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# Nets

Angles and shapes · Solids

<!-- Speaker note: Students build nets on a grid and watch the board fold them into a cube, then find the net area of a triangular prism (AC9M7SP01, node 1). About 35 minutes (Predict and Run 8 min · Investigate 8 min · Modify 10 min · Practise and Make 9 min). -->

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## Today

**We are learning to** a net is a flat pattern that folds into a solid. Six squares make a cube only if they land on six different faces; a triangular prism has two triangles and three rectangles.

- 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.

<!-- Speaker note: 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). -->

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## Why it matters

> A cereal box starts as one flat piece of card. Which flat shapes fold up into a box, and which ones jam?

<!-- Speaker note: A **net** is a flat pattern that folds up into a solid. A cube's net is six squares joined along their edges. A **prism** is a solid with two matching ends and flat rectangular sides; the net of a triangular prism is two triangles and three rectangles. -->

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<span style="background:#dbeafe; color:#1a1a1a; border:1.5px solid #3b82f6; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">💬 Discussion</span>

## Predict

**Six squares joined in a straight row. Will they fold into a cube?**

- Only if the row is bent
- Yes: a cube has six faces
- No: some squares would land on top of each other

<!-- Speaker note: What happens: No. Fold the row round and the sixth square lands on the first. A net needs six squares on six different faces. Take two or three predictions before anyone runs it. -->

<!-- Speaker note: Teacher: ask which square would land on the first one. -->

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<span style="background:#fef3c7; color:#1a1a1a; border:1.5px solid #f59e0b; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✍️ Activity</span>

## Try it

{{embed: https://studio.learningwaypoints.com/tutorials/_playground-board/index.html?id=deck%2Fmaths%2Fangles%2Fnets%2Fstep-2&code=widget%3A+net%0Amode%3A+cube%0Acells%3A+0%2C1%3B+1%2C1%3B+2%2C1%3B+3%2C1%3B+4%2C1%3B+5%2C1%0A&fresh=1}}

[Open this step in the tutorial](https://studio.learningwaypoints.com/tutorials/maths/angles/nets/?full=step-2#step-2)

<!-- Speaker note: Click a square to add it or take it away. The colours show which face each square becomes. -->

<!-- Speaker note: Teacher: ask students to find a net before they check it on the board. -->

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## What happened?

* No. Fold the row round and the sixth square lands on the first. A net needs six squares on six different faces.

<!-- Speaker note: Reveal after running. Ask who predicted it, and what made them think so. -->

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## How many squares?

**A net folds into a cube. How many squares does it have?**

* Answer: 6

<!-- Speaker note: A cube has 6 faces, so its net has 6 squares. -->

<!-- Speaker note: Teacher: ask what Zara could do to check her block. -->

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## Find the mistake

**Zara says her block of six squares folds into a cube. Click the line where her reasoning goes wrong.**

```
 1  Zara draws six squares in a 2 by 3 block.
 2  A cube has six faces.
 3  Her pattern has six squares.
 4  So her pattern folds into a cube.
```

* Answer: line 4

<!-- Speaker note: 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. -->

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## The test

**What is the best way to test a net for a cube?**

- Check that it is a rectangle
- Fold it (or roll a cube over it) and check that every face is covered once
- Count that it has six squares
- Check that it is symmetrical

* Answer: Fold it (or roll a cube over it) and check that every face is covered once

<!-- Speaker note: Fold it, in your head or on the board: each face must be covered exactly once. -->

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<span style="background:#fef3c7; color:#1a1a1a; border:1.5px solid #f59e0b; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✍️ Activity</span>

## Other nets and other solids



- **A cross:** 
- **Six squares that fail:** 
- **A prism:** 
- **Count the rectangles:** 

[Open this step](https://studio.learningwaypoints.com/tutorials/maths/angles/nets/?full=step-4#step-4)

<!-- Speaker note: What this step is for: 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. Hints, in order: Start with a row of 4 squares. / Add one square above and one below the row. / Move one square so that two squares would land on the same face. / A row of five with one square on top does not fold. / The net area is the area of 2 triangles plus 3 rectangles. / Slide the length L to 5. For students who need more support: Give students six linking squares or a card net to fold before the board. For early finishers: A cube has 11 different nets (turning or flipping a net does not count as new). Can you find them all? 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: A student says any six joined squares fold into a cube. Ask: Which two squares would land on the same face? Fix: Roll the cube across the squares, or fold a paper copy. / A student forgets the two triangles when finding a prism's area. Ask: How many faces does a triangular prism have? Fix: Five faces: three rectangles and two triangles. / A student halves the net area. Ask: Is the net the whole surface or only part? Fix: The net is the whole surface laid flat. -->

<!-- Speaker note: Teacher: for the prism, ask which side of the triangle each rectangle matches. -->

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<span style="background:#fef3c7; color:#1a1a1a; border:1.5px solid #f59e0b; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✍️ Activity</span>

## Nets

{{embed: https://studio.learningwaypoints.com/tutorials/_playground-board/index.html?id=deck%2Fmaths%2Fangles%2Fnets%2Fstep-5&code=widget%3A+net%0Amode%3A+prism%0Aslider+a%3A+1%2C+10%2C+3%0Aslider+b%3A+1%2C+10%2C+4%0Aslider+L%3A+1%2C+8%2C+3%0Aunits%3A+cm%0A&fresh=1}}

[Open this step in the tutorial](https://studio.learningwaypoints.com/tutorials/maths/angles/nets/?full=step-5#step-5)

<!-- Speaker note: What this step is for: Prism surface area and other nets, mixed; counting faces is the planted slip; the triangle area review keeps the prism's end faces fresh. -->

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## A pyramid

**What is the net of a square pyramid made of?**

- 4 squares and 1 triangle
- 2 squares and 4 triangles
- 1 square and 4 triangles
- 5 squares

* Answer: 1 square and 4 triangles

<!-- Speaker note: A square base and four triangles that meet at the point. -->

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## Net area

**Read the net's area on the board. The prism's surface area is how many square centimetres?**

* Answer: 168

<!-- Speaker note: The net is the surface laid flat, so its area is the surface area. -->

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## Review: triangle area

**Review: a triangle has base 8 cm and height 5 cm. What is its area in square centimetres?**

* Answer: 20

<!-- Speaker note: (8 × 5) ÷ 2 = 20 cm². -->

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## A box

**How many rectangles are in the net of a rectangular prism (a box)?**

- 3
- 4
- 5
- 6

* Answer: 6

<!-- Speaker note: A box has 6 faces, all rectangles, in 3 matching pairs (some may be squares). -->

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<span style="background:#fef3c7; color:#1a1a1a; border:1.5px solid #f59e0b; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✍️ Activity</span>

## Make: a net to fit

Then: why does a net show the surface area exactly, when a 3D drawing does not?

[Open this step](https://studio.learningwaypoints.com/tutorials/maths/angles/nets/?full=step-6#step-6)

<!-- Speaker note: What this step is for: Choosing the length of a prism to meet a target area applies the net as faces added up. Hints, in order: Each extra centimetre of length adds 3 + 4 + 5 = 12 cm² with a 3, 4, 5 triangle. / The two triangles give 12 cm² whatever the length. -->

<!-- Speaker note: Teacher: ask why the area has two parts, the ends and the sides. -->

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## 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.

<!-- Speaker note: Students answer on paper or a mini whiteboard before the reveal. Anyone who cannot answer needs the main idea again next lesson. Where this 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. -->