# Triangle sort

Pretty standard activity, but I liked this one a lot. First I wrote each of the sets of numbers below on sticky notes.

Non-triangle Right triangle Non-right triangle
8, 9, 17 5, 12, 13 9, 10, 15
8, 12, 20 6, 8, 10 9, 14, 15
3, 6, 11 3, 4, 5 5, 12, 15
6, 7, 16 9, 12, 15 8, 12, 13
8, 12, 21 9, 13, 2√22 4, 2√55, 16
1, 6, 7 5, 10, 5√5 4√2, 6, 9
6, 11, 19 2√2, 2√2, 4 5, 4√10, 14
4, 6, 12 √57, 13, √226 √5, √10, √14

When students came in for the day, I chose a sticky note for them (woohoo, differentiation!) and told them to wait for further instructions. When class began, I told them to figure out if their set of three numbers represented the side lengths of a non-triangle, a right triangle, or a non-right triangle. Once they were confident in their answer, they were to put the sticky note in the appropriate location on the window.

Once all the sticky notes were placed, I looked to see if they were all in the right spot. If there were any mistakes, I had everyone grab a different sticky from what they had before, and check whether it was correctly classified. Then we repeated the process until all were correctly classified. Students were encouraged to work together to make sure they knew how to categorize three side lengths—and they actually did!

This was on an otherwise-individual work day, so after students had placed their sticky note on the window, they worked independently on other work. I definitely recommend doing it that way if you’re going to be mean like I was and insist on 100% accuracy without giving any hints as to which sticky notes are incorrectly categorized. Also I used my super-sticky Post-its, which are awesome and withstood an entire day of sticking and unsticking.

# Operations on Rational Expressions Partner “Game”

Sometimes when I call these types of things a game my students get a little cranky. I think it’s because they can see through my lies. This isn’t a game. It’s just a fun worksheet (for certain definitions of fun). I like it because students traditionally struggle with both simplifying rational expressions and doing operations with them. This worksheet gives students practice doing both, and forces students to work together to make sure they actually understand what they’re doing.

I split students into pairs and give each pair one worksheet to share. Then they spend an hour working like the perfect little angels they are. They know if they did everything correctly because the answer that zeta gets for #1 will be the same as the one phi gets for #1.

Student: Help! We didn’t get the same answer! Is that okay?

Teacher: Oh noes! Better work together to figure out who made a mistake where. Isn’t this a fun game?!

I use a custom paragraph style to make it easy to keep the answers in the same document as the problems. To hide & show the answers (in Word 2013) you should:

1. Find the Answers style on the style ribbon at the top of your screen.
2. Right-click and select Modify.
3. Change the text color to white (to hide) or not-white (to show) using the color box in the middle of the pop-up window.
4. Click the Ok button.

If you don’t have the style ribbon, it’s hidden away in some menu somewhere :). You could also just delete the answers. Or print it out and then white-out over the answers.