This post was inspired by Suzanne blogging about the precise language she wants by not naming a method "difference of squares" when it could pigeonhole students into a procedure without knowing really why it works. I can also empathize with teaching students the definition of a function through examples. It can be disheartening when the only answer you get is it passes the vertical line test. I like when students on their assessments would draw the vertical line and the points it passes through, labeling those as the input that has 2 different outputs.

New blog post! Weighing how robust math vocab in the classroom can both help and hurt comprehension. #mtbos https://t.co/NvukQP3Cjv— Suzanne von Oy (@von_Oy) January 28, 2017

I was concerned about how my students were processing the attributes of similar figures. CPM has a great lesson where there is an original quadrilateral with a bunch of other shapes that are similar except for 2 of them. One is horizontally stretched, while the other is vertically stretched. As students compare the shapes, they can see that the corresponding angles of the non-similar shapes are clearly different measurements. Also, corresponding sides that should be parallel are intersecting. They also should be able to count how many times a corresponding side can fit into another similar shapes corresponding side to figure out the scale factor.

Since I was concerned with students understanding, I gave students a post it note, 5 or 6 minutes, and the following prompt:

How do you know if two shapes are similar? When does a dilation make the shape bigger? Smaller?

A complete answer would mention all of the following words:

size, scale factor, angles, congruent, corresponding, parallel

I got a variety of responses. Some students included the words, but not in the correct context.

Surprisingly, many students said that similar figures are congruent. To this I commented, "always?" It was hard for students to use the word corresponding and angles in the correct way.

We don't take notes that often, but synthesized their thinking. Students realized a similar figure that was enlarged would have a scale factor greater than 1, a shape that shrunk would be a fraction between 0 and 1, and a congruent shape would have a scale factor of 1.

This work was after dilating on the coordinate plane, and this was nailing down all the academic language.