It’s been a great start to the new school year and I am so excited to work with two new classes – Grade 9 and Grade 10 – both at the applied level. I have enjoyed working with both of these groups of kids – but today I want to show you some of the great thinking I saw in the Grade 9 class as we near the end of our ratios and proportions unit.

Know that this is a quiet and very shy class. I have not seen such quiet and reserved Grade 9 students quite like this. I have had a difficult time getting them to talk to one another and asking them to work together in pairs or groups is like asking them to fly a rocketship to the moon. I’m still working on the math talk community – and will keep you updated on that as the term continues.

We have re-introduced fractions and thinking fractionally. We also have solved problems using ratios, rates and proportional reasoning. We just started to look at scaling up and down.


As they were getting ready to leave class, I told them about my experience on the weekend when I stayed at a hotel and wanted a bottle of water. The vending machine down the hall had just what I wanted – and I paid $1.25 for one bottle. I had just been to the local grocery store last week and paid $4.99 for 24 bottles. I asked them if my vending machine price was fair or not.

In my mind, I imagined that most of them would take $1.25 and figure out that 24 of these bottles would cost me $30.00, which is much more then $4.99. That shouldn’t pose much of a challenge to most of them.

One by one, they handed in their slip of paper as they left the room. Not much was discussed as they each wrote something down – and nobody asked me any questions.

So here’s what happened:

First one: I know I’m not supposed to “expect” any particular solution – but I have to be honest – this one was anticipated by me.


Then I came across the next one:

I particularly liked the set up of the proportions of $:# on the side. There’s also a check on the right side of $1.25 x 24.


There were various others comparing 24 bottles or one bottle in two different situations. But wait – there’s another one.

This one is pretty cool – with $5.00 you can only get 4 bottles from the vending machine but for the same cost, you can buy 24 bottles from the store.


And just when I was ready to pack up and go…I noticed another one. At first glance, I have to admit I wasn’t sure I knew what he was getting at here. I talked to him the next day and he explained.

“If you buy a case of bottles at the same rate as you did in the store, then you would get a case of 6 bottles for $1.25. This is more bottles then you get for $1.25 at the vending machine.”


So there you have it. A class of twenty students – each showing evidence of their thinking. They are not demonstrating their knowledge of the memorized steps needed to set up and solve a proportion. They are showing me how they can use proportional thinking to answer a question – but encouraged to do it in their own way.