Algebra tiles for equation solving

Today I was invited to work with a grade 9 class to introduce equation solving with algebra tiles. We looked at what the tiles were, reviewed some of their understanding about combining like terms and making zero pairs, and then set off to solve.

We started with simple equations like x+3=-7 where students could likely solve by inspection, but we were introducing how to build the expressions with tiles and use the tiles and zero pairs to solve.

We worked through a sequence of problems adding more complexity as we went. After doing several similar questions with x on one side, we made a coefficient for x, e.g, 2x+5=1

Then after a few of those types of problems we introduced a question that would result in a fractional result e.g. 3x+1=5

The final step caused some discussion. We can split the x term into 3 groups, but we can’t split the 4 into 3 equal groups without cutting up a tile. Some students showed the answer as x=1 and 1/3, some said the answer is x=4/3 since it’s 4 tiles split into 3 groups. Pretty neat!

Next we did some questions with x on both sides like 2x+1=4x-3. We needed a strategy of using zero pairs to get x on one side only to start with, and then we used zero pairs to get the constant terms on the opposite side. Finally we made enough groups for each x to have a group.

finally we levelled up to doing problems with distributive property and x on both sides. The class had recently worked with distributive property with algebra tiles so this was a bit of a challenge, but not something completely new to them.

We did questions like 2(-x+3)=3(2x-1)

By doing questions in this sequence students became confident with what becomes the final steps of solving, so in each subsequent level of challenge they will review those final steps over and over again building up their understanding and confidence.

It was a really interesting visit with the class. The tiles unlocked understanding for several students who had not always participated with confidence, and they told me that math class was great that day, and that they were feeling good about their skills for a change. I was glad to see a strong reception by some. Other students seemed a bit more hesitant to buy in and try.