Christopher Danielson recently released “A Better Shapes Book” for free on his blog. Before you read on, go take a look at it, download it, and enjoy!

Our Hallway Display

Since some of my classes are studying geometry this trimester this was a fortuitous release.  My students, who are in self-contained special ed classes, can identify benchmark shapes (squares, rectangles, triangles and circles), but we are currently investigating how squares and rectangles relate as quadrilaterals.  This book was the best way for our students to explore shape properties without having to read, write and remember a lot of vocabulary.  We were able to discuss what they saw and critique the arguments of classmates in a safe space, because all arguments were valid for one reason or another.  The elimination of the potential to be flat out “wrong” created a safe space for my student population.  As long as there was some semblance of justification, you were “right.” The students liked that!

First we reviewed the book pages on the Smartboard as a group.  For each page the students would have about a minute to pick which shape didn’t belong and why.  Then each student had an opportunity to share their choice and justification.  Students would subsequently have an opportunity to respond to each other’s arguments.  Then we moved on to the next page and repeated the process.

@Trianglemancsd@MathMinds “which shape doesn’t belong” in class today! pic.twitter.com/BNsE5nMtb7

— Andrew Gael (@bkdidact) January 9, 2015

As a group we got an opportunity to discuss why each shape could or could not belong depending on the property in focus.  After the whole group activity, students were asked to create their own pages.  They created first drafts and shared with a partner, then with me.  After going through the two editing stages (peer-to-peer and student-to-teacher) they were able to make final drafts of their pages in full technicolor (well, really just colored pencils).

Here are their final drafts:

Some students showed full understanding by making pages where all four shapes could belong or not based on their properties.  Others showed partial understanding by creating a page where at least one shape could not belong based on its properties.  All in all it was a successful investigation.

Thanks Christopher!

PS – Christopher is looking for an elementary teacher in Minnesota who would like him to visit their class! More info here. (Disclaimer: This may already be sorted out by the time you read this post!)

PPS – If you liked this post read more like it here and go to get the Global Math Department Newsletter here!