I am having difficulty helping my fourth grader solve the following math problem:

A bicycle shop has 5 bicycles and tricycles to repair. They have 12 wheels. What strategy would you use to determine how many bicycles and tricycles need to be repaired?

Any help you can provide would be greatly appreciated.


Hi Sally,

It is helpful to actually think that you are going to build 5 "cycles" using 12 wheels. Suppose I have 5 workers, and each worker is going to build one "cycle". I start by going to each worker and giving her two wheels (they each need at least two wheels). But I had 12 wheels to start with, so I have two wheels left. I give these two wheels to two of my workers. Thus two workers have three wheels and the remaining three workers have two wheels. Hence two of them can build tricycles and three can build bicycles. Now check. Count how many "cycles" you have and how many wheels you have used.

Sometimes working with something in your hands helps. You could give her 12 Cheerios as wheels and ask her to "construct" 5 "cycles".

Claude and Penny

Dianne added,

In regards to the bicycles and tricycles problem, a strategy that grade four students would use to solve this problem is the guess and check method, where a student would make a reasonable guess and check it out. The student might use this method and make a chart to track his or her progress using this method. Older students would use algebra to solve this.

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