When I started teaching grade 3 last year, I printed out the Program of Study and went over it with three different colors highlighters. One for the concepts introduced or explored deeper in grade 3, one for the numeracy skills my students need to master (e.g. subtraction of three-digit numbers), and one for applications (measurement, data analysis and representation). Oftentimes, I intentionally integrate my “applied math” lessons with other subjects, sometimes the need to measure something arises in a context. I try to be sensitive to these contexts to catch the teachable moment and to turn it into a lesson. Last week, we ended up learning about measuring length.
On Tuesday, I gave the prompt to my class; we noticed, wondered, and counted everything from shoelaces to letters on the box, to dots inside the shoes. It was wonderful. One girl said, “I have these kinds of shoes at home, I’ll bring them tomorrow and we can check how many shoelaces are inside them.” I said, “Sure”.
After school, we had another Mount Holyoke College session, this time with Dan Meyer. The big question from the session: Can you involve your students in the co-development of the activity, rather than just assigning it? I didn’t have an idea yet, but it put my mind into the “search” mode.
Wednesday: Estimating and Measuring
The girl handed me her shoes first thing in the morning. We were about to take the shoelaces out, when someone asked, “How long are the shoelaces?” This was perfect!
Here is the Outcome from Alberta Program of Study Mathematics:
Students will demonstrate an understanding of measuring length (cm, m) by selecting and justifying referents for the units cm and m, modelling and describing the relationship between the units cm and m, estimating length, using referents, measuring and recording length, width and height.
First, we recorded what else we might be able to measure: shoe size, width, weight, how tall the boots are. We discussed what units we need to use to measure the shoelaces. The moments like this I appreciate that I teach in Canada and I don’t need to figure out Imperial units. I brought in the meter stick to use as a referent point.
Then, we gave our too high, too low and just right estimates.
After students used post-it notes to give their just right estimates, they tried to figure out the length of one shoelace by measuring anything they need to measure without taking the shoelaces out. Someone asked if they could use the rulers. “Yes, if you think it’s helpful.” The math notebooks were used to document and explain students’ thinking and to write down their final estimate. Some students tried to get the answer out of me. “I have no clue, these aren’t even my boots.”
The reveal was truly grand with lots of cheering and jumping. The shoelaces had the total length of 125 cm! We put some estimates on the number line to see who managed to get the closest estimate.
We discussed the possible sources of error.
-”Shoelaces go inside the holes.”
-”Centimeters are different on different rulers.”
-”Everyone was touching the shoes, pulling and stretching the laces.”
-”Some people would start a little bit ahead, not at zero.”
We had to pause for a discussion of “centimeters are different” to compare personal referents to standard units of measurement.
Then I had another moment of insight. “Let’s have a challenge. We can measure the shoelaces in my boots on Friday.”
Here is why it was a “challenge”. What is your estimate?
When my students saw my boots they looked at me like I am a magician who just pulled a rabbit out of a top hat. We went through the same routine, but this time we had a new referent point. The knowledge of the length of our Wednesday shoelaces. I honestly had no clue again how long the shoelaces might be, and my own estimate was quite a bit off. I loved the range of the strategies that my students employed to support their problem-solving.
Saturday: Thoughts and Questions
I do estimation challenges with my students somewhat regularly. They know the routine which is helpful when your audience is eight years old and the logistics can interfere easily with the flow of the lesson. Dan asked us to think about the verbs in our lessons. With my students, we noticed, wondered, selected tools, compared, modeled, estimated, discussed, measured, and some of us jumped and made not classroom appropriate sounds when our estimation was close. Most of us came up with reasonable answers, and all of us tried. Some students estimated that the shoelaces in my tall boots will be shorter than in student’s boots. I had to explicitly point at it for them to notice the disconnect. I wonder what I could have done differently to encourage them to make sense independently. I think that during our next estimation, we should have spent more time comparing our strategies and reflecting on our work.
I have previously done one week estimation challenges and I am considering bringing this format back . I would introduce the challenge on Monday and do the original estimation,(usually some kind of physical prompt), then leave it around for a week to allow students to get their ideas together. Finally, on Friday we would do measuring, calculating, summarizing, checking and reflecting.
I wonder what we can measure next?