I taught a disastrous lesson about two step equations in my 1st hour collab class one day. Painful really isn’t even strong enough to describe it. It was too much too soon. I tried to lead with some real-world type situations to get the kids to discover more of using two step equations on their own and it flopped. The kids left confused and I left frustrated with both myself and them. I have about 4 minutes between 1st and 2nd hour so I used it to revamp the entire lesson in hopes of salvaging the day. I can’t tell you how thankful I am for the MTBOS as I remembered reading Julie Reulbach’s blog on magic numbers which led me to Sadie’s blog on the same topic. I have absolutely no idea why it took me so long to jump on this band wagon. I guess I always thought my kids were getting it using traditional instruction but this year they most definitely weren’t. Those 4 minutes between classes were some of the best planning I have done all year.

I started class by telling the kids we were going to take a little break from math and do some magic tricks. I was going to secretly pick a number and give them some clues to help them guess it. The first person to guess the number would get 100 e-bucks (our team money incentive system). I started out with simple things like I take a number multiply it by 2 and add 2 to get ten, what is my number? A couple hands go up and say “four”. Great. We step it up a bit. I take a number and divide it by 9 and add 12 to get 15, what is my number? More hands go up than the first time with a correct guess of 27. I start to think maybe we are on to something here. I kept making up examples on the fly with more and more hands going up each time. When I see I have nearly everyone I ask them to jot their own magic trick down on their table and miraculously they all do it with no complaining. They were hooked. I started letting them guess each other’s numbers until it seemed they had it down backwards and forwards. We started discussing their methodology and how they were guessing these numbers. Almost everyone said they worked “backward” if the clue said multiply by two add four get 10, they subtracted 4 and divided by two to get the magic number. I knew that was my window to move on.

I handed out these Steps sheets and started guiding students through turning their magic tricks into equations. Some of their work is below:

All the kids did beautiful work and once their equations were written they quickly began to see the connection between “working backward” and finding their magic number. I began selecting their equations and we began solving them using the equality properties rather than just “magically”. The transition was so smooth for them it was hard to believe…why did I wait to so long to try this?!

Here are a few of the kids comments:

It made me understand the equation. It made it so easy.

This helped me because its easier.

I like it because it helps me learn hard math.

I like magic number because you have to think really hard and it is also really fun.

I like magic number because it helped me understand how to get the answer through the steps.

It helped me because when we did examples of it it started to get to me. When we did it into steps it made sense like adding or subtracting the opposite. Then once we got it, it finally made sense!

I understand it more now than yesterday.

I like it because it is fun to figure out and challenges my brain which I love. It helped me a lot!

Thanks MTBOS for the inspiration and “involuntary collaboration”!

I love your steps sheets. Great addition!

Did this today with one section of pre-algebra with some success. They got tripped up when they did a number plus there then times 4; led into conversations of the distributive property which we just learned last week. Two other sections tomorrow.

What an awesome way to lead them into the distirbutive property. Have you ever done this activity http://map.mathshell.org/lessons.php?unit=7220&collection=8

It is one of my favorites and really gets at the distributive property!