This was how we kicked off our Math class today. I put the challenge up on the board and walked off to the side of the room and pretended to read a book, letting them deal with the problem as a group. While they spoke, I took notes on how their ideas evolved. Here the rough translation of their sequence of thinking:

- How do we measure the bucket?
- What unit should we use? (they choose cm)
- Group worked together to measure around the bucket
- Great teamwork
- Got a piece of string and wrapped it around the bucket, cut it, then measured the string
- Found that the string was 81cm
- Hold on, that is just around, how about how deep it is?
- Another piece of string to find the depth of the bucket
- One student drew a 3D picture of a bucket on the floor and started to write the measurements onto it
- Found that the bucket was 21 cm deep
- Next, do 81 x 21 = 1701 (got a calculator for this)
- Done!
- What does this mean? this doesn't look right
- You can't times the around part by the deep part
- It is not a square, its round
- it is cm3?
- No, it has something to do with pi, the radius and the diameter
- Student draw a picture of a circle and labels it with pi, radius, and circumference
- But that is a 2D circle, this bucket is 3D
- If we times the circumference by the radius we get......
- I'm confused
- Wait a minute, What are we measuring?

Full circle. Back to the initial question. They started off down the wrong path because they asked the wrong question. Not

*how*do we measure the bucket, but

*what*do you measure? I interjected here and asked them to start their conversation over with the question of

*what*. Within a minute they had a list of ideas or concepts they could measure. It strayed away from the bucket a little and was more of general measurement, but that is okay. We wrote them all down on pieces of paper and then sorted these ideas into piles that were similar. In the end, we ended up with four broad categories

- Volume
- Area
- Weight
- Length (all measurement of things that are straight lines)

Once we had our list, we grouped off into concepts and we will begin to research and inquire into each one. Each group will do a different concept, and then bring their learning back to the larger group. How? I have no idea, but I'm sure they will come up with something.

And we forgot to actually measure the bucket.

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