Star Bundles

In early February, quilting expert Lynda Shapiro flew in from Manitoba to help students design and sew together their own star bundles.

Everyone worked diligently during this three day project, sewing together diamond-shaped fabrics into an eight-pointed geometric pattern.

These star bundles display the colours of the medicine wheel: red, yellow, white, and black.

Star bundles are typically used to keep together traditional and sacred pieces collected over a lifetime.

Check out our < VIDEO LINK > on YouTube to see how it all turned out!

Posted by Karen

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

Rock Crystal Candy

A couple Fridays ago we set up an experiment in class to make Rock Crystals.

These ones are just made of sugar mixed in water. The trick is to heat the water so that it can dissolve even more sugar than normal (called "super-saturation"). When the solution evaporates, sugar crystals should be left behind.

We used a kettle to boil the water in the classroom, then mixed it with as much sugar as we could in a large mixing bowl. Each of us came up with our own colour combination using food colouring mixtures.

The following Tuesday... nothing had happened. That was a surprise! The instructions called for crystals forming overnight but three days had passed with no effect!

By the following Friday, some small crystals had started to form on the surface of the sugar solutions. The red one solution by far the best looking crystal growth -- it had been the last one from the mixing bowl, which meant it had all the extra sugar from the bottom.

Next time we should try to keep a constant heat on the water and really try to super-saturate the solution before it cools.

Some brave souls tried to eat the rock crystals... Check out this YouTube < VIDEO LINK > to see what happened!

Posted by Karen

Portfolios and the White Ribbon Campaign

This morning before lunch we took a short field trip out to the Dollarama just down the street. We helped choose a ton of supplies for making our portfolios. Keep posted for updates!

Sneak peak: metallic paper, feathers, colourful beads, wacky letters, words, pipe cleaners, earth tone card stock, ribbons...

Since December 6th is coming up. This is the National Day for Remembrance and Action on Violence Against Women, Centennial College invited a guest speaker to kick off the White Ribbon Campaign in the Auditorium over lunch...

Carlos Andres Gomez challenged the audience's definition of masculinity through performances of his poems and led animated discussions, truly getting "Behind the Masc". Gomez is an actor, a playwright, a spoken word poet, and a teacher with a ton of experience influencing young minds and perceptions around North America. He left us wanting to hear more.

Back in math class for the afternoon, we discussed the talk and then listened to a podcast Kevin helped develop for a previous White Ribbon campaign called "Tie Your Shoe With A White Ribbon". The project delves into issues such as gender, violence, and healthy relationships. < PODCAST LINK >

"Our future has no violence against women." Wear a white ribbon if you agree.

Height of a Tree

This morning in math class we worked on our own for a little while, finishing off some tests and surveys from last week. Later we worked together to figure out the height of a tree using some simple trigonometry concepts.

In the activity, we were asked to accurately find the height of a tree using only a measuring tape and a protractor. So we brainstormed how to figure out the different measurements we could take with our tools... We had to assume that we couldn't just climb up the tree and dangle the measuring tape down to the bottom!

First we drew a tree outline on the chalkboard to help us visualize the dimensions. Using the tape measure, we then measured the distance between the chalkboard and where we were standing. (This formed two sides of a right angle triangle.) Then we put the protractor at our feet and measured the angle from the top of the tree down to the pivot point of the protractor (with the help of a bit of string).

So what was the calculated height of the tree? It was 183 cm multiplied by the tangent of 49, or about 211 cm tall... and the measuring tape confirmed it!

Mobius Strips

Yesterday in Math class we did a short activity on Mobius Strips.

To make them, we took a strip of paper and taped the ends together. Some we put in one twist, some two. Then we cut the strips in half length-wise to see what happened.

It was mind-boggling! Some of them turned into bigger mobius strips, some of them cut into two linked circles, and one of the bigger ones turned into a square!

Mr. August Mobius (shown here) lived over 150 years ago in Germany. He is best known for his work in topology, but is especially known for creating these two-dimensional surfaces with only one side.

Interestingly, Mobius studied astronomy under Gauss, a famous mathematician in his day, and later studied mathematics under Gauss' teacher, Johann Pfaff.

Just Another Friday?

This morning an Elder came into our classroom to talk about the sweat lodge and associated traditional teachings. Next Friday our class will be going on a field trip to a sweat lodge ceremony.

Traditional sweat lodge ceremonies were used to cleanse, purify and renew old energies. They involved a ritual process of a physical cleanse or "sweat" as well as a spiritual, emotional, and mental cleanse. It was considered a ritual rebirth or renewal of the self, though participants often joined family and friends as a community event.

This afternoon in Math class, we listened to Native music from Danny Beaton, Eagle & Hawk, and Crystal Shawanda. The newest math assignment (due next week) is on Cryptograms, those puzzles where each letter is replaced by a corresponding number. We also watched the end of Part 2 of the movie, "The History of Mathematics".

Welcome to Our Blog!

It's November 11th, Remembrance Day. We attended a ceremony in the auditorium to remember fallen soldiers and the Canadians who risk their lives to honour our country's rights and freedoms.

We are currently working on a take-home math assignment about Remembrance Day and the poem, In Flanders Fields, written by Canadian Lt. Col. John McCrae.in 1915.