A few weeks ago I tweeted this:

This post will list a few of the interesting trends and what I ended up using with my class.

The first assignments we did in the class revolved around the kids observing and talking about the patterns that they could see in visual patterns, and some instructional activities. These usually involve seeing some shape change as it grows from one iteration to the next.

Variables start appearing once students see that there are parts of the pattern that add on more shapes and use Length x Width, or the corresponding area formula, to make some kind of equation.

There are also area tasks that involve fixing dimensions, and then finding the area. Here’s an example from NRICH. If you give students a certain amount of fence and ask them to find the dimensions of the largest rectangle, or even other shapes, then result will be a quadratic function. The resulting function compares the variable x representing one changing side, to the area of the shape.

Another type of tasks could involve changing rates, by that I mean a rate that is constantly changing. One relationship that was suggested via twitter was that ‘price x quanity = revenue’. So like if kids have a price, and then quantity is allowed to vary, then they could make a linear function to find the revenue based on the price. Well sure Carl, but how could that be a quadratic when you just showed it’s linear?” Well, what if the price depended on quantity as well? This is actually a real phenomenon, as the price of products typically go down as producers try to get you to buy more products. Then students would first have an equation that would make sense for price.

I made a task based around this principle that was talking about the ‘pay rate x hours = paycheck’ relationships for my old college job. As a dishwasher I was paid in both a constant, hourly rate, and a changing “tip share” that was handed out in increasing increments as I worked more hours. This meant that the worksheet shows a dishwasher with a pay rate that changes! It’s a pretty interesting situation to explore. Click below to see this task which both looks at the linear function for the pay rate after each hour, and also the quadratic function for total pay after working a number of hours.