Today's estimation was the third measuring tape. A lot of students saw it as a linear pattern and though it may be 20 feet because it the first pair grew by 4 feet. I liked this connection to their previous thinking.

Students devised a way for finding the scale factor between any two similar shapes. It was important that they made the distinction between the original and new shape. For the first problem, students instincts were to say it was scale factor of two. Then students thought and realized the order mattered and that the shape was getting smaller, so it couldn't be 2.

In the second example, they really had to devise a strategy. Some once again reversed it and thought the scale factor was 0.8. I asked students why that didn't make sense. They said if it was larger, the scale factor had to be greater than 1.

So, students came up with the definition: to find scale factor, divide a side on the new shape by it's corresponding side on the original shape. It gives you a ratio, new over original. Rich discussions were had about the equivalence of 5/4, 1.25, and 1 and 1/4. For students struggling with seeing this connection, I said what if the scale factor was x. 4 times x is 5. What equation is that? Now solve it. Ohhhhh...

As you can see I asked students if 6 divided by 3 is the same as 3 divided by 6? Does order matter when dividing? Yes... |

Here you can see a discussion about one apostrophe is feet and double apostrophe is inches. |

Here I stressed that dividing by a whole number 2, multiplying by a fraction 1/2, and multiplying by 0.5 get you the same result, yet they look so different from each other. |

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