Algebra played the same dice games I wrote about on Day 151 for geometry a month or so ago. There was an assembly today so I didn’t have geometry.
Geometry is shifting into a little bit of stats for geometric probability. I started students off by playing three different dice games:
For each game, I had the winner raise their hand and say if they were Player A or B. We discussed why or why not the game was fair. The last thing students looked at was if there was a way to fix the game and make it fair.
Today is Friday; one strike.
I also introduced factoring trinomials; two strikes.
It ended up being one of the best days of the year.
I was frantically digging around the MTBoS looking for activities to introduce factoring. I came across a whole lot of crazy techniques; X method, diamond method, bottoms up…. Honestly, none of them made sense.
Then I came across this gem over at Dan Meyer’s Blog.
I pulled out a whole lot of dice from the department closet and after our opener I rolled a couple in front of the class. I told ’em that my dice added to 9, paused for about 15 seconds, them told ’em that the two multiplied to 18.
We did a couple more, then I broke the class into groups of two. Each group had two dice; a red and green and a folder to shield their dice. One person rolled the dice, calculated their sum and product then the other guessed.
They messed around with those for a while, this got old for some of the groups, so I gave ’em two more dice.
They added the red dice to create a number and did the same with the green dice. Then one student calculated the sum and product while the other student guessed the value of the dice.
For some groups, this wasn’t even enough. So… I kept increasing the number of dice.
Somewhere in between one, two, and three pairs of dice I upped the difficulty even more:
Green = Positive
Red = Negative
So now the sum is -2, and the product is -80.
This activity lasted about 15 minutes. I had 100% engagement across the board in 4 periods of algebra. No joke.
Students went back to their seats and I put this up on the board.
Last year I had students expand out binomial products till they picked up on the pattern. This year they looked at why A and C wouldn’t work here. We talked about how FOIL works, which I have actually been referring to as F (O+I) L this year.
Then things clicked.
Students understood where all that work with the dice came into play.
After a couple more multiple choice sort of problems, they were on their own.
I am fully aware that the dice activity only serves as a stepping stone in developing factoring skills. However, I threw up a couple of trinomials with a = 2 and students took them down. They understand that factoring these things is a guess and check process, and with more practice things will get easier.
Monday will be the true test to see how well they absorbed everything after a weekend passes.