Monday, December 17, 2012

Solving Equations Odds & Ends

This week will be the end of my solving equations independent study unit.  Since this was a new idea for me, much of what happened during the unit was created as we went.  These are a couple aspects that either I haven't explained before, are new, or address questions that people have asked.  Overall I really enjoyed this unit a lot and would definitely do it again.

Small Group Table
Until recently, this small round table was being used as my teaching table.  My projector was on it and it was in the middle of the room.  When my wall mounted projector was installed I didn't need it there anymore though.  So I moved the rug over there, put the table on it and pulled up a bunch of chairs creating our extra help table.  

Some days I was having trouble getting around to help each student that needed me so instead I station myself at this table and call them over to me in small groups.  Sometimes all of the kids will be working on different things and I'll just help one at a time.  When I feel that they're good to work on their own I'll send them back and let someone else take the seat.  Other times I'll call up a group of kids all working on the same skill and will give a mini-lesson/activity to all of them.  The kids really seem to be liking going to sit over at the table with me.  One afternoon I had two kids beginning to work on combining like terms and then three other kids spoke up that they were also stuck there so they came over too.  Instead of doing the worksheets I had them work on a paper cutting activity and dry erase boards to practice/learn the skill.  They enjoyed it and it worked really well.  If I'm still at my desk after a few minutes into the period kids will ask if we can go over to the table yet, or sometimes they'll just go sit there and call me over.

Mini Lessons and Activities
Originally the practice/check/quiz system was working out well because none of the concepts were really new.  As kids reached topics that were new however, they needed some instruction.  I started by just explaining the problems to the kids individually but felt that I could be doing better.  So what ended up happening was small group mini lessons and activities.

When kids got to combining like terms I worked in a small group on a paper cutting activity that I've used before and really like.  I had pre-prepared strips of paper ready at the round table.  I would give the kids an expression and they would write it out big on the paper.  They would then physically cut the paper apart and rearrange it, grouping like terms together.  Then they would add up each group.  For the activity I'd have them go through enough examples until I felt that they had the hang of it and then transition to doing the same thing on paper.

When kids got to special case equations I had them complete my scale activity.  Then I had them complete four problems (two one regular ones, one identity, and one no solution) and would then relate their answers to the scale activity to demonstrate the meaning of the identity and no solution and how they are different from a regular equation.

ISN Notes
When I put out the notes for the topics I wasn't 100% sure what my intention was.  I do know however that I need to keep things organized and uniform so I wasn't ok with each kid creating different numbered pages.  Instead I had them all title a set of pages "Solving Equations" and decide what needed to go there.  If a kid started with one step equations they put in the one-step equation notes, and then the two-step notes right underneath (taping it so it flips like a book), three step right underneath that and so on.  For kids that started at multi-step equations, those would be the only notes they had on that page.  

This is an example of a kid that took the notes for one, two, and three step equations:

Someone that started on two step equations might only have the two and three step notes.

The "notes" are just a sample problem with the steps written out.  As far as knowing what to write, they would just borrow my notebook where I had all of them done and taped one right on top of the other.  For kids where this wasn't enough, I would work through it with them.

This way, everyone in the class still has the same numbered pages called solving equations, but they only have what they need on those pages.

These are what I gave out:

Wrapping it all up
At the beginning of last week I mentioned that I'd like to finish up within a couple days and the kids protested.  I said ok.  If they want to keep working and they're being productive, I'll certainly let them go for it.  This week though will be the end of it.  All of my kids are not going to be done though.  The kids that are still working are the ones that at this point need more of my attention.  So what I plan to do  is set up a good amount of extra help time and have them come in specific groups.  I'll invite kids (like 4 of them) that are in the same place to all come on the same day and work through it.  I told them up front that my goal of this whole thing was for all kids to end up with a perfect grade because it'll mean they have mastered the skills.  This is still my goal.  I want to continue pulling them in for extra help until they have all finished all of the sections.  I will continue this all the way until the last day of the marking period if need be because knowing how to solve equations is non-negotiable.  

I also don't plan to accept laziness or apathy.  If they don't want to come or make the effort then I will make them.  Instead of giving them zeros and saying, "oh well, you never came to make it up" I will  go get them and escort them to my room if need be.  Failure is not an option with me and I mean it. 

Overall, I think that my favorite part of all of this was how well I got to know my kids.  I had no idea how smart some of them were and how quickly they were able to move through the levels.  They had been doing well in my class before, but I didn't know just quite what they were capable of.  On the other side of things, I also know my struggling kids so much better too.  I know EXACTLY what they are doing and where they are making mistakes so I am able to help them focus themselves better on what to work on.  I think that all of this is extremely valuable information to have if I want to be able to help them.

A couple people have commented that they have used my idea to do something similar in their classrooms.  If so, I would absolutely love to hear details! 


  1. I happened upon this series of posts tonight and it couldn't have come at a better time. I've done boot camps like this before, but not for solving equations. I've done it for operations on rationals and on graphing linear equations. My students this year are struggling with integers and equations, so I'm going to start boot camp this week over these two skills. I'm really liking your recording sheet and I plan to get my version copied first thing tomorrow morning!

  2. This is absolutely a lifesaver! Thank you so much for the detail you put into this. I am trying interactive notebooks for the first time this year, and as our curriculum has now changed for the 3rd year in a row, I can't tell you how much I appreciate that you have already laid these notes out for anyone to use. I appreciate all the time you took to do this-thank you:)

  3. Hi! Is there a special download for your foldables? It seems the last picture/download is no longer available. Thanks!

  4. I would also love the print out of these foldables :) Thanks!