Monday, 28 December 2015

Manipulatives in Math

Before the semester had started, I had stumbled upon Joe Sisco's (@joe_sisco) interactive word walls Google Drawings for Google Drive (Link to complete folder here:

I started by using first the Linear Relations drawing and the drawing for Quadratic Functions. As I progressed in the Quadratics units, I kept going back to the "! - Using Algebra Tiles" Google Drawings with both of my MPM2D classes. I used it to launch into many ideas or concepts, or I made my own drawings to quickly illustrate ideas.

It all started when we started to need to expand terms and factor trinomials. I remembered the awesomeness of using algebra tiles with my MFM1P class from long ago. I also remembered how students either rolled their eyes and groaned and then refused to use the tiles because I couldn't really assess them/get them to hand anything in. IN STEPS GOOGLE CLASSROOM!

To start, we practiced modeling trinomial expressions. All I wanted students to do was to review how to visualize the terms in a polynomial expression. Here is what students received:

Using Google Classroom, each student got the above Drawing file. I gave them the verbal instructions to model the expression, using the tiles on the side. The goals of this first sheet were for students to model the expression with algebra tiles, learn how to get and hand-in work within google classroom.

Here are some examples of student work:

 I switched it up in the second activity and gave them the drawing and got them to give me the expression (in standard form):

In the third slide I had students collect like terms and use the "zero pair" principal:

I wish I could say that I am a math genius and that I put the zero pairs concept in there on purpose, but when we got to completing the square much later on, WOW, was I happy that I had introduced this at this point, much earlier.

I finished off with expanding (there was a ton of guidance given in class to pull this off). 

Student work:

Really this was the goal of the lesson, but by doing the algebra tile work on the previous three examples, it really helped later on. Using google classroom was a huge help. Students really focused and knew that they were handing their work in. It added to the "validity" of the activity and my buy-in was huge. I cycled around the classroom and was able to provide feedback on the spot for students who seemed off track. I would finish each manipulative worksheet off by showing off a couple examples and discussing the work. It was a great learning opportunity for all (me included).

BUT it didn't stop there!

I then used the template to make "perfect square" examples and questions for Peardeck. Great to visualize perfect squares and their roots.


And Finally:

There were a lot of numerical examples too (don't worry).

When we got to completing the square, there were examples of how to complete the square visually, using algebra tiles. So I set-up 4 practice questions using Google Drawings and Google Drive. Note in the question about "Zero-pairs". When I brought this up, it was not a crazy idea or concept due to the work we had done before.

I gave them this (for our first example):

And they made me:

I even went so far as to showing them (not making them do) an example for when "a" is not equal to one. I really enjoyed making it too.

So I was thinking about fractions and some work I had done with helping students in grade 9 with EQAO prep and general math concepts help from some years ago. I had used the Pattern Blocks for visualizing fractions and I started wondering if there was such a thing made on Google Drawings. I couldn't find anything, so I made these:

Link to google drawing file:

I hope to use them in the future with other teachers within my board, but I'd love to hear how you use them in your class and/or any feedback (I tried really hard to align them properly so they actually work).


  1. This is GENIUS for teachers that don't have algebra tiles or pattern blocks. I just got a set of algebra tiles this summer from redditgifts for teachers and haven't used them yet. Now that I see this post, I could have used these last week when I started factoring! I'll definitely be saving this for next year.

    1. Thanks so much! I have not regretted the use throughout my course. Make sure to grab the template too. It saves the work. I am thinking next time to include a shortcut key area that has duplicate and multiple select on it to speed things up too.