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.

Super prompt. The first words out of my Geometry student's mouth when ask "what are similar figures?" is, "the same," and that is after we have been introduced to similarity. After a bit someone will say proportional and then we are on a roll. I asked this question on my last test" Jamie says all dilations less than 1 are reductions. Is this true? Use words and or pictures to support your claim.

ReplyDeleteThanks Amy! It really uncovered that they really had no idea how to articulate all of the ideas. I understand though because corresponding, congruent, parallel, are not words they use on a daily basis.

DeleteI'm sure when your students said "the same" you replied, "the same what?" Definitely the same shape.

Also, in response to your test prompt, were you trying to see if they would mention a dilation of -1 rotating the shape 180 degrees but not shrinking it?