Thursday, February 21, 2013

Add Em' Up - 3x3 Systems

We've just begun our second unit this term in Algebra 2 and the first stop was 3x3 systems. These, as I explained to my kids, can be very tricky. The smallest error, not making a negative a negative or adding incorrectly, can ruin an entire problem that might have taken a whole page to accomplish.

After a lesson on solving these systems using elimination, I decided that my kids needed even more practice in class. Practice makes perfect! Rather than having my kids do some boring classwork without any external motivation, I searched to create a game that had all the classes competing against one another.

My pinterest board is full of ideas across the curriculum. An idea that I had pinned originally was for Add Em' Up using exponential equations (originally intended for my Trig kids) so I decided that I could easily modify the game to fit into systems.

Now this isn't an original idea, and I must give credit to original Add Em' Up creator, so thank you. I love finding and tweaking everyone's ideas out there in cyber world! But here is how it goes....

I split my classes into groups of 4 kids (I varied their ability based upon their first unit score, etc.). Each group was given four pieces of paper (pink, yellow, green, blue) that had four systems problems on each. Each color paper varied in difficulty. Students were to solve one problem on each of the papers. After solving these systems, students added ALL the solutions (so 12 numbers on each paper) and checked to see if this added total was the same as mine (hidden in the folded paper on the board). As soon as I gave this detail out, there was a gasp (recognizing that they might not know which problem was wrong).

I set it up as a race throughout the day so that each group in each class was competing against one another. In the first class, I had one group get 3 of the 4 papers done. I grew worried.

4 kids in each group. 4 pieces of paper. 4 problems on each paper. 16 problems total.

So this had each kid doing 4 problems total. My thought was, okay so about 10 minutes or 15 minutes on each problem....... This of course leads into the discussion of, okay so come test time, what if I give you 2 systems problems.... you can't take a half hour on this part of the test. Thus, the new part of the conversation became that this activity was supposed to help you practice your speed when solving these problems efficiently.

Conversations that I heard during this activity:
"This is hard!"
"I see what you did, you forgot this...."
"Ooooh, I see where I screwed up, I did something stupid."
"Can you help me find the error?"
"Can there be decimals?" <--- I used problems that only gave "nice answers"

I have to say my favorite part was the fact that I had "pockets" in each group who I knew could help someone else in the group. The grouping was great, they were continuing to help one another. But not only were my "pockets" helping out, all the kids were trying to help each other and find the mistake. Of course, Miss Rudolph got called on a few times and the mistakes were very very small.

Now a few things to change for other classrooms: remember, we are on block scheduling so I had over an hour for kids to solve these problems so you might need to tweak this or do this after spending a week on these problems. In certain classes, I had groups of 5 and these groups had a "checker" who was to be assisting in spotting mistakes. Some of my kids also thought that the yellow page was easier than the pink page but it's dependent upon the person I suppose.

Another way that this activity could be changed would be going from 3x3 systems to doing this with 2x2 systems. This would probably go a lot faster.

Overall, I really did love this activity and the kids were really into it. Small mistakes kept many of my groups from finishing and also made them grow very frustrated. I did like turning this into a life lesson though.

Update: So I went to do this activity and bam, schedule change, wait it's OGT week and you now only have 40 minute classes. Anyways, my solution is just giving each group one of the sheets (different ones per group) and they race to finish their groups worksheet. Short, sweet, to the point.


  1. I love the idea of doing this with systems. I've done something similar with my middle schoolers, but they solved equations and added up their solutions. I put the 4 equations in the corners of a worksheet with a circle in the middle for the group to put the sum. The kids loved it!

  2. Add Em' Up can be used in so many topics! I'm thinking of trying it out if I teach trigonometry in the fall when we do equations for exponentials and logs. It'll work perfectly! Or even trigonometric equations.... oh boy!!!

  3. This looks awesome. I intend to use this idea for my 6th grade classes!! Thank you so much!!


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