Question

For each set of figures, show how the green colored tiles in the border can be grouped to allow for quick calculation. Each set of figures has two figures of different sizes for you to work with; use a different grouping method on each and provide a mathematical expression that connects with your grouping method. grouping method 1 figure size 3

Answer 1

We can write,

n = inside triangle size

Label and explain grouping method :

I grouped the covered triangles, each had 3 colored tiles.

That were 3 sets,

                         3 * 3 = 9

Then I noticed the left over colored border tiles were the same amount as the inner triangles minus 1,

So,

The equation is,

                           9 + 3(n-1)

3 because triangles have 3 sides

A mathematical expression to represent grouping strategy :
                          9 + 3(n-1)      or        9 + 3(x-4)

Number of green tiles,

                           = 9 + 3(8-1)

                           = 9 + 21

                           = 30

Let us assume, green colored triangles = 72

So,

We can write,

                       9 + 3(n-1) + (n x n) = 72

                       9 + 3(n-1) + $n^{2}$ = 72

                        $n^{2}$ + 3n + 8 = 72

                        $n^{2}$ + 3n = 66

                        $n^{2}$ + 3n -66 = 0

Therefore,

The mathematical expression = 9 + 3(n-1)

Learn more about event correlation here: brainly.com/question/8599681

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