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:
- These scales are all currently balanced. You must choose a number to fill into the boxes in each problem that will keep them balanced.
- Whatever number you choose for a problem, you may ONLY use that number.
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.
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!
ReplyDeleteYes 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.
DeleteI 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."
ReplyDeleteI 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.
DeleteThis 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.
ReplyDeleteAwesome! So glad to hear that it was useful
DeleteThis 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!
ReplyDeleteYes! 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.
DeleteThis 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!
ReplyDeleteEquations are equality of two or more expressions. Balancing Equations is a great way of teaching math. thanks for sharing.
ReplyDeleteThis is perfect. I start this next month. I tried to do this last year, but it wasn't the best. This is what I need.
ReplyDeleteTeaching in an Organized Mess
This is the second year in a row I have used this activity. I wouldn't change a thing! Thanks,
ReplyDeleteJan
http://equationfreak.blogspot.com/
"Are you trying to trick us, Mrs. Burwitz?" Loved it! The kids really appreciated it. And my fellow teachers also commented on what a great warm up this was for our kids. Thanks!
ReplyDeletehttps://mburwitzwahoo.wordpress.com/
Brilliant Sarah, many thanks for sharing. My Canadian colleague introduced me to INBs I definitely think they are the way to go for notes, better higher order thinking (for teachers as well!)
ReplyDeleteFrom Aotearoa (Land of the long white cloud)
this is amazing Thank you so much! I am so excited to try this out with my 8th grade students!
ReplyDeleteI wonder if rewording the directions as "each of these scales need to be balanced" or "your goal is to balance each of these scales" would create less student frustration. I have a feeling some of my students would not be happy with the fact that the directions "lied" to them!
ReplyDelete