## Monday, March 7, 2016

### Costco-the Proportional Reasoning Store

Check your local curriculum: if it's like ours, sometime around grade 6 students are asked to deal with the interrelated concepts of rates, ratios, and percents. This is part of the growth of thought in the area we call proportional reasoning. In grade 4 (Ontario), students start to think in more relative, and less absolute terms. This often includes starting to see relationships as multiplicative, not additive, as they have been doing since Kindergarten.

I tend to think that unit rates, in particular, used to be more mysterious before Costco became ubiquitous. Their entire business model is built on an economy of scale, or what we recognize as "buying big stuff, so they can sell it to us for cheaper."
The entire store is filled with very interesting possibilities for proportional reasoning problems, particularly due to how they do their price labels.

In this example, you see that the unit sold is actually 2 bottles. Each has 830 mL. Their go-to rate for liquid capacity is price per 100 mL, in this case \$0.409.  And of course, how much  you actually pay.

I see lots of opportunities for interesting tasks here. Comparing the price per Litre of various liquids in Costco, for example.

How much is Coca Cola per litre?  How much should it be?

A general question you can ask about Costco prices is: "are they fair?"  You could then compare the price of water, or other liquids at various grocery stores.

As far as Costco goes, fair, and cheap, for me depend on this: can I store the item in my house?  If so, I often calculate the unit rate in my head and decided to make a purchase.

I do think other grocery stores would be cheaper on some items, so it would be interesting to compare, say using the Flipp app or other stores' websites.

This one uses the price per bar as their unit rate, in this case \$0.15. The price per kg is also interesting though.

Compare to these granola bars:

Which one is cheaper? Which one would you buy? Why?

There are nearly endless possibilities for interesting math tasks in Costco. We thought it would be interesting to take a bunch of teachers there, and snap away with our phones, interesting materials for math tasks. Would you come?