Now imagine this: a classroom where students are working in groups of three or four, collaborating on a problem/project at hand. They are in discussion and using manipulatives (the 1' by 1' by 1' tiles on the floor or the 1" by 1" by 1" connecting cubes) to solve the different questions brought to their attention. The classroom has a slight buzz to it from all the conversations occurring at once and all students seem to be engaged in the task at hand.
Those seem to be completely two different pictures of a math class!
To introduce volume, our school curriculum uses Cathy Fosnot's Box Factory. I think that this is a fabulous way to get kids thinking about volume and surface area (and even multiplication) without even mentioning those specific math-content vocabulary words!
Students explored these questions on different days:
1. I have 24 items and I want to send them to a friend. How many different boxes are there and what are the dimensions? How do you know that you have all the possibilities?
2. How much cardboard is needed to make all the different boxes we found in the first question?
3. I have three different-sized boxes: small (2 by 2 by 2), medium (3 by 3 by 3), and large (4 by 4 by 4). How many items does each box hold and how much will the packaging cost if the cardboard costs 12 cents per square unit?
4. How many 4-inch by 4-inch by 4-inch boxes will fit into a cardboard shipping box that is 4 feet by 6 feet by 4 feet? How many of a smaller 2-inch by 2 -inch by 2-inch box would fit into the same shipping box?
Whoa! Now that is some different math from when I was in fifth grade! I remember getting the equation for finding volume that didn't completely make sense to me! Now it makes sense!
Here are pictures of our learning walls that students created on the last day, reflecting on what they learned throughout the Box Factory unit!
Now after this unit was over, I actually did have to go to the FedEx store to ship a box of running gear to a friend in New York City. And guess what I saw when I got there that made me chuckle?!?!
When I showed my students this picture, one delightful student asked, "Are you going to make us do some math with these boxes?!?!"