Estimation is more than rounding.

Most of the time we don’t teach this, but it is.

Tabitha (8 years old) had a homework assignment the other night that asked her to imagine she had $100 to spend in a catalog, and to make a list of things she would like to buy from that catalog. She found the latest *American Girl* catalog and got to work.

There was a table to fill out with three columns.

- Description of item
- Actual cost of item
- Estimate

A couple minutes later she asks, *What’s the estimate if it costs five dollars? Should I write $5.01?*

She has discerned that *estimate* means *write down a number that is not the exact value*.

But that’s not what estimation is about at all. Estimation is about finding a number that makes sense, and not worrying about whether it’s the exact value or not.

The image below seems to be going nuts on the Internet today (despite my exhortations to the contrary! Oh, Internet! When will you learn to listen to me?)

“Is this reasonable?” is a *great *estimation question. Rounding is one way to answer the question. But if a kid can quickly *find a number that makes sense* and it happens to be a precise number, then we probably haven’t asked a good estimation question. Rather than mark it wrong because the kid didn’t round, we should ask this kid a more challenging question next time.

What does a good estimation question look like? What would be more challenging?

I’m glad you asked.

Estimation 180. Thinking of a number that makes sense is much more interesting when you have to bring your knowledge of the world to bear.

Is 75 inches a reasonable answer for the difference between the father’s height and the son’s? Is 75 centimeters reasonable?

Oh! And here’s the first in a nice sequence about numbers of pages.

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*Related*

We must not confuse approximation with estimation,and neither needs to be a nice round number. But the language is the same : around (or about) 75

Gah, I have had to hold my breath, both as a teacher and as a parent, for these estimation lessons. It’s giving me palpitations just thinking about it…

I’ve been loving using the family version of the game Wits & Wagers in my classroom (5th grade) for this very purpose!

I started doing Estimation 180 with my sixth grade mathematicians every day as bell work. I learned about it at TMC this summer. My students LOVE it and it is so good for our community of learners on so many levels!

What was Tabitha meant to do in the third column (estimate)? In case it isn’t clear, I’m confused because the second column already asks for the precise price. Maybe cost+tax+shipping (if the latter two weren’t part of the advertised price)?

On the other hand, I think there could be a fun class activity here:

students go home and fill out the first two columns. They bring those back to class and tape a strip of paper over the second column. Then give their paper to another classmate who fills out their own estimates. The estimators have two pieces of information:

(a) description of the items

(b) overall total must be around $100

Sounds like something worth doing with one of our classes!