Math CentralQuandaries & Queries


Question from Makayla, a student:

I've just started the 4th grade and I am having trouble with a question on my homework. The questions is: Carrie is arranging sticks to make shapes. she has made a closed figure, with 10 sides How many vertices are there? I believe the answer is ten but I'm not sure.

We have two responses for you


Since the title of your problem is 'problem solving', I think the key is to look at your reasoning.

I suspect that you drew an example, and found that your example had 10 vertices.
This is certainly a good start. If you imagine shifting them around a bit, or making some longer and shorter - does the number of vertices change? This is also part of your reasoning.

You can back up the reasoning in a couple of ways: is 10 a magic number?
Is there a pattern that works for three sides, four sides, five sides? This pattern gives some back-up for your reasoning. (Good problem solving works for more than one problem!)

If you imagine walking around the shape: edge vertex edge vertex .... because it is CLOSED (have to use that somewhere) you can write out a 'cycle' with 10 edges which is general enough that you can just 'count' the vertices.

Hope this helps.

Walter Whiteley


You are right, Makayla!

In a closed figure, each side attaches to two vertices and each vertex joins two sides, so it makes sense that the number of sides and vertices is the same.



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