**If you've been following**my thoughts lately, via Twitter (#estimation180) or this blog, I've really been investigating the relevance of estimation for some time now. However, the past few days have really had a great impact on my approach with students, leaving me even more intrigued with the relevance and application of estimation with students. Over the next few days, I plan to share a few of the interactions: here's part 1.

**Today, I visited a fourth grade classroom**at my school. It's a personal goal of mine this year to visit as many classrooms as possible during my prep period and learn, learn, learn from other teachers, especially elementary teachers. I love observing elementary classrooms and seeing how so many children are still excited about learning. I'm constantly looking for strategies to bring back to my own classroom that will create a sense of excitement with my middle schoolers. The fourth grade teacher and I will be working on creating and implementing 3 Act lessons this year, so I was getting acquainted with the climate of her classroom. It was destiny: the class was discussing estimation and guessing.

**First off, she's a fantastic teacher**. Second, she did a wonderful job comparing and contrasting what the students thought estimation and guessing meant in their own words. She created a list for each on a huge giant sheet of paper, like a giant Post-It note. She does this often and sticks them around the class for students to refer to. The fourth graders decided that

**guessing**could be something:

- you don't know
- you think could be the answer
- 50% sure
- or anything

**estimation**, the fourth graders decided it could be something:

- you round
- you think is close to the answer and reasonable
- you look at and use clues to carefully give an answer

**This last definition**was very insightful for a fourth grader. The teacher proceeded to pick up a cup in front of the class and tell the class there were cubes inside. She asked them to make a guess and students were stretching their necks to gather any information about the cup in her hands. She did a great job concealing it, but many students had already mentally logged characteristics of the cup. She had a low-entry point for the students. They all wanted to know how many cubes were in the cup. They wrote down guesses in their journals and she took them to the next level. She showed the students how full the cup was with the cubes and asked them if this would be a good time to keep guessing or make an estimate. Students agreed, they had more information to make an estimate and they jotted this new number down in their journal. Lastly, she passed out cups, requesting students to not touch, but think of a strategy with their small group to get an even better estimate of the cubes in the cup. Students shared their theories:

- I counted the cubes in the top layer and then counted the layers down and multiplied the two numbers.
- I counted the number of cubes around the cup on each layer and made a reasonable guess for the hidden cubes inside.

**The teacher asked the class**who had similar theories and many of them chose the first. I really enjoyed how the teacher didn't once offer her theory on how to estimate. She let the students take ownership. As the lesson drew to a close, she requested the students work together to quickly count the cubes inside their cup and compare it to both their guess and estimate. The teacher had a low-entry point for all students, she let the students define their own vocabulary, she took them up the ladder of abstraction with gradually revealing information they needed/wanted and going from guessing to estimation. Lastly, the payoff was huge as she allowed students go hands-on with the cup and cubes to validate their learning for the day. I left her class inspired. But before I left, the teacher and I had a valuable brief discussion. A few things came out of that conversation I will touch base on in part 2.

**Part 2 will connect**estimation with guessing and the space between, sometimes referred to as a guess-timation. I want to create a low-entry point that's even more inviting for students. Lastly, I want to discuss how number sense can be strengthened as we transition from guessing to estimation before the payoff.

Part 1,

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This is a great way to get kids to start estimating and it gets at the heart of it by allowing them to count some of the blocks, and then use that "chunk" as a reference to figure out the rest.

ReplyDeleteYea, the teacher did a fantastic job with her students!

DeleteGreat post! I am just starting to follow several math blogs - and I teach grade 7 and 8 as well.

ReplyDeleteThe language you mentionn from the grade 4 class, actually links to our grade 7 and 8 probability expectations - using language to describe different degrees of probability. (Ontario, Canada)

I like to tie estimation to calculator use - tell the kids "calculators are dumb - they only answer what you ask" and warn about mis-keyed questions (especially losing a decimal, or having a sticky key repeat) It is so important that they keep estimating as they use algorithms for arithmatic with fractions and decimals - I hope to teach them that if their estimates are far from their answers, they are probably mis-using the algorithm.

(The best example for me - multiplication and division with zero and one. Kids oftten guess wrong, and I bring them back to mental math with questions like "there are 5 people, and I want to give each of them ZERO cookies - how many do I need" .... they all know the answer! (then extend to 100 people, 793 256 - or other large random number to confirm that they DO know this fact, and extend it to 7/5 of a person, or 8.05 or whatever)

Sarah