Nets

Classroom resources

Load these into Waypoints Prepare: choose Load URL and paste the copied address, or download the file and import it. In Prepare, the worksheet's Teacher edition shows the answers; the student copy hides them.

• Slides Download Copy address for Prepare Present from the browser, or export to PowerPoint or PDF.
• Worksheet Download Copy address for Prepare Print the student copy; the Teacher edition has the answers.

Students will be able to

• I can tell whether a net folds into a cube, and say how I know.
• I can name the faces in the net of a prism or a pyramid.
• I can find the surface area of a triangular prism from its net.

Timing

Predict and Run 8 min · Investigate 8 min · Modify 10 min · Practise and Make 9 min

Before class

Do the Run board yourself first, then fold a real cube net from card if you have time.

The one idea: a net works only if every face is covered exactly once. Counting six squares is necessary but not enough (Zara's mistake).

The board folds by rolling a cube over the squares, so the colour on each square is the face it becomes. The cube has 11 different nets; the Make task is not about finding all of them (see Stretch).

Running the lesson

1. Predict: ask which square would land on the first one.
2. Run: ask students to find a net before they check it on the board.
3. Investigate: ask what Zara could do to check her block.
4. Modify: for the prism, ask which side of the triangle each rectangle matches.
5. Make: ask why the area has two parts, the ends and the sides.

The hard part (on purpose)

Picturing the fold. Let students build a cube from paper or linking squares beside the board; the board's colours say where each square lands.

When students get stuck

Answers to the checks

1. six in a row: Six squares joined in a straight row. Will they fold into a cube?
   No. Fold the row round and the sixth square lands on the first. A net needs six squares on six different faces.
2. fold the net: Click squares to change the row until the board says it folds into a cube. Was your prediction right?
   
   Folding needs six squares on six different faces. A row of six wraps back on itself.
3. How many squares?: A net folds into a cube. How many squares does it have?
   6
   A cube has 6 faces, so its net has 6 squares.
4. Find the mistake: Zara says her block of six squares folds into a cube. Click the line where her reasoning goes wrong.
   line 4
   Line 4: six squares is needed, but they must land on six different faces. A 2 by 3 block has squares that fold on top of each other.
5. The test: What is the best way to test a net for a cube?
   Fold it (or roll a cube over it) and check that every face is covered once
   Fold it, in your head or on the board: each face must be covered exactly once.
6. A cross: Make a net of a cube with a row of four squares in the middle.
   
   Four in a row with one above and one below folds: the row wraps round and the extra squares are the top and bottom.
7. Six squares that fail: Make a net with six squares that does not fold into a cube.
   
   For example a row of five with one square on top, a 2 by 3 block, or the row of six: two squares land on the same face.
8. A prism: The triangle has sides 3, 4 and 5 cm. Set the length to 5 cm. What is the net's area?
   
   Two triangles of 6 cm² and rectangles 3 × 5, 4 × 5 and 5 × 5: 12 + 60 = 72 cm².
9. Count the rectangles: How many rectangles are in the net of a triangular prism?
   3
   One rectangle for each side of the triangle: 3, plus the 2 triangles makes 5 faces.
10. A pyramid: What is the net of a square pyramid made of?
    1 square and 4 triangles
    A square base and four triangles that meet at the point.
11. Surface area: A prism has a right triangle with sides 6, 8 and 10 cm and length 5 cm. Set the board to match.
    
    Two triangles of 24 cm² and rectangles 6 × 5, 8 × 5 and 10 × 5: 48 + 120 = 168 cm².
12. Net area: Read the net's area on the board. The prism's surface area is how many square centimetres?
    168
    The net is the surface laid flat, so its area is the surface area.
13. Review: triangle area: Review: a triangle has base 8 cm and height 5 cm. What is its area in square centimetres?
    20
    (8 × 5) ÷ 2 = 20 cm².
14. A box: How many rectangles are in the net of a rectangular prism (a box)?
    6
    A box has 6 faces, all rectangles, in 3 matching pairs (some may be squares).
15. a net to fit: Make a prism net with a surface area between 90 and 100 cm². Use a 3, 4, 5 triangle.
    
