# Tag Archives: algebra

## Algebra – from Simplifying Expressions to Solving Equations

While we were working on measuring circles; circumference, area of circles and volume of cylinders,  I noticed that manipulating the formulas was a mystery for some students.  For example, the formula for the area of a circle is:

most students could find the area when given the radius but if I gave them the area and asked them to find the radius they were stumped.  I could just show them how but I realized that the issue lay in algebra so that is where we have returned.

Algebra is often a huge stumbling block for students.  I’ve been doing a lot of reading and research that I may post about later but for now I’ll focus on what we are doing in class.

First we revisited that the equal sign means that both sides of the equation are balanced or the same.  Surprisingly, some people don’t really realize that.  To reinforce this idea we used Cuisenaire Rods as models.

The students made a “train” with the yellow and black rod.

They had to find other trains that were equal in length to the yellow and black together and then write down equations to express equality.

This photo shows our progression through simplifying the equation.  The letters represent the colours of the rods.  The rods can also be given numerical values.  The distributive property came out during the discussions!  I was so excited I actually jumped up and down and squealed a little bit!

At this point, I knew I had to be explicit about the commutative property of addition and multiplication and the distributive property of multiplication over addition (which you can see in the photo above).

I struggled with how to present it and luckily Kyle Pearce wrote a post that helped me out (and I attended three online webinars presented by Kyle).  These animations by Kyle really helped me to present the distributive property first with numbers (modeled by Cuisenaire Rods) and then with variables.  We did this on the SMART board with Cuisenaire Rods but, alas, I did not take photos!  I know some of the students did though so I may update this post with their photos.

Next the students practised a few times on their own (we NEED a Cuisenaire Rod App for the iPads!) like this (sorry I can’t embed it):

TapintoTeenMinds

Then, still following Kyle’s lead we did this:

I did a few more examples using Alge Tiles and then the students proceeded to practice making models and writing down the simplification of the expressions.  Some still needed a fair bit of scaffolding, but they are getting there.  I also had some students who did not like models and just wanted to simplify using the numbers and letters only.  I think it’s important to use the models though so they aren’t simply memorizing procedures.

This went fairly well, but there are still a few students struggling.  We will move forward into solving for the variable by performing the same operation on each side of the equation.  Then we will circle back to formulas for circles and apply what we’ve learned about algebra to measurement concepts.  Most posts to come to show you our path.

Don’t forget, we’ve also learned the origin of the root word circ in English!  It all ties together in room 133!

Posted by on April 10, 2015 in Math, Patterning & Algebra

## Luke & Brad Discover a New Subtraction Algorithm!!!!

Yesterday I put this problem on the board and asked the students to solve it with mental math:

72 – 9=

I was hoping to get a strategy like using 10:

72 – 10 = 6 2+ 1 = 63

An some students did come up with that.  But Luke came up with the following, and it was an accident.  He accidentally did what many students do and he subtracted the minuend from the subtrahend instead of the reverse – but it worked!

This image will explain the terms for subtractions numbers:

At first I couldn’t figure out what he had done but Bradley understood it.  We tried some different equations to see if they worked and they did!  We still couldn’t really explain it though so I brought it to the staff room where five of us looked at it and tried it out with different numbers (and we tried double digit numbers which also worked!).  We figured out that they were subtracting in stages or using algebraic methods.  Watch the videos to see what I mean.

and this is their explanation

The explanation that makes the most sense to me is the algebraic way:

(72-2) – (9-2) =

70 – 7 = 63

Because the 2 was subtracted from both the minuend and the subtrahend, the difference is the same.  Or you could look at it like this:

9-2 = 7

70-7 = 63

Subtracting the 9 in stages, first 2, then the remaining 7.

Super Cool!!!!  It’s so true that when students come up with their own ways to solve problems their understanding is so much deeper.  These two are examples of that constructivist theory.  If we had more time for math, imagine the possibilities for all students!

Has anyone else seen a student solve a subtraction equation this way?  I’d love you comments please.

Posted by on February 19, 2014 in Math

## Mrs. Barker visits to teach Patterning

We were very fortunate to have our Math Coach, Mrs. Barker come into our class for 100 minutes to do some math with the grade 5s (the grade 4s had the same opportunity in Mme Lafond’s class).

We were very excited to be doing grade 6 math!!!!!!!!  No problemo!!!!!!  We chose to do grade 6 because we had already completed the grade 5 expectations for Algebra & Patterning (still need to do equations though).

Here are a couple of groups explaining their patterns:

We all had a blast as you can see from the photos below.

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