This week I was tasked with teaching Volume to year 10 and I thought that this would be a fairly straightforward lesson. I decided to start with a starter whereby I told the class I had 24 cubes and I wanted to arrange them into a cuboid (using all the cubes) I gave them some time to discuss this problem. Some students took to drawing cubes in their books, others sat looking blankly so when one student pointed out that I had a box of unifix cubes in the room and could he use some. I allowed the students to use the cubes to help them with the problem. One girl built a cube with dimensions 2x3x4 but the rest made frames without cubes inside or were unsure how wide to make the cubes. They didn’t seem comfortable putting cubes together and seeing how it went. We looked at the cuboid that was made and worked out what the dimensions were. I tipped the cuboid over and asked them what the dimensions were. It took a few moments for someone to recognise it was the same numbers;2,3,4. I asked the students how many cubes there were in the cuboid (which was now on its side) and I was surprised to see some students counting cubes. One student shared that she thought we were looking at Volume (which was displayed as the title) and so you work this out by doing length x width x height so it was 2 x 3 x 4. After a pause the answer was given; 24. I assumed that they would know that as i hadn’t removed or added a cube that the volume would stay the same. For some the idea of conservation was still not concrete in their minds and it seemed the commutative law wasn’t either.
So I started on a series of tasks designed to test this. I’ll report back once I have a response from the class on the tasks below.
[Conservation refers to the ability to determine that a certain quantity will remain the same despite adjustment of the container, shape, or apparent size. – Piaget]
Students have used Plan, Elevation and Isometric drawings to help them understand Volume of Cuboids. The discussed the idea of layers of cubes and how many cubes in each layer.
I gave a class this task and it was interesting to see how they used the idea of layers to help them answer it. A few students used 27 minus the cubes they could see but a number of students ‘filled’ in the missing cubes to make the 3cm cube. My thanks to Prof Smudge (Maths medicine) for this task.
I will be giving my year 10 class this task tomorrow