    With a 3, 4, 5 triangle the area is 12 + 12 × L, so L = 7 gives 96 cm².

Solutions

One possible solution for each task. Other correct programs are fine.

other nets and other solids › A cross

Open task: any program that does what the step asks.

other nets and other solids › Six squares that fail

Open task: any program that does what the step asks.

other nets and other solids › A prism

Open task: any program that does what the step asks.

other nets and other solids › Count the rectangles

Open task: any program that does what the step asks.

a net to fit

Open task: any program that does what the step asks.

Stretch and support

Stretch: A cube has 11 different nets (turning or flipping a net does not count as new). Can you find them all?

Support: Give students six linking squares or a card net to fold before the board.

Coach prompt (optional)

For a student who has done the lesson and is still stuck. They paste it into an AI tool your school allows; it asks questions about this lesson's one idea and doesn't give answers. Students see it on the course recap page only through a link ending in ?coach=1: recap with coach prompts.

You are a patient maths coach for a Year 7 student in Australia. Help me understand ONE idea only, from the lesson "Nets".

The idea: Nets of prisms and other 3D objects: I can Students identify, draw and construct nets of prisms and other common 3D objects.

What understanding looks like:
- Correctly identifies valid nets for a cube and rectangular prism.
- Draws a net that folds correctly to produce a given 3D object.
- Does not include overlapping faces in a net.

Mistakes students often make here:
- A student says any six joined squares fold into a cube.
- A student forgets the two triangles when finding a prism's area.
- A student halves the net area.

How to coach me (rules from the Waypoints Kit coach):
- Ask me one short question at a time (2 to 4 sentences) and wait for my answer. Never give me the answer before you have heard my thinking, and don't hide the answer inside your question.
- Start in Discover: ask me to explain the idea in my own words, or to predict what happens in a simple example. I can switch any time: "teach it back" (you play a beginner and I explain), "spot the flaw" (you show me an answer with one common mistake and I find it), or "check" (I explain, and you tell me what is solid and what to revisit).
- If I am stuck or say "just tell me", ask what I think first, then give a small hint or a simpler example. Explain only after I have had a real go.
- Stay in this idea: don't teach later ideas or add extra content. If I ask about something else, say it is for another lesson and bring me back.
- After you help, ask me one reflective question, such as how I know my answer is right or what I would check.
- Praise my effort and method, not my ability.
- You can be wrong: if I rely on something you said, remind me to check it against my notes or the lesson. If you don't know, say so.
- Use simple words.
- Stop when I can explain the idea in my own words and get one new example right. Then tell me to go back to the lesson "Nets".

Exit ticket

A net of six squares has four in a row, one above and one below. Does it fold into a cube? How can you tell?

Yes. The row of four wraps round the sides, and the extra two squares are the top and the bottom, so every face is covered once.

What each step is for

• six in a row: Committing to whether six squares in a row fold into a cube shows whether they count squares or picture the fold.
• fold the net: Changing the squares of a net and watching the board fold it shows that a net works only when all six squares land on different faces.
• six squares is not enough: Six squares is necessary but not enough (Zara counts only); the test is whether the faces differ; a prism net adds up its faces.
• other nets and other solids: Different cube nets (a cross, six squares that fail) and the prism's net area: faces of a prism are two ends and a rectangle for each side.
• nets: Prism surface area and other nets, mixed; counting faces is the planted slip; the triangle area review keeps the prism's end faces fresh.
• a net to fit: Choosing the length of a prism to meet a target area applies the net as faces added up.

Where it leads

This starts AC9M7SP01.

Where it leads: views and isometric drawings (next lesson); surface area and volume of prisms (Measurement); Year 8 volume of prisms and cylinders.