Category Archives: Patterning & 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

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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Posted by on December 12, 2013 in Patterning & Algebra

Grade 4 are inferring & patterning!

In English Ms. Schinkel is teaching the class about inferring.  Inferring is a very important reading comprehension skill.  When reading we read between the lines, connecting our background knowledge to the information in the text to make inferences.

In this activity there is a mystery with clues that come in Postcards.  Ella has gone missing!  Where could she be?  Read the clues on the cards to solve the mystery using inferring.

In math we are working on patterning and algebra.  For this activity the students designed a growing pattern with a letter from the alphabet.  Their pattern had to grow (have more squares each term).  They made a table of values for their pattern and wrote the pattern rule.  They also had to predict what the 5th term would be.

Next, they walked around the class looking at their friends patterns.  They had to figure out the pattern rule from the drawing of the growing pattern.

If we look at Dusty’s patter here we can see that it starts with 7 squares making his u and he adds 6 more squares each time the pattern grows (each term):

Here is what the table of values looks like:

In grades 4 & 5 the curriculum expectations are to predict a term number that can be easily figured out by extending the pattern in the term value column (adding 6 each time).  By grade 6 the expectation is to use the algebraic equation to find other terms, like the 100th term or even the 1000th term.  In this case I’ve written the algebraic expression at the bottom of the table of values:  6x+1 so the 100th term would be 6 x 100 + 1 = 601 There would be 601 squares in the 1ooth letter u made with tiles.

Patterning

The grade 5s have been working on Patterning & Algebra for the past week and the 4s are starting tomorrow.

Our student teacher, Ms. Schinkel, has been teaching this unit and is doing a fabulous job!

In grade 5 the students learn how to use a table of values to determine pattern rules. We started out by playing “Guess My Rule”. Guess my Rule has an input/output machine. You put a number in and the machine spits out a new number, based on a pattern rule.

There are three types of rules.  In grade 5 we look at two (from Emily’s notebook).

The recursive rule (from Emily’s notebook):

The explicit rule is the relationship between the input number and the output number:

The Algebraic Rule is an algebraic expression:  3x

Here’s a fun online Guess My Rule game for practice.

Tomorrow we will use what we have learned to solve the problem of how many table we need at a dinner party.