Algebraic Reasoning Class Summary 10/28/13

with Kim Rodgers

Back it Up!

We warmed up the class by discussing strategies for solving 33 x 5. We came up with three ways to arrive at the same answer using different processes. One of the strategies involved multiplying 33 by 10, since 10 is an easy number to multiply by, and cutting the answer in half. Another student mentioned that this might not be a good strategy to use if we were multiplying by 4, which led into a discussion about using strategies in our Algebra Tool Kit. We don’t use all of the strategies all of the time -- we find the ones that suit the problem.

We moved on to reviewing what we had worked on in class the previous week with our Morph Machine, catching up a couple of students who had been absent. Going Backwards was added as a strategy to solving a problem using inverse operations. After performing some steps together on several examples, the students began to understand the value of this strategy. Because this may be a new concept for many students, I am providing a more detailed description of Monday's class in case any of our families would like to review the material at home. Here’s what we worked on in our Morph Machine: 

Students picked a number between 1-20 for n and wrote it in their journals. They then took that number through a series of operations.

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n=                _____
Add 1             +1
Multiply by 3   x3 
Add 4             +4 
Subtract 7       -7 
Morphed n = _____

Once they morphed their numbers, volunteers were called on to share them. Together as a class we used 3 of these morphed numbers to work our way backwards to find the original numbers. For instance, if the morphed number was 6, we worked backwards using inverse operations like these: 

Morphed n =     6
Add 7              +7 
Subtract 4        -4 
Divide by 3       /3 
Subtract 1        -1 
n=                     2

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Inverse Operations

Here’s where the tricky part came in. We discussed how variables can define a rule for each step so that any number n will work. So, using 6 as the morphed number, we look at the first step to work backwards -- subtract 7. We know the answer is going to be 6, so we set it up like this:

n - 7 = 6



What is the inverse operation of subtracting 7? Adding 7! So we must do that, but we must do that to both sides:

n - 7 + 7 = 6 + 7
n + 0 = 13
n = 13

Taking 13, we move one more step backwards to add 4.

n + 4 = 13

What is the inverse of adding 4? Subtracting 4! So we must do that, but we must do that to both sides:

n + 4 - 4 = 13 - 4 
n + 0 = 9
n = 9 

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Balance it Out

We continued doing this together as a class until we got back to our original number, n. I then had them pair-up to further practice these problems. Many were still stumped. As I made my way around the room giving hints and advice, some students began to have a glimmer of understanding. As soon as I saw that, I had those students help others who were having trouble. Time went so quickly! As class ended, I told them that we would be working on this again next week, and if they felt like they still didn’t understand, that was okay. It’s a difficult concept to grasp. I will be presenting the same concept next week using a scale as a visual -- to drive home the point that both sides of the equation need to be balanced. Whatever happens to one side has to happen to the other!

I’m not a big fan of computer games, but I do have one to recommend from Mrs. Yoder who teaches Computer Science at Mosaic. It secretly teaches kids Algebra, but don’t tell them that! It’s called DragonBox. There are two versions. If Algebra is a new concept for your child I would start with the beginner version. If your child has had some practice with it you might want to check out the 12+ version. It really drives home the point that whatever is done to one side of the equation has to happen to the other side, as well.

See you next week!