When (Slightly) Wrong Answers are Better than Precisely Correct Answers

Many children get the idea that mathematics is all about precision. In order to be right, you have to be exactly right. After after all, there is only one correct answer to 7 X 6. 

But precision isn’t always what’s called for. Sometimes estimating is more useful. 

Estimation can be better than precision

Estimation is better than precision when you’re trying to get a feel for something, and the time spent calculating something precisely would distract from the question at hand.

Imagine you’re in the grocery store deciding which coffee you should buy. Small bags are better from a freshness perspective, but saving money is important. Should you buy the 20 oz bag for $22 or the 7 oz bag for $14?

Estimation to the rescue! 7 oz is about ⅓ of 22 but $14 is about ⅔ of $22. The small bag is way more expensive! 

Or imagine you’re a contractor. Your client will give you a nice bonus if you finish the job in two weeks. You need 2,000 more man hours to finish the job. You’ve got eight guys on the job. Is that enough to finish in two weeks?

Not even close!

Estimation helps us make better decisions

Estimation is valuable because it helps us make better decisions quickly. With the rough sense of where we stand that we get from estimation, we can decide if it’s worth it to invest more time to get more precise. 

Getting a rough sense of things quickly is so valuable because people make thousands of decisions per day. If you’re good at estimating, dozens or hundreds of those decisions are going to be better than they would otherwise be. In fact, an official UK research report found that estimation was the single most valuable workplace mathematics skill.1

Estimation Banter is a great way to introduce kids to estimation

One great way to introduce your child to estimation is with what I call Estimation Banter. With Estimation Banter, you’re figuring out an approximate answer to a problem, not an exact one. To make this work, you want to pick numbers that are difficult to work with that are near numbers that are easy to work with. 

For example, you could ask your child: 

What approximately is 49+51? Answer: It’s about 50+50, or 100

What approximately is 391+404. Answer: It’s about 400 + 400, or 800.

What approximately is 3006 + 1953? It’s about 3,000 + 2,000, or 5,000.

What approximately is 397 X 50. Well that would be 400 X 50, which is 20,000. 

Make sure your child understands that the purpose of this game is to get approximate answers, not exact answers. This is hard for some kids because they think math is only about precision, about being exactly right. But you can explain that sometimes it’s more useful to be approximately right than exactly right. You can also share examples of how estimation is valuable to you in your daily life.

It might take a little playing around to find the right level for your child. Once you do, you can gradually increase the difficulty of problems. Approach Estimation Banter with a playful attitude, and never push it on your child if they’re not interested.

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When (Slightly) Wrong Answers are Better than Precisely Correct Answers
  1. Jo Boaler, What’s Math Got to Do With It?,  p. 25.