1 cup, but eventually he settled down and took the challenge. Rather quickly he came up with two valid solutions.

First he filled the three cup and then filled 1/5 of the 5 cup. I wrote what he did on paper for him.

3 + 5(1/5) = 5

Next he filled the 5 cup and used the water in the 5 cup to fill the 3 cup so he was left with 2 in the five cup. He saved one-half of the water and added it to the 3 cup. Again I wrote his solution.

(5-3)/2 + 3 = 4

Although he had solved the problem twice he wasn't able to measure exactly. In both cases he estimated amounts of water; 1/5 in the first solution and 1/2 in the second.

I let him think about it over night and in the morning he came up with a third solution. He filled the 5 cup and used the water in the 5 cup to fill the 3 cup so he was left with 2 in the 5 cup. He saved the 2 and repeated the process so that he had 4.

2 x (5-3) = 4

There are many more hands-on math activities on our Math Page.

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