Tipene and his friends have scissors, tape and sheets of A4 paper to construct closed containers from a single sheet of paper.

Tipene's net is a single piece that can be folded or bent to make the container. (He joins the sides with tape not tabs.)

Miri makes a shape where the net is not one piece but can be taped together to make the container (making a more efficient use of paper).

Pepe makes a shape where one face is a square. Who makes the container with the biggest volume?

In this problem students explore shapes and investigate how large a closed container they can make. They should be encouraged to construct shapes other than cubical boxes. Some may need to be reminded of the formula for the particular volume that they make.

Other problems in which students find the biggest or the smallest of a set of objects include: Square Milk Crates, Rectangular Milk Crates and __Penny’s box__

### Problem

Tipene and his friends have scissors, tape and sheets of A4 paper to construct closed containers from a single sheet of paper.

Tipene's net is a single piece that can be folded or bent to make the container. (He joins the sides with tape not tabs.)

Miri makes a shape where the net is not one piece but can be taped together to make the container (making a more efficient use of paper).

Pepe makes a shape where one face is a square.

Who makes the container with the biggest volume?

### Teaching sequence

- Begin by giving the students a piece of A4 paper and ask them to make a closed container. At this stage keep the requirements open.
- Display the containers and discuss:
*Which is the largest?*

What criteria have you used in making your decision?

Which container has the largest surface area? How do yo know?

Which container has the smallest surface area?

Which container has the largest volume?

Do any of the containers have square faces? - Pose the problem to the class.
- Ask for their initial ideas about which container has the greatest volume. Ask them to explain the thinking behind their guess.
- Take votes for the containers. List results on the board.
- Have the students investigate the problem in pairs
- As the students work ask questions that focus on their understanding of area, volume and perimeter.
*What is the area of this faces? How did you work it out?*

What is the volume of your container? How did you work it out?

What sort of container do you think will have the largest volume? Why?

How did you start on this problem?

What understandings are you using to solve this problem? - When the students think that they have a solution for the largest container, ask them to make the container from a single sheet of A4.

Share and discuss containers. Ask:*Do you think we have found the container with the largest volume? How do we know?*

#### Solution

There is no one solution to this problem. The idea here is to explore shapes and to find ways to measure their volume.