Volume.
It's a big skill that seems to trick so many students without a strong number sense, yet it seems so easy to the rest of us. Just l x w x h, right?
I enjoy teaching volume because I find it to be a topic that is easy to make very "hands on." I start out on my whiteboard building a list of different ways we can calculate volume. We start with "adding up all the unit cubes." We talk about how volume relates to completely filling up an object and look at filling up a rectangular prism with unit cubes.
They usually figure out that counting each one manually is quite time consuming and many can "figure out" lwh before I even have to explain it to them. It's so refreshing to see them figure out that they can "simplify the problem" by just multiplying length, width, and height.
Then, we work backward. I give them a volume and they must create rectangular prisms that meet that volume.
Letting your students build specific volumes with specific dimensions can help you see misconceptions with the skill. This group thought they had built a prism with dimensions of 6 by 3 by 3. This let me know I needed to work with them on rectangular prisms and volume--they aren't understanding yet that volume completely fills an object nor how dimensions work quite yet.
After we build rectangular prisms, we move into book problems that give a length, width, and height for them to calculate with large numbers, decimals, or fractions.
After this, I give students a box and a ruler. They must measure the dimensions themselves and then calculate the volume.
Finally, I let them take a yardstick and go calculate how much their locker will hold! They LOVE finding the volume of their beloved locker!
