MFM2P - Day 23 (Solving Systems of Linear Equations with Manipulatives)

We did this balance bender as today's warm up:

I had a student write his solution on the board - it is below, but just the numbers in black! We spent a bit of time going through explaining what each of the numbers meant and why it is important to include this information as part of a solution.

I also told them that what they were doing to solve this was the same reasoning they do with algebra.

I went through it throwing in variables so that they could see that the process is the same and I told them that if they prefer to work with the pictures, they can turn equations into pictures.

Today was our first day solving systems of linear equations. I gave them this handout and told them to get into groups or 2 or 3. I had pattern blocks and pennies out for them and set them to work. I circulated and helped get each group going.

Here is one example:

and this is what it looks like, solved:

The orange squares represent jujubes and the blue diamonds (what's the plural of rhombus?) represent Smarties. They took 33 pennies for the right side and 18 pennies for the left side and moved them around until they had the same number of pennies for each jujube and the same number of pennies for each Smartie. That was the solution.

Had I given them a system written like this:

they would have stared at me and given up. But this is the same system they just solved!

Here is another:

and the solution:

They worked through the handout at their own pace. One group finished solving all the systems and started creating their own. The others all understood the process and what they were trying to find. A good way to finish up the week!