One of the downfalls of my job is that I don’t always get to spend as much time as I would like in classrooms – I don’t have my own students to test things out with. Luckily, my husband does so when I need some students I can sometimes borrow his for a while. I was feeling teaching withdrawal after a few days of meetings and after having the opportunity to finally hear Dan Meyer speak at OAME, I wanted to try out some new things he had me thinking about.

I knew the class was working on re-activating their prior knowledge of volume and surface area. They had looked at rectangular prisms the day before and the plan was to do some work with cylinders.

I had this image from 101qs on the screen when the students were coming into class.

As they came in, they were already asking the questions I would hope for:

- What is that? Is that a sinkhole? Where is that? How big is that?

Once everyone was in the room I had the students write down one or two questions they had on their mini-whiteboards. I recorded their questions on the board:

- Where is that?
- What is a sinkhole? How do they happen?
- Why do people build houses in places where sinkholes happen?
- How big is it?
- What is the radius?
- What is the volume?

When Dan did this with us he quickly moved to the questions that focused on his goal for the “lesson” and let the answers to the other questions come out or addressed them at the end. We decided in the moment to have my husband answer the first few questions quickly (he was their science teacher as well) because we knew some of the students would actually have a hard time working on the other questions without the answers to the first few.

I asked them what they meant by “how big is it” and the students that asked that said that they felt that the next two questions would answer that.

I then had them focus on the volume of the sinkhole and asked them what information they would need to figure this out. How wide and how deep came up.

I then took a move from Dan and had them try to predict the diameter of the hole. They first estimates ranged from 10m – 300m but they narrowed it to 10 – 50m using other objects in the image to help (the street looks about as wide as 3 cars plus the two sidewalks). I then gave them the dimensions from the National Geographic article of 18m wide and 100m deep. I asked if they needed any more information and there was some discussion about if they needed a length too but they decided that just those dimensions would be enough. I was surprised that no one asked for a formula but they did have a formula sheet available to them from another day.

Students worked for a while and sorted out a variety of issues by working with a partner. Some accidently found surface area but were corrected by a peer. We discussed the answer but the number was so large it was hard for them to imagine how much dirt it would to take to fill that hole. One student said “I wonder how many truckloads of dirt that would be”

We decided to help them make this volume more understandable by having them think about how many classrooms full of dirt that would be. We estimated the dimensions of the room and then had the calculate the number of classrooms of dirt it would take to fill the hole.

This was an in-the -moment decision that we were happy with because it helped them connect even further with the problem and gave them some additional practice with volume from their previous days lesson.

For the students that had calculated surface area we tried to brainstorm reasons why you might want to know the surface area – we didn’t come up with many reasons other than one suggestion “if you wanted to turn the sinkhole into a very deep pool and tile the entire inside walls…..” At least they understand what surface area is!

They then had time to do some practice with calculating volumes and surface areas of other objects. They worked well the rest of the period, I think largely because they saw the connection to the rest of the world.