--- title: "Nets" subtitle: "Angles and shapes · Solids · Lesson 10" --- # Nets **Name:** {{field-24}} **Date:** {{field-15}} **Class:** {{field-15}} > **Key question:** A cereal box starts as one flat piece of card. Which flat shapes fold up into a box, and which ones jam? :::teacher-note **In one sentence:** 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). **Students should be able to say:** 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. **Width:** the unmarked parts are the floor every student does (predict, run, investigate and make). Typical adds the modify practice; wider adds the real-world contexts. They add contexts, not difficulty. Students work in the online tutorial alongside this sheet. ::: ## Predict Picture wrapping the row round a cube: where does the fifth square go? :::keep-together **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 My prediction, and why: {{lines-3}} ::: :::teacher-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. ::: ## Run Try it on the board in the tutorial. Was your prediction right? What was different? {{lines-2}} ## Six squares is not enough :::keep-together ### How many squares? **A net folds into a cube. How many squares does it have?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 6 A cube has 6 faces, so its net has 6 squares. ::: :::keep-together ### 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. ``` Line: {{field-15}} Why is it wrong? {{lines-2}} ::: :::teacher-note **Answer:** 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. ::: :::keep-together ### 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 ::: :::teacher-note **Answer:** 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. ::: :::typical ## Other nets and other solids **A cross.** **Six squares that fail.** **A prism.** **Count the rectangles.** Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ::: ## Nets :::keep-together ### 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 ::: :::teacher-note **Answer:** 1 square and 4 triangles A square base and four triangles that meet at the point. ::: :::keep-together ### Net area **Read the net's area on the board. The prism's surface area is how many square centimetres?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 168 The net is the surface laid flat, so its area is the surface area. ::: :::keep-together ### Review: triangle area **Review: a triangle has base 8 cm and height 5 cm. What is its area in square centimetres?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 20 (8 × 5) ÷ 2 = 20 cm². ::: :::keep-together ### A box **How many rectangles are in the net of a rectangular prism (a box)?** ☐ 3 ☐ 4 ☐ 5 ☐ 6 ::: :::teacher-note **Answer:** 6 A box has 6 faces, all rectangles, in 3 matching pairs (some may be squares). ::: ## Make: a net to fit Then: why does a net show the surface area exactly, when a 3D drawing does not? Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ## Exit ticket :::keep-together **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?** {{lines-3}} ::: :::teacher-note **Answer:** 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. :::