# Feel the Math, or, you don’t need to write to figure out what’s right

Are you facing a child who “hates math”? I’d embarrass someone dear if I were more specific, but I tried to prevent one girl from develop math fear. I’m sorry to say it didn’t work. But I learned, and now my favorite way to teach math is through natural situations. My son has never been able to write or type numbers independently because of his motor control issues. Nonetheless,  he does math in his head. I realized he’d learned how to calculate 15% from years of teachers doing “discrete trials” with him. They would have him do something 10 or more times in a row and calculate whether he’d done 85% correct before giving him a fraction of a mini M&M. With so many repetitions across months and years, he learned the feeling of 15% wrong, not the long division or multiplication.

When he was about 13, he went with a family to a restaurant. The mother told me he laughed when she said what she was going to tip for the meal. She checked, and she’d done it wrong. A tip is 15% of the total. I checked, and indeed he was good at calculating tips in his head and telling me which tip amount was better.

I used to be involved in pricing and gross and net sales calculations for a Kraft food product, so I know “sales” work. But are they really the best price? When we walk around the store with coupons or checking out sales, I always calculate in my head which price is better and ask him. Over time he’s more and more accurate. So here are some examples:

BOGO: buy one get one free. There are two types of BOGOs. The items are the same and at the same list price, or the items are not the same and probably are different prices.

When we sold cups of yogurt, the items were the same original cost, so here’s the math.

Get 1 cup of yogurt for \$1 + 1 cup of yogurt for free = 2 cups for \$1 or 50 cents/cup. You would otherwise have paid \$2. So you saved \$1 of \$2, or 50% off, for two.

When you go to a clothing store and see a BOGO, the items are not the same, so here’s the math.

Get 1 T-shirt at \$10, and the second one free, instead of \$9. You paid \$10 for 2 t-shirts, but you would otherwise have paid \$19. That means you saved 9/19, or 47%, not 50%.

NOW LET’S GET EVEN MORE DEVIOUS!

Sales on top of Sales? The department stores, Macy’s especially, love to layer sales upon sales. Take 50% off already reduced prices. If the original price reduction was 20%, how much money are you saving? You might say 70% (=20+50), but no. Pants originally marked at \$50 were marked down 20% to \$40, and now are 50% off that, or \$20. How much did you actually save from the original price? Remember that’s all that counts. You paid \$20 instead of \$50, which is saving \$30 on \$50, or 60%. That’s a lot less than saving the 70% your brain on sale thought you were saving.

Okay, if we buy one at \$1 and get a second at 70 cents, we paid \$1.70. That’s instead of \$2 for two. So we saved 15% on two. It doesn’t sound so great now, does it?

Now here’s another example.

Which is better, 30% off, or buy two and get one free?

If you were following along, you can guess the answer. You don’t have to prove it with calculations to me, but you should try to feel the math. Part of feeling the math is knowing that the retailer isn’t giving it away.

Feeling the math comes from practice in school and experience in the world. If someone doesn’t feel the math inside, they won’t be programming complex systems or fixing their own programmable self-driving cars. And they will give some of their money to retailers without even realizing it.