## Thursday, October 18, 2012

### Solving Equations woes

We've been solving equations in my Integrated Algebra 1 class for the past few weeks, and as a whole I've been pretty impressed with their work.

There are basically two different reactions:
1. These are too hard! I don't know what to do next!
2. Can you make them harder? These are fun! Can we have some more?

The problem with a couple of my kids who are struggling with the equations is that they can't keep their work organized.

So here's my plea for help: Does anyone have a special template or something that they give to the kids to keep their steps lined up?  Should I give them grid paper and make them write one number in each box?  Unless I hear from some of you in the next oh, 5 - 10 minutes, that's what I'll do.... but if you have any additional ideas after that I'd love to hear them! :)

(I just wrote this up to give to those kids... think it'll help?)

1. I like this! I always say it acts like the great wall of china so you have to get all your troops together (aka combine like terms on each side) before they can cross over.

2. Thanks, Ashley! I like the great wall of china analogy. :)

3. My colleague does the vertical line too so her kids coming to me all do that which is great! ALL math work for me must be done on grid paper.

The only thing is the problem number (#12) may get mistaken as part of the equation. I have my kids write it like this: 12)

4. Thanks, Fawn! I don't usually use grid paper but may make it more available for the kids who I know will benefit from it.

I was hoping that by skipping a square the problem number won't run into the problem. :) We'll see how that works!

5. I teach my kids to underline the like terms. It's a visual way to remind students of what to simplify.

6. STEPS are clutch for my kids.

1. Simplify each side by:

a) Distributing (I call it the wink and smile, which they love - draw an arch connecting the value outside the parenthesis to the first value inside the parenthesis on the top, then another arch connecting the value outside to the second value inside the parenthesis along the bottom...looks like a smiley face!)

b) Combining like terms (here I use shapes. Constants and any non-like terms each get a different shape placed around them (square, circle, triangle, etc) AND THE SYMBOL IN FRONT OF THEM. This helps the students maintain the sign of each term as they apply the commutative property. Then, they group like shapes in the equation and combine them.

The rest is just following the remaining steps:
2. Get all variable terms to one side.

3. Use inverse operations to isolate the variable.

7. Just starting using FLOWCHARTS to teach multi-step equations, instead of writing the work out for all my kids. The majority of my students prefer just to write the steps out, but I introduce this content by demonstrating "undoing operations" on a flowchart.

You start with the variable in a box, then draw an arrow to a box where you write what operation is being done to the variable. Continue with boxes until you get the answer. Then reverse the direction of the boxes below the original, and do the opposite operation as above.

For example: 3x - 6 = 12

x --> times 3 --> subtract 6 = 12

BACKWARDS

12 = (add 6) --> (divide by 3) --> x

x = 6

Some of the kids who like the visual representation really thrived in this intro to two-step equations!!