## Friday, July 20, 2012

### Solving Special Case Equations

I loved this lesson.  It went SO well, especially with my older kids.  I think that no solution and identity equation are sometimes hard for kids because they don't really get what they are.  They may be able to identify them, but I want more.

The past few days we've been solving equations and they're doing great.  Today I started class by giving them this worksheet:

When I handed it out I said two things:
1. These scales are all currently balanced. You must choose a number to fill into the boxes in each problem that will keep them balanced.
2. Whatever number you choose for a problem, you may ONLY use that number.
I told them that if they were stuck on one to just move to a different one but that I wasn't going to help them find the answers, they really had to think hard.  Most of them were of course easy.  Numbers 3 and 6 were not.  They just kept trying though.  We were all laughing as they tried to trick me into giving them a hint; instead all I did was to repeat my instructions to them.

At one point a boy asked if they could use negatives.  I referred back to the two rules, as long as it is a number they could try it.  The other kids heard this and decided that MUST be the trick.  It has to be a negative number.  No luck. The same thing happened when using 0 and decimals were suggested.

After letting them suffer for a little bit [note: they never stopped trying, not a single one of them gave up..they all wanted badly to be the one that figured it out] we went over them.  I went around the room and had every kid call out their answer to each one, writing the answers down as we went along.  Also I saved #3 and #6 for last which killed them.

For #1 & #4 everyone got different numbers and we discussed if that was ok.  They decided it was ok.  I asked which one of the numbers was the "correct" one and they agreed that they were all correct possibilities.

For #2 & #5 everyone got the same answer and we discussed whether there were any other possible answers.  They said there was not.

On to #3. They were so excited.  Everyone got real quiet. They couldn't wait to hear the answer.  I started by covering up the numbers 20 and the 13.

Made sure that we were all on the same page and agreed that at this point every single number would work (like in #1).  Then I asked what would happen to a balanced scale if we put 20 onto one side and 13 onto the other side. They said it wouldn't be balanced anymore.

I revealed my secret to them that there was in fact no possible answer.  Discussed that the real problem was when I lied and told them that all the scales were balanced.  Then they went crazy saying they KNEW it wasn't going to work!!  They were thrilled that they were right.

Afterwards we made the following foldable for their notebooks:

I love lessons that go like this. It is so rewarding and fun when they get so into an activity.  These are the times when I feel like they are really learning.  They will remember their frustration over the no solution scales and they really developed an understanding of exactly why equations like this do not have an answer.  They also have a much stronger understanding of why identities have infinite solutions.  I feel now that when they give these as answers to equations they know why they are writing those words down.

1. Where were you a year ago? My algebra 1 students last year had a hard time grasping the concept of infinite solutions and no solution, I kept relating it to a scale but never had the thought occurred to me to put it on a scale! I will definitely be using this!

1. Yes please do! It's a tricky idea to really understand. The best part of this was with the scales you don't have to mention anything about at equations at all. My kids actually thought it was more of a puzzle like sudoku than anything to do with math..silly teenagers.

2. I apologize for the anonymous name, but I don't know what else to use. My question is how far into the ISN do you start the WWK section? I love all of your ideas! We use a similar notebook in fourt grade, but call it our "Learning Log."

1. I leave the first 4 pages for the table of contents and then the next six for wwk...you can always do or more or less though depending on your kids. If your kids write big you may want to set aside more or you can always tape in additional pages or some have suggested doing it in the back and working backwards.

3. This is GREAT! My 8th graders and I thank you (although they may not know they should). Getting "No solution" is so abstract that I had no idea how to make it concrete enough.

1. Awesome! So glad to hear that it was useful

4. This looks very similar to hands on equations! I don't know if you have seen it, but it teaches the kids how to solve equations with manipulatives. Very cool!

1. Yes! That is funny you say that because that's exactly where I got the idea from. When I taught 8th grade, we used the whole hands on equations kit. Since then I've used bits and pieces of it here and there. Recently I was excited to find that all of hands on equations is available now on the iPad as an app.

5. This looks very similar to hands on equations! I don't know if you have seen it, but it teaches the kids how to solve equations with manipulatives. Very cool!