I’ve got a bachelor’s degree in advanced math, and a 12-year-old daughter who hates anything to do with the subject.

I’m an unschooling mama who loves to do math puzzles and logic problems for fun.

I’m not sure if that combination makes me an expert or just crazy, but because of it, I agreed to take part in the iHomeschool Network’s “5 days of…” series this week with a look at 5 days of real-world math.

Today, we kick off the series by looking at three types of math you need at the grocery store. 

Unit price: A fancy way to say “Which one is the better buy?”

This is probably the most important real-world application of multiplication and division (and fractions) that I know. If you can get a 2-liter bottle of soda for $1.50 or a 1.5-liter bottle of soda for $1, which would you choose?

You need to know how much you’re paying per liter, or per unit. The 2-liter bottle is costing you 75 cents per liter (in my head, I just half the price to know how much one of the two liters costs). The 1.5-liter bottle is costing you 66 cents (about) per liter, so it’s the better buy. (In my head, I figure 1.5 liters is the same as three half-liters; divide the full price by 3 and you get 33 cents per half-liter, and two half-liters is a whole liter and that means two sets of 33 cents is 66 cents).

Consumers are famous for getting unit price “wrong.” Our grocery store kindly includes it on its signs – BUT only on the full-price signs, not the ones where things are on sale, and when you have coupons, of course those aren’t factored in either.

Many people tend to assume “bigger is better.” I call it the Costco or Sam’s Club factor – surely it’s cheaper to buy 80 rolls of toilet paper than to buy 8 sets of 10 rolls, right? Sometimes, but not always.

This is an area in which mental math is really important. If you can walk through the process I followed above to calculate the per-liter price of soda, YOU ARE DOING WELL, MATH-WISE.

Where to start: Take this step by step. If you’re just starting out, as a family, look to see if your store notes unit price at all and explain that it’s a way to be able to compare the relative value of different sizes of an item!

Then, see if you can “work out” how it’s arrived at for a particularly simple item. Find a bottle of 200 Advil and notice that the cost per unit is usually given in hundreds for those, if the store calculates it. (Why, I have no idea, but there you go.) You and your child should be able to see that the cost-per-unit (in this case, per hundred) is half the cost of the whole bottle.

From there, go on to actual real-world cases. If you want to drive me crazy for hours, set me to this in the toilet-paper or paper-towel aisle where you have to factor in regular rolls with mega rolls with jumbo rolls with Godzilla rolls or whatever they’re calling them now. In anyone else’s case, I’d suggest starting with something more reasonable, like figuring out whether the small, medium or large container of peanut butter in your favorite brand offers the best buy.

Dealing with those annoying “percent off” signs

Ah, percentages, the favorite thing of no one ever. Grocery stores (and other retail spots) often use percent-off signs to make things look like a better deal than they really are. That means it’s especially important to understand how to figure them out.

Any time you’re working with percentages, work from whatever 10 percent is. If I see a $45.00 item that’s 30 percent off, I first go, “OK, 10 percent is just dropping a digit, so that’s $4.50. 30 percent is three sets of 10 percent, so that’s $4.50 times 3, or $13.50 off. That means I’ll pay $31.50.”

30 percent off can sound like a good deal – but it really depends on the original price of the item. On a $2 purchase, you’ll save 60 cents, so if you have a choice between the 30-percent-off $2 item and another brand of the same thing with a $1 off coupon, TAKE THE DOLLAR!

Where to start: Skip all the garbage about ratios and proportions and percentages. That stuff is COMPLICATED. All you really need to know is that 10 percent of something is one-tenth of it, and, like I said, even that’s more than you need to know if you can just accept the whole “drop the last digit” thing.

Start by figuring out what 10 percent of the price of anything you like is. From there, explore the idea that, just like 20 is 10+10, 20 percent of any number is the same thing as 10 percent of it, times 2. And then there’s the idea that 5 percent is HALF of whatever 10 percent was!

Finally, put this into practice. The case I always work through is that our grocery store offers you the option of a free turkey (up to $20) or 5% off your next grocery order around Thanksgiving. Our average grocery order is $340 every two weeks, so 10 percent of that would be $34 and 5 percent would be half of that, or $17. If I can use the turkey, I “get more” that way. When they offer a 10% certificate, though, the situation changes, and suddenly I’m better with that than the turkey!

Volume: Or, how do you fit all that in the cart?

I am not kidding when I say volume is a major part of our grocery trip. You do not want to be that family with four people and two carts. We’ve been there and it stinks.

This is where volume, area and general geometry come into play. Square boxes take up less room stacked neatly (like building blocks) than thrown into the cart with a lot of odd-shaped air pockets between them.

Organizing the cart as we go keeps us from going home with smushed bananas, and it makes bagging easier for either the checkout bagger or my husband, who usually gets that job.

We have fewer bags to carry into the house when everything is well-packed, and the pantry is easier to organize for the same reason.

You might laugh, but that’s important math. In a very practical sense, it saves us time – and probably money.

Where to start: Before you worry about organizing your cart as you go, hit the pantry or a cupboard. See if you can more easily see what you have, and get it all to fit, when things are arranged and fitted together by shape and size.

If you really want to freak yourself and your kids out, have a challenge to see how LITTLE room on the shelf you can take up with the items that previously filled it.

Even if you end up rearranging it all later, it’s a great example of volume in action! Then, next time you go to the store, see if you can get a bit more into the cart without losing the milk off the top in the last aisle!

The rest of the series

Sunday: When numbers matter: A look at math in the real world (introduction)
Today: The math you need at the grocery store
Tuesday: The math you need in your kitchen
Wednesday: The math you need to manage your money
Thursday: The math you need to play sports and do other fun stuff (yes, really!)
Friday: Real-world math resources you’ll love

You can read all the posts here!

More five-day fun

This post is part of the iHomeschool Network’s summer “Five Days Of…” series. Click the collage below to see how some of my fellow bloggers are spending their “five days,” and to learn more about our series sponsor, the BEECH Retreat bloggers’ conference!