I am very much enjoying the itty-bitty geometry in Grade 7! We have been working a lot with hands-on investigations to develop concepts around triangular areas, shearing, and square roots.

For tomorrow, since it's the end of a week, I am going to use a short discussion to re-focus their attention on the idea "What do we know? What do we NEED to know?" which I think is so key to understanding Geometry.

So, I made this powerpoint file to guide that discussion. (You have to actually play the slideshow in order to see the animations properly.) We're going to look at different basic shapes, initially without any values labeled; I'll have volunteers go up to the board to show what values we NEED to know in order to find the areas, and then I'll click the mouse to reveal a bunch of values (including extraneous info), to actually calculate the areas. The last slide will be an introduction into quadrilateral areas, which we will explore next via hands-on cutting and pasting.

(I am very happy that all of my 7th-graders are drawing rectangles around triangles to find areas, and that they are un-doing shearing in order to find areas of oblique triangles! Way to not memorize formulas!!)

Any last-minute recommendations??

When doing triangle areas, you can use "cut-and-rearrange" to turn the triangle into a parallelogram. Doing this after turning the parallelogram into a rectangle can help kids see where the A = 1/2 bh formula comes from. You can basically do this with any polygon, but it's a nice progression.

ReplyDeleteThanks for the suggestion! We did triangles first and they figured out the 1/2 bh rule themselves by playing with rubber bands on a geoboard (and then later they extended this to sheared triangles, when they decided after cutting and shearing and pasting back down a sheared triangle, that its area remains constant). But, I am intrigued by the triangle-parallelogram connection. I've never seen that transformation before (but I checked it out on Wolfram Alpha to see what you mean), so thanks for the tip!!!

ReplyDeleteI don't teach 7th graders, but the 8th graders I have for algebra still don't quite know the relationship between base and height. Oblique triangles freak them out! Cutting and rearranging is so key, like you're doing, instead of memorizing formulas! I do teach geometry to 8th graders ("advanced" group) and I have the kids draw trapezoids and rhombuses on grid paper and reshape them in whatever ways to figure out the area on their own. Funny, one student even said to me, "So later you'll expect us to figure out the VOLUME formulas on our own also?" Thanks, Mimi!

ReplyDeleteI love your blog!! You seem to have some great math-teaching ideas, Fawn, that are both fun and conceptually relevant. What a gem for me to follow (and I liked your riblet recipe as well!!).

ReplyDeletexoxx,

Mimi