Making the decision to buy a used printer - June 22, 2009

I own a small laser printer that prints 2000 pages per toner. I can buy a toner for $50. This gives me a cost of printing per page of 2.5 cents.

The gentleman who sells me toner, offered to sell me a used printer for $200. I know that printers can get expensive, but I didn’t really want to spend $200 on a used printer especially when I had a printer already.

The thing about this printer is the toners print 10,000 pages! The cost per toner is $100. This gives me a cost of printing per page of 1 cent.

What I wanted to decide was, at what point would I break even.

Here is where I used Grade 9 math:

• What I didn’t know is how many pages I was going to print, so I called that x.
• The cost to print with my current printer was 2.5 cents times the number of pages or 0.025x (in dollars)
• The cost to print with the new printer would be 1 cent times the number of pages plus the $200 OR 0.01x + 200
• So, what I needed was when these two expressions would be equal.
• 0.025x = 0.01x+200
• 0.025x-0.01x=0.01x-0.01x+200
• 0.015x=200
• x=200/0.015
• x=13,334 pages

Now, the question is will I print 13,334 pages???

For me, since we print a lot of exam reviews for the students and everything else for the business, I knew that yes I would.  Add on to that the benefit of not having to replace the toner all the time, and the decision was EXTREMELY easy.

After I did the math that you see above, I determined that the gentleman that was offering to sell me a printer, was actually offering to GIVE me a printer.  Math made the decision easy.

If I were someone else, who doesn’t do a lot of printing, and I didn’t do that math, I may have been tempted to buy it because I can see that I would be saving quite a bit per page.

I mentioned this to some of my students, some of the adult students, and they said, “Well that is easy for you because you are so good at math, we can’t use it everyday”

Notice what I mentioned before the calculations:  This is a Grade 9 math question, it isn’t Calculus or second year Physics.

Goal Setting and Hard Math Questions, September 18, 2008

I always encourage students to set HUGE goals. What many students are preoccupied with, is how they will accomplish the goal. That is why goals are seldom set.

For example, a student may have a strong desire to be a millionaire by the time they are 30 years old, but only the few that actually BELIEVE they will do it, actually do it.

Often times, it is as simple as that. You need to take the first step: Set a goal, and believe you can achieve it.

Let me give you an example from mathematics. Take one of those long math questions, one that requires multiple steps and, often times, results in multiple anxieties. The problem with these questions is that students sit there and stare at them because they have no idea what the answer is. I am sure that any teacher, no matter how comfortable they are with the material, would look at the same question and not know the answer. The answer requires multiple steps.

The answer won’t come just by looking at the question. What students need to understand is, they don’t need to know what the answer is! They don’t even neccessarily need to know how to get to the answer. What they do need to know is how to take the first step.

As long as you are moving forward to a goal, you are approaching it. Obvious statement?

So, my advice to students is: do something, anything, take a step.

Goals are the same way. You don’t need to know how you are going to get to your goal, you just need to take the first step.

Relevance of High School Mathematics to the Real World, August 26, 2008

It is an age old question in math classes: “Why do we have to learn this? When are we ever going to use this in our lives?”

There is of course, a very fine answer to this that any teacher can be proud of. It consists of something along the lines of : What we are learning in class, whether it be how to factor a quadratic, how to graph a sine function, or anything else, is a building block to further education and to eventually lead to awesome applications in engineering, science, finance, etc.

This answer does not satisfy the student. That is, of course, because the student is convinced that they have no interest whatsoever in going any further than Grade 11 math.

So then, this is what we say to the student: “It is not relevant to you, and you will never use this in the real world.” But don’t leave it at that.

Let’s face it, most students may not ever use the subject for any practical purpose in their career. Sure, math is important day to day when balancing your cheque book, and taking change at the store………… but here is the real purpose for it.

Math, like no other subject, prepares students for the everyday problem solving that they need to succeed in the real world.

Now, in life, we all face many problems each day, where we are required to make complex decisions. The school system can’t possibly simulate all of the different things that are going to happen to all of the different people to prepare them for life. It can, however, put the students in a situation where they don’t know what to do, and they have to figure out what they have to do, rather than memorize a solution. Math does this. It forces the student to follow some logical rules, and solve problems in a step by step manner.

If you are looking for a way to motivate yourself to succeed in mathematics, try this: Make your math class like a training ground for the real world. See the questions as problems that need to be solved, and you are given the tools to solve them. It is a simulation for real life. Start to have fun with the questions, looking at homework as practicing the skills you are taught.

Your brain needs to be exercised just like your muscles, and math class is the gym where this exercise takes place.

So you may not use the actual topics you learn in the real world, just like a hockey player doesn’t actually lift weights in a game. But your brain is getting stronger because of the math, and this will help you unlock more of your mind and your potential for success!