My third graders are currently learning volume. They've already done perimeter and area, but volume is really a hard concept for them. The kind of stuff we have to work with is basically, "Look at the picture. How many cubic units does it take to make it." I've given the kids connecting cubes and we have recreated the figures very slowly and step-by-step as a class. We've talked about the different layers of a figure, and how cubes can't just float (there needs to be a cube underneath it if it's not on the bottom). Right now things just aren't clicking with them. It's a hard concept to visually move a drawing on paper in all dimensions, and if they can't see all the cubes, they struggle with knowing that they are indeed there. I can certainly understand why they are having trouble. Does anyone have any good ideas for helping teach this challenging concept? I hate seeing the frustration on their faces, and I want to make this as engaging and understandable as possible for them.

Maybe try empty containers, the amount of [beads, water, marbles...] that can fit in each represents the volume? Then they can try different containers to see how the size of the container relates to the volume, experiment to see if a thin/tall container can fit the same as a large/low container or things like that. Then you can start illustrating filling things with cubes -- how many rows/columns of cubes fit in it? (e.g. it's 5 cubes long by 3 cubes wide by 2 cubes high) How many cubes are in the whole thing? They can see how the LxWxH formula works if you want to take it there... but at the very least they can see what volume represents and then memorize the formula... Just some random thoughts. And, btw, thanks - you've just given me a great idea because I need to write a lesson plan using manipulatives for a hypothetical class. I think I'll use this so if you do please let me know how it goes!

Yes, you should use containers that they can fill with various objects - counters, pennies, beads. Or you could use centimeter cubes or wooden cubes of any size to build a base (find the area of it), then stack it high. The area of the base times the number (or use repeated addition) of levels high will give them the volume.

S Dubb, If you are like us, you must teach cubic volume (so the beads in the container isn't applicable.) I've been teaching this for years, and first, it isn't developmentally appropriate which is why they are having the problem -- but I know, you have a standard you must teach. After years of arguing with our state, they have removed it from our curriculum until grade 5!!!!!! yeah!!! But I've had to teach it for a while, and I know exactly what you are going through. First -- stop using snap cubes!!!!!!!!!!! You need to use regular cubes that are not interlocking. Otherwise, they will not get that a cube can't "float" because with the interlocking, they can make it "stick" in some ways. The cubes help your kinesthetic learners, and while your visual learners will get it when they use cubes, they will not be able to translate it to line drawings -- even with shading. For my kinesthetic leaners I build a cube wall that is 3 layers of 3 cubes (going up like this: XXX XXX XXX I then build a second layer behind it, and turn it slightly so the students can see the front and the angle view of the side. I ask them how many must be in the back row, then we tear the front row off an check. Same thing for a third row. Teach them to count the front "wall" and then do repeated addition for the walls behind it. Somehow, this works better than doing "flat layers" and building up. They just seem to get it better. Second, I had to teach this again to my 2nd graders this year -- and I designed a computer simulation that really seemed to help them (especially the visual learners and special needs learners.) My simulation uses no words at all and you don't need powerpoint or any other specific computer program to run it. If you pm me with your email address, I'l be glad to send it to you and you can see if it helps. Like I said, it won't really help you kinesthetic learners, but it can help you visual learners.

Thanks all for the suggestions, but yes, I am doing cubic volume (I should have specified). RainStorm, thank you SO much for the tips. Check your PMs.