This is a lot to cover in a single lesson so I split it into two parts.
First we looked at proportions with area. This lead to the proportions of length squared (m/n)^2.
Then we looked at proportions of volume. (m/n)^3.
This lead to an interesting propoerty that the exponent is just the power of how many dimensions we have. I think that when volume and area came together with dimension the students understood this better.
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I'm a student learning this. For example, 6 is the height of triangle A and 12 is the height of triangle B. The area of triangle A is 72 cm^2. To find the area of triangle B would you square the heights or what? Thanks!
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