Monday, June 25, 2012

Estimation is Key

First Day of summer school.
This morning, I snapped a picture of a portion of our school parking lot. My intention: use it as the daily estimation question included in the warm-up.
Q: How many total parking spaces are in the parking lot?

We did our warm-up. I first asked for numbers that were too low and didn't make sense. Then too high. Finally, I asked for their estimates, but didn't validate any responses. We then jumped into our lesson for the day: ESTIMATION.
Opening the lesson, I asked my students to think of one good thing and one bad thing about estimation. Here's what they listed.

  • Doesn't have to be correct
  • It's easy
  • Can be made mentally
  • It's an educated guess
  • "It's free! It doesn't cost you anything." (Oh, I added that one)
  • Not precise
  • Could be wrong
After comparing the pros and cons, the good guys won! Estimation FTW!
It gives anyone a chance to cast an answer based upon specific information. It's a starting point. It keeps your number sense in check. It allows the brain to think abstractly for a brief moment. It's free!

We went outside and delegated the work. Students counted staff, reserved, preschool, handicap, and ordinary (unlabeled) spots. We got a total of 141 parking spaces. One kid was two away with 143 as his estimate. Go figure. Another kid was in the five hundreds. Go figure. After the empirical data produces the answer, we always circle back to our original estimates. It's important for students to see the difference so they can improve their number sense and estimation skills for next time.

Tomorrow, we extend the lesson: convert those itemized numbers into percentages in order to make a pie chart of the allocation of parking spaces.

Check it: Steve Leinwand Case 4: Number Sense
He hits some great points at 2:25. It's worth watching the whole thing in my opinion.
Steve exclaims about estimation, "We need to build that into ALL the things that we do!"

Think how many times a day we estimate:
Time to get ready in the morning. Time to get to work. How long is this darn red light? How long before I get my cup of coffee? How many? How many? How many?

Please share with me!
What can I do to make estimation better with my students?
How do you use estimation effectively?
How do your students benefit from it? (or not)
What are some other daily estimations you make?



  1. Cool stuff. I want to do more with estimation in my class.

    I've always wanted to talk about ancient forms of measurement. Cubits, palms, etc. and how they were used.

    Also, have you seen these bad boys ? They pretty much rock.

    1. I love the QAMA calculator. Estimating before evaluating is such a great skill to have and I like how the calculator supports it. I'm intrigued by the ancient forms of measurement. I'll have to work that in somewhere. Thanks Timon!

  2. One thing I've noticed with estimation is that there is an intrinsic need to see if you were right about your guess, and it doesn't matter how good at math you think you are. Kids get very excited to see whether or not their guess is right.
    One thing I've struggled with is whether or not to make those guesses public to the class. Some kids really want that and some are embarrassed by it. If I ask the kids, how many blades of grass are on the football field and somebody says 100, then the others will certainly give him or her a hard time about it. Is this a healthy process or will the student become more withdrawn from participating?

    1. There definitely is some intrinsic value to knowing the accuracy of an estimate. Students making those estimates public can surely be challenging. Part of me stands by the fact that students need to take risks, learn from their mistakes, overestimate, underestimate, etc. so that next time they evaluate their number sense with more thought. The other part of me doesn't want to completely squash a kid if their estimate is way off. Suggestions: write in the corner of their paper, circulate the room, glance at their estimates, share their estimate with a friend/partner, before giving them the option to go public with it. Another way might be to ask the class, "Who has estimates between 0-100, 100-200,etc.?" Give them a range. No matter how off that estimate, I will never squash the kid. I'll also do my best to prevent the class from doing so. I can always find a way to turn a wild estimate into something positive. I love that challenge.

  3. Just want you to know I left a rather lengthy comment here when you first posted this. But my iPad (was traveling) had done it again, screen keyboard just froze up in the comment box and my copy-and-paste didn't work either. :(

    I'll never forget one time a kid REMINDED me to ask for guesses before they did the calculations because I just forgot too. I think it was the cupcakes lesson where we guessed just about everything there was to guess! I need to remember to use QAMA also.

    @Nathan: I love the public guesses though, and I think the kids do too. I think it helps that we do math "fun facts" weekly so the kids are used to giving all kinds of guesses and we just laugh at whatever. I really believe we've built a culture of it's "safe to share" in this class. I also like Dan Meyer's asking for an additional guess that they know is "way off."

    I really like your "range" estimates too!

    1. I agree, we need to laugh at silly guesses at times, even ones that were serious and way off. Safe to share. I agree. Safe to fail too. How else will we learn, right? That guy, Tom Edison, light bulb, he failed many times or something like that.

  4. I'm a grade 6-12 math coach, so I deal with middle school teachers and kids often, but my most recent teaching experience was at the high school level, particularly AP Statistics. Even with the older students, I challenged the kids on a daily basis to ask "What does my Spidey Sense tell me?". Too often, students want to just get to the conclusion quickly and move on. For example, if we survey 500 males and 500 females and ask them if they like chocolate, and 430 males and 410 females say yes, will this be a significant difference? I want my students to have a feel for a plausible result before touching a calculator or looking at a formula. Developing a feel for what is happening before we crunch numbers, and discussing and sharing thoughts, should be embedded in everything we do. It's just good teaching!

    Bob L.