This week we were working with volume and surface area, so our warm-ups had to do with those topics.
This one was interesting. I asked it purposely because of the work we had been doing with The Box Factory investigation for the last week–which is all about how to build boxes that hold 24 objects–and was about volume. We hadn’t named it as volume yet, though, and I wanted to see how many people would make that connection. Many of them did not. I saw many “thinking faces” as they struggled with how to answer this one. I heard someone say, “I don’t remember what volume is…” and then several people answered with what it was, but didn’t tell how you’d find it. We had a great conversation about this one, and I heard lots of “oh!” when I told them that they’d been working with volume for a whole week.
This one was again related to the work we’d been doing during Math Workshop. They are used to seeing this kind of equation, since we’d spent a couple of weeks on order of operations recently, and we had been using this kind of equation in our volume work–the parentheses told the equation for the bottom of the box, and the last number told how many layers there were. But I wanted to see if they could explain the formula for finding volume, and tell how they multiplied length x width x height. They don’t need to know this yet, but I thought they were ready for it, so I threw it at them. And many–probably most really–figured it out. We brought the rest of them along through the conversation we had around it.
There was not a math warm-up on Thursday because we needed those ten minutes to work on our volume projects.
The dimensions on this warm-up were from three boxes we’d been working with this week. We’d talked several times about how this was really the same box, turned two different ways to make a new base, so with different dimensions. We’d already talked about the Commutative Property in warm-ups, and so I wanted to see if anyone knew about how this illustrated the Associative Property. Again, a great conversation and many connections were made as we talked. Have I said before how much I LOVE these warm-ups? So many great things happen in just a quick discussion. Love it!
Happy solving! What do you know about volume and surface area? What can you teach us? 🙂