# A first-grade math homework question

I found this a few years ago in my kid's first grade math homework:

Analysis: How does identifying the equal shares in circles and rectangles help you think about why shapes are partitioned?

This was phrased in such a convoluted way that it took me a few minutes just to parse what was being asked. But, leaving aside the general clumsiness of the question, is there a rational part of it that could be answered in a meaningful way, or do you think it's complete garbage?

• I think it's as simple as: Because equal partitions allow for equal sharing. Some shapes (e.g., circles and rectangles) allow for easy equal partitions. – quasi Dec 20 '17 at 20:29
• @quasi But isn't that kind of a tautology? – Alexander Burstein Dec 20 '17 at 20:31
• At the first grade level, that's probably what they want. For the student to recognize the practical value of symmetry. – quasi Dec 20 '17 at 20:32
• @quasi Yeah, maybe. – Alexander Burstein Dec 20 '17 at 20:34
• I hope the question poser had the underlying idea of getting the first-graders to see that counting (equal area partitions) is easier than estimating area. It would tie in nicely with followup concepts (especially my favourite, using math as a tool, rather than just winging it/estimating everything/learning details by rote; and wielding math is less effort). – Nominal Animal Dec 20 '17 at 22:09

## 2 Answers

I've spent a fair amount of time in first grade math classrooms.

Presumably this question follows some play with pictures and manipulatives dividing pies and rectangles into equal parts. That will make a good foundation for work with fractions later on. But none of the excellent first grade teachers I've worked with would use a question like this to find out what a kid has absorbed. I might not go so far as to call it complete garbage but wouldn't hesitate to call it useless.

The question appears to be asking about representing the equal distribution of areas by dissecting geometric shapes into congruent parts.

For example, if I am at a birthday party and I wish to divide a circular cake into 12 equal parts, the most obvious approach is to use the radial symmetry of the circle. I would first cut along any diameter, then along the diameter perpendicular to the first, creating four equal wedge shaped slices. Then I would "eyeball" dividing slices into equal thirds by cutting along additional diameters such that the central angle of each sector is as close to 30 degrees as possible. The result should be 12 equally sized slices of the same shape.

It is strange to use language and syntax that is above a first grade level to ask such a vague question.