Categories
graphing linear functions systems of equations tasks unit analysis

The Mathematics of Laundry Soap

The grocery store is a brain workout for the mathematically inclined. Not only do the varying metric and imperial conversions tease out the micro-savings of bulk, but neon yellow discount signs encourage percentages and good ole’ multiplication tables. Often you find adults transfixed in a complex division trying to figure out which ham will be cheaper. Once that calculation is complete, they turn their attention to making sure the portion will be enough to feed their whole family. The sheer volume of available estimations overloads me; coupons just complicate the matter–significantly.

Categories
graphing linear functions pattern

The Linear Relations of Hamburgers

Maybe you have seen the Burger King Stacker commercial where “Meat Scientists” work on an interesting problem. Needless to say, it piqued my curiosity the second I saw it; it was not long until I was trying to suck every ounce of mathematical value from the video. I am sure that I did not accomplish this goal, but I did manage to find some interesting problems and questions.

Categories
numeracy ratios tasks

NHL Dream Team

My thoughts have begun to turn to the new school year that will occur in August. This may be jumping the gun, but I like to enter prepared. This is partly due to the possibility of job action, and the surety of football, in the fall. I like to spend the first couple days of school working on basic numeracy skills with my grade 9s and 10s. I find a nice task is much more effective than a few worksheets. I do, however, keep a supply of worksheets on hand to offer to kids who just want the assignment. This idea came to me while I was reading an old edition of “The Hockey News” earlier this year. It has been taking up space on my desk, so I figured blogging about it would allow me to file it away for the beginning of next year.

Categories
probability reflection

Life’s Not Fair

The school year is now over for me. That is a bittersweet statement, because I still have mountains of grading and report card comments to do, but there will be no more direct lessons in the 2010/2011 school year. I found myself nostalgic this morning, and began to recount the good times in the classroom. I recalled the probability mayhem that ensued with my Grade 11s. It was very amusing to see them come up with ways to describe “fair”. I would always tell them that I would only do something if it was “fair”. This, to them, meant a coin flip, draw from a hat, or a roll of the die. But whose hat? Who rolls the die? On what surface? Do these factors actually have an impact on “fair”?
 
Most questions with elementary probability include a fair clause. For example:
Categories
pattern squares tasks

Induction Squared

I came across an interesting problem recently that I gave to my students in need of enrichment. 
 
Given a square and the ability to divide that square into smaller squares, can you divide a square into ‘n’ smaller squares. The squares do not have to be the same size. For which values of ‘n’ is this possible? For which values of ‘n’ is this impossible?
Categories
classroom structure investigation reflection

Maths’ True Form

I teach mathematics at the high school level, and know all about the various theories surrounding school mathematics. I can still remember the intrigue when the term “Math Wars” was introduced to me through some undergraduate reading. I immediately took to the history of my art, and found a very convoluted and bloody past. The constant pendulum between retention math, new math, back to basics, and now the new-new math is dizzying. Whenever I converse with a colleague about a new way of thinking in math education, I am sure to remind them that we are in a war. It is this idea that has appealed to the more militant teachers (myself included).

Categories
Pythagorean theorem reflection

Life Without Euclid

This post has nothing to do with geometry. I guess I can’t say that exactly (because of the possible geometric representations), but I am not dealing directly with these. I am always intrigued when I think like I want my students to think. It is these moments that keep me going into the classroom hoping for new understandings. There have been times this year where students have made connections that I never have. These innocent realizations are mathematics manifested in its purest form. A similar experience happened to me this morning.

Categories
classroom structure problem posing reflection

Review: The Art of Problem Posing

I consider reading an essential part of my professional development. I enjoy a morning glance through a chapter or two, and like to wind down a winter’s day with a book and a cup of coffee. Sometimes reading is the only way to relax my mind at the end of a day. (Naturally, some professional literature is better at putting me to sleep than others). To this point in my young career, no book has changed my perspective on the teaching and doing of mathematics more than The Art of Problem Posing: Third Edition by Stephen I. Brown and Marion I. Walter. The duo writes quite a bit for “Mathematics Teacher” (the high school journal for the National Council of Teachers of Mathematics) as well. The processes introduced in the book have been crucial to the penning of many posts on this blog. The book creates a framework from which creative mathematics flows.  

Categories
probability

Balls and Bins

One of my pervious posts mentioned the problem of the balls and the bins. I got this problem from a source on twitter that I have since forgotten. Regardless of its origin, the question has been a fun one to pose to students and colleagues alike (I even asked my in-laws with some very interesting results). For those of you who haven’t read “Practice What You Preach“, The problem is as follows:

 
You have 8 balls, and 2 bins. 4 of the balls are Red, and 4 of the balls are White. Your job is to arrange the balls in the two bins however you like, but every ball must be put in one of the bins. (ie. no throwing balls away). I will then choose one of the 2 bins, and then draw a ball from that bin. If I draw a White ball, I win; if I draw a Red ball, you win. Which arrangement gives you the best chance at winning the game?
Categories
probability

Practice What You Preach

I have already expressed my views on the value of probability within the school curriculum. When posed in a creative context, the nature of the subject leads to excellent exploration. I tell this to every class that I teach probability to, and this year my explanation caught up with me.

I gave my first day lesson on a counter-intuitive problem, and then began using experimental probability to verify our results. I reserved the end of class to remind students what we were doing. I got onto my soap box and began preaching the importance of reality; although we were calculating odds, probability is a risk assessment. Lady luck can be fickle.