Introduction to Algebra

Are there similarities between algebra and Native war record robes?

War Record Robe

This morning we looked at pictures and learned more about the counting coup concept. These war robes and coup sticks were worn by Native warriors (especially from the Plains) as badges of honour, showing the history of their prior battle actions. The more dangerous the action, the more prestigious the coup.

Counting Coup Stick

If you think about it, the robe and the stick are just story-telling devices that group together: a) different symbols representing the elements of the story, b) the actions taken, and c) the consequences of those actions. We found that we can relate these ideas specifically to: a) numbers in a math equation, b) the operators, and c) the results. (This idea was modified from an Australian aboriginal study.)

In class, students drew up several stories using their own meaningful symbols. For example, one student recounted the events of last week's full moon ceremony using just a simple addition story. It contained people coming in from different communities, a full moon and stars, as well as items needed in the ceremony (for example the water and drum). Another student commented how similar these picture stories are to the ancient Egyptian tombs, recounting the histories of the kings with hieroglyphs.

From a mathematical perspective, these stories are important for us to analyze. You might recognize that taking away an element from the story will change the story's consequences -- much like in a math equation. We explored different ways of compensating for making a change, much like you would do in algebra.

For example, if we have the equation 3 + 4 = 7 and we change the 4 to a 2, we tried to find different ways in which we could do something to the story to compensate for the change. (We came up with four ways -- how many ways can you come up with?)

Joke: What kind of clothing does a mermaid wear? ... An algae-bra! 

After the break, we played a counting game with 12-sided dice and Monopoly money. Everyone started with $20 and we took turns rolling the dodecahedra. Integers between -6 and +6 are on each die: a negative roll meant we had to give away that amount; a positive roll, we were given it. Rolling two together meant we had to solve the overall value first!

Dodecahedron: a polyhedron with 12 flat faces

 After a few rounds, we had to start keeping track of IOU's, a perfect example of how negative numbers work in business. We found that negative numbers and subtracting are similar concepts (but they don't always lead you into the hole!).

Tomorrow we'll continue our algebra introduction with some more activities...

Posted by Karen

Tangram Video #1

Just before the holiday break in December, our math class took lots of photos for several stop-motion videos made of tangram pieces.

A tangram is just a small math puzzle where a square has been cut into seven simple pieces (5 triangles, a square, and a rhombus) -- see the picture to the right as a reference. These seven pieces can then be formed into all sorts of funny shapes and characters...

Here is the < VIDEO LINK > to the first stop-motion movie. We made two other ones based on nursery rhymes so check back again for updates!

Posted by Karen

Frieze and Fractal Fun

This morning in math class we started a new topic: Geometry!

Rather than just keep to the typical "What-is-a-point? What-is-a-midpoint? What-is-a-coplanar-line?" geometry introduction, we took a step further to look at the Native American friezes in clothing and quilting works. It turns out that there are just seven ways to manipulate a tile into a border pattern.

(Seven is a happy number that shows up everywhere: 7 Grandfather teachings, 7 ages of man, 7 days of the week, 7 classical planets, 7 musical notes, 7 pillars of wisdom, 7 chakras, and seven also represents the Universe with the 3 of heaven combined with 4 of the world.)

After that, we started making our own friezes and patterns.

For inspiration, we watched a video from NOVA, "Fractals: Hunting the Hidden Dimension". A fractal is just a repeating pattern where the smaller parts actually look like the bigger parts when you zoom in all the way -- happening over and over again, forever!

Here are some colourful examples of fractals -- sometimes fractals are used to show naturally occuring examples in nature, like mountains and cauliflower and tree branches. Sometimes they're just amazing patterns:

Notice how the smaller parts look like miniature versions of the overal picture? That's what makes the pattern a "fractal". Check out how the following simple geometric shapes gradually turn into complex fractals -- see if you can come up with your own pattern:

Posted by Karen

Snow Day!!

Yesterday, Toronto was blanketed in more than 20 cm of white, fluffy snow.

For some schools, there hasn't been a snow day called in over a decade!

 

 Too bad classes were cancelled though. :(

Posted by Karen

Virtual Stock Exchange

A week ago today in math class, we set up a virtual stock exchange game online.

Each student was given a pretend $100,000 to invest in U.S. companies of their choice. (There wasn't a Canadian version available.)

So on Tuesday mornings, we log in to monitor the rankings and make trades with new and old stocks, and basically check out what everyone else is investing in. Each trade is followed up with the calculations governing them, so everyone is practicing decimal multiplication and addition skills.

Within one day, one of the portfolios increased by more than 4.5% -- that translated into a gain of over $4,000! The rankings change every day though, because the markets fluctuate a lot even over the course of one hour.

Centennial is certainly not recommending that we gamble our money on the stock market but this game does provide good math exercises and is a fun, friendly, competitive group activity.

Posted by Karen