Math should be fun. Students should play with math in the real world rather than be subjected to the sort of artificial math we usually give them. And students should write about math.
Here’s an example I just found online of a typical “percent mark-up” problem:
A computer software retailer used a markup rate of 40%. Find the selling price of a computer game that cost the retailer $25.
The right answer is: “This is a silly question. If I want to know how much a computer game costs, I will ask the clerk in the store; also, I’ll probably buy it online anyway.”
But here’s a real-life example that teaches percents and smart shopping. This is the sort of real-world math we will do at Triangle Learning Community middle school (opening for sixth graders in 2013).
Imagine a student writing something like this blue text:
Yesterday, I bought some blue corn chips at the store. Here was my first option:
And here was my second option:
Which bag of chips should I buy?
Because the price tags have that strange 12/8.1 and 12/16 thing going on, and you can’t see the bags, let me clarify:
The 8.1 ounce bag cost $3.39, and the 16 ounce bag cost $4.39.
The store actually tells you the unit price per ounce — 41.9 cents per ounce versus 27 cents per ounce — right on the label. But is the store right?
Well, the store rounded off, but it’s giving the proper information — $3.39 divided by 8.1 ounces is $.41851851851 per ounce. And that’s an opportunity to review — in context — repeating decimals.
The other price is pretty close too — the store says it’s 27 cents per ounce, and more precise math tells us it’s $.274375 per ounce.
So who would ever buy the smaller bag? It’s almost twice as expensive. If it were twice as expensive, it would be about 54 cents per ounce, which would make the 8.1 ounce bag cost what? About $4.
The point here isn’t to “solve” the problem. The point is to use math to think about pricing strategies in the store. It’s also a chance to make estimations — we could multiply 54 cents times 8.1 and get $4.374, but a potentially more important skill is being able to look at “roughly 8” and “roughly 50” and know that if you multiply those together, you get around 400.
It’s not that we don’t need to know about repeating decimals, estimation, and percents — it’s that we need to find authentic ways for students to interact with the math that’s all around us every day.
So here’s another real-world problem — what is the percent reduction on this bottle of wine? It was on sale at the store because the label got scuffed:
And here’s what the store is offering:
Is this a good deal? How good of a deal is it? Do you trust the store that the wine is fine? It probably depends on which store we’re dealing with, right? Reputation matters.
By having students write about math (which we will do on a regular basis at Triangle Learning Community middle school), rather than answer problems nobody cares much about, students will come to own the mathematical concepts they are applying.
Why do we persist in asking students something like this:
A shoe store uses a 40% markup on cost. Find the cost of a pair of shoes that sells for $63.
Here’s what I think the right answer is to problems like that one: “it doesn’t matter to me how much the store paid for the shoes — I want to know if I can get a discount.”
Make math real and it becomes fun again.
The sample problems in green writing come from a website called Purple Math, which is a fine math site to consult if you are stuck doing someone else’s math problems.
A nutrition application for this problem would be to ask whether we should be consuming blue corn chips in the first place…