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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  1. Another way to solve this problem with the exact measurement of 4ml, without using any other container to save the water and without having to estimate is:
    1) Fill the 5ml cup.
    2) Pour from the 5ml cup into the 3ml cup. You have 2ml exactly left in the 5ml cup.
    3) Pour away the water from the 3ml cup and transfer the 2ml from the 5ml cup. Now you have 2ml water in the 3ml cup. Your 5ml cup is empty.
    4) Fill up the 5ml cup again.
    5) Pour exactly 1ml from the 5ml cup over the 3ml cup (from step 3, you have exactly 1ml space left in the 3ml cup).
    6) Now you have exactly 4ml water in the 5ml cup.


    1. Cool! That looks like another valid solution. I think it's funny how we both posted pre-algebra activities this week.


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