Math SAVES the day!

This weekend there was a Criminal Minds marathon on, and I was glued to the television. I did take some time to enjoy the warm weather, but otherwise I was in front of my television with my computer on my lap working away at different tasks I had to complete and needed to work on. All the characters on the show are fascinating, but the most fascinating is Reid who has an eidetic memory and is a great asset to the FBI team who profiles serial killers in order to find them. 

The episode in particular that caught my attention was one that included the reference of the Fibonacci sequence. Back in my undergrad, I worked for a leadership spring camp at Brock University (called Youth University). We did many things with students in grades 5-8 for the 2 ½ days they were visiting with us, including high ropes, rock climbing, leadership games/activities, nature walks, etc. One thing in particular that I recall doing (6-8 weeks in a row, 2 camp sessions per week) was making a necklace on our nature walk (usually on the first or second day) representing the Fibonacci sequence through the colours we chose to put on. (For example, there would be one blue bead, then one red bead, then two yellow beads, then three purple beads, then five green beads, etc. to make up the Fibonacci sequence).

What is the Fibonacci sequence you ask? Well, if you don’t know, the Fibonacci sequence is a set of numbers that starts at 1, with each subsequent number is the sum of the previous two.

So, we start at 1, and the number before it is 0. Creating the sum 0+1=1 to get the next number; so the first two numbers are 1,1. Then you add, 1+1 to get 2; and if we add 2 the sequence you get: 1,1,2. Then you add, 1+2=3 so we add 3 to the sequence to get 1,1,2,3. Add 2+3=5 to get 1,1,2,3,5; and add 3+5=8 to get 1,1,2,3,5,8 …etc.

Here’s the sequence with no words and you might get it a bit better (if you don’t already):

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144…(I think you get the point now…)

Anyway, the point of this whole blog, is the fact that something that we teach in middle or high school CAN really be used in real life. Even something as abstract as the Fibonacci sequence and that it can show up in the simplest of things (sitting and watching a television show, for example). Even if your mind isn’t doing the mathematical equations while watching television, you are aware of it and able to connect with the content that much more. (I even posted a picture of Pascal's Hex (or triangle) which has elements of the Fibonacci sequence in it during my last blog post and didn’t even notice it – although recognized the ‘pattern’ as I called it – because I haven’t reviewed the concept in a long time!)

I think students need to see the relevance of what they learn as an incentive to learn. I know that I sometimes have a hard time sitting in a class where I don’t find relevance to it, so I know the importance of providing students with that incentive to learn – and answering that “why are we learning this” question…and not by answering with the simple answer of “because you have to” or “because I’m told to teach this”. Everything has a purpose!

To close this off, I wanted to let you know that because of Reid’s discovery and use of the Fibonacci sequence, the FIB team were able to crack the case and save some people’s lives (as well as their own)!! Yay for math that saves the day!

Patterns, Patterns, Patterns!

I LOVE patterns. I love how they are evident in almost everything and anything that we look at each day. Many patterns that we see today are physical patterns, whether it's your patio stones and the way they interlock together to make a pattern, or an embroidered pattern on some fabric, or the pattern the windows in a high rise building create.

Growing up as a kid, I loved being creative. At summer camp, my favourite activity was arts and crafts, because I got to create patterns of my own through friendship bracelets, mirrored images, stamps, and more. I got to create the patterns myself and explore what it meant to me.

This is where my love for patterns started, with the physical patterns, but patterns have always continued to excite me when it came to numbers as well. Number patterns are a different "breed" compared to physical patterns. Number patterns are so delicately put together and have so much depth to them. Hm, this isn't that easy to explain...let me provide you with an example.

Pascal's Hex has always been a neat pattern for myself. The way it forms itself by adding two numbers together to get the number below it (for example, in row 2: 1+1 = 2, which becomes row 3). As the rows continue, the numbers get larger and "more complex", but the pattern and the steps toward each row is exactly the same.

Being primarily a primary/junior teacher myself, patterns begin fairly mundane and easy. Square, traingle, circle, square, triangle, ( circle ). Students get to draw in that the next answer is square (because obviously, the question was in 2D shapes, not words like I use). Advancing into intermediate levels of mathematics, I have noticed in the curriculum that it becomes much more than shapes and an understanding of order/repetition, but it becomes about applying the knowledge and being able to create their own patterns (more complex patterns) and being able to describe them using variables and in algebraic terms. Patterning in the older grades is about compounding the way you describe a pattern (the curriculum provides this example, take the number patterns 3,5,7,9...the general term is the algebraic expression 2n+1; evaluating this expressiong when n=12 tells you that the 12th term is 2(12)=1, which equals 25). Instead of simply saying, each number goes up by 2, they create an expression that helps them determine the 12th, 24th, etc. term without having to write out 12 or 24 numbers themselves. Oooooh how it all works and is beautiful!

Patterns are a beautiful thing, and something that students can relate to if you present it in the right way for them. It's less complicated then can sometimes be described (and I admit, I don't think I did a great job of explaining it here...SORRY!). Let the kids explore, give them an example and let them off their leashes to try it themselves and see how much success and fun they have with patterns!!

As I like to sign off with...Happy Math Teaching!