Solving equations using algebra tiles - 3 examples

There are so many cool ways to use algebra tiles in math. Last week I wrote a post about using them to factor. In this post I wanted to show 3 examples for using algebra tiles to solve equations. I'm using a set of paper algebra tiles in the photos, mainly so that I could cut one in half for example 2 that involves a fraction. So let's get into it!

Example 1: Solve 2x + 3 = 11 with algebra tiles.

>>A paper version of the solving mat can be found for free here orhere. My friend Laura from EngagEDucate reached out about making a digital Google Slides version. That digital version can be found here.

The rectangular tiles are used to represent x and the small squares are each used to represent 1.

In this photo, the 3 squares on the left got recycled along with 3 squares on the right, leaving 2x = 8.

Here's the fun part! We can split the 2x into x and x and make equal groups of the small squares on the other side.

After recycling one group, we get x = 4. Using algebra tiles to solve 2-step equations is an incredible way to introduce the topic.

Example 2: Solve ½x + 4 = 7 with algebra tiles. Here is a quick video showing this example:

It's nice to use paper algebra tiles (free here) for this example so that an x can be cut in half. (We still keep the other half for the end.)

First I cut an x in half to show the ½x.

Here we can see our equation set up.

We recycle the 4 squares on the left and 4 on the right, leaving ½x = 3.

Now we bring in that other ½x from earlier. Because we just doubled our x, we have to double the other side. This gives us x = 6. Example 3: Solve 2x - 3 = 7 with algebra tiles.

To get negative tiles with paper, you can print on 2-sided paper, like astrobrights, or glue two pieces of paper together before cutting. Here we have 2 x tiles and 3 negative tiles on the left and 7 tiles on the right.

To get rid of that -3 on the left, we +3 to make a zero pair. Then we have to +3 to the right, too.

The zero pair gets recycled since it's 0. Now we have 2x = 10.

And now back to the fun part: splitting into equal groups.

And recycling the extra stuff to get x = 5.

Video: Here is a video showing all 3 examples in this post:

Resources: Algebra tiles can be found here. Paper solving mat can be found here. Digital Google Slides solving mat can be found here. Solving equations activities can be found here.

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