Quandaries and Queries


Dan is 4 inches taller than Mike. Together they are 8 feet 8 inches tall. How tall is each boy in feet and inches.

I am a parent who needs to know not only the answer, I need to know how you do it. K-5




The best way to do this for a student at this level is "guess and check". The method is more accurately described as estimate, check and then use some logic to improve the estimation.

Dan and Mike are almost the same height and the sum of their heights is 8 feet 8 inches. If they were exactly the same height then they would both have to be 4 feet 4 inches tall. Dan is a little taller so suppose that he is 4 feet 5 inches. In this case to keep the sum correct Mike would be 4 feet 3 inches and hence Dan would be 2 inches taller than Mike.

Dan must be taller than that since the difference is 4 inches. Hence try Dan at 4 feet 6 inches. In this case Mike would have to be 4 feet 2 inches and the difference is 4 inches as required.

I find it helpful to use a table to keep track of the estimations.

Dan's height Mike's height Difference
4 feet 4 inches 4 feet 4 inches 0 inches
4 feet 5 inches 4 feet 3 inches 2 inches
4 feet 6 inches 4 feet 2 inches 4 inches
I hope this helps,


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