# Possible and Impossible Graphs

See this post:

I first saw this a few years ago at Shodor Interactivate. I think it is a good way to start thinking about functions. My favorite part is having students make up stories for each graph.

# Creating equations from solutions

The idea: give kids cards that have numbers written on them. Challenge: write an equation that has your number as a solution. Write them on a card. Hand them to me. I rate them for difficulty. Then I hand them out again.

Kids get to pick — do you want an easy or a hard problem? I hand them out. They solve ’em.

# File Cabinet

Not this yearDan Meyer’s 3 Act lesson format is here to breathe life into applied math. I was staring at this file cabinet at the back of my room, saw a stack of Post-Its on my desk and thought, how many Post-Its would it take to cover this rectangular son-of-a-prism… and so it began.

 Forget wrapping paper, Post-its FTW!

I filmed File Cabinet – Act 1 (watch video here before Act 3) last Monday, posted it to 101qs.com and every day I chipped away at sticking Post-Its for about 40-60 minutes after school. Yes, it was a lot of work, but totally worth it! This math lesson/project instantly became a huge conversation piece in my classroom. Students came in completely intrigued by what was going on in the back of my room. They stared at it. They did weird finger, arm, and eyeball measurements. They walked around it numerous times before I finally said, “Make an estimate. It’s free! Write it on the board.” My whiteboard at the front of the class had about 30 kids’ names on it with their estimates. It was so invigorating to hear them discuss or argue their estimate. One student made an estimate within 1 Post-It of the actual result.

# Estimation and Volume

In the weeks leading up to teaching volume, one could try to get at the core ideas through a series of estimation problems. Thoroughly stolen from Stadel’s site, this candy corn would be a good starter. But then we could move to rice in a jar, or pennies in a roll, or dice in a box, or any other series of 3d containers with stuff in them.

# Mental Math and the Distributive Property

Following a problem in the CME Project’s Alg1 book, I’ve been teaching the distributive property via mental multiplication. Kids see how quickly they can do this multiplication, and the fastest way to do a lot of these is to split the factors into two summands. This provides a great context for the distributive property, which we then work hard to express clearly without variables (which will come later).

Another version of this problem that I’m throwing in to the opening set today: “Sam is doing mental math. One of his steps in his calculation is (100 x 7) + (15 x 7). What was his original problem?”

I think that this will help everyone focus in on a clearer expression of the distributive property.

# Combinatorics and the properties of arithmetic

1. How many different ways can you fill in the question marks to make the equation true?

? x ? x ? x ? = 210

B. How many different ways can you fill in the question marks to make the equation true?

? x ? = 735

Hint: 21 x 35 = 735.

# via Kaleb Allinson

I play a game in class called guess my dice right before we do factoring. I made this up when I taught a low level Algebra 2 class. I roll two dice that have more than six sides. (I started with six siders and then very quickly went to a local game store and bought some 8,10, and 12 sided dice.)
I tell my students that my dice add to 19 and multiply to 88 and ask them to guess my dice. I try to play this at the end of class for a week or two as I have time leading up to factoring. Then when they discover how to factor this dice guessing skill is very helpful. They always realize what I’ve done and think I’m really tricky.