--- title: "Views of a solid" subtitle: "Angles and shapes · Solids · Lesson 11" --- # Views of a solid **Name:** {{field-24}} **Date:** {{field-15}} **Class:** {{field-15}} > **Key question:** An architect shows a building from above, from the front and from the side. Why not just one drawing? :::teacher-note **In one sentence:** Students build piles of cubes and compare the isometric drawing with the top, front and side views, finding what each view hides (AC9M7SP01, nodes 2 and 3). **Students should be able to say:** I can draw or read the top, front and side views of a pile of cubes. I can say what a view hides. I can say one advantage and one disadvantage of a net and of a 3D drawing. **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 a tall tower with a short pile directly behind it. :::keep-together **You see only the front view of a pile of cubes. Can you tell how many cubes there are?** ☐ No: cubes behind the front ones do not show ☐ Only if you also know the side view ☐ Yes: count the squares My prediction, and why: {{lines-3}} ::: :::teacher-note **What happens:** No. A front view shows the tallest pile in each column; cubes behind it, or lower down, are hidden. ::: ## Run Try it on the board in the tutorial. Was your prediction right? What was different? {{lines-2}} ## What a view shows :::keep-together ### Hidden cubes **A column has piles of 3, 1 and 2 cubes, one behind another. How many squares does the front view show for that column?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 3 The tallest pile is 3, so the front view shows 3 squares for that column. ::: :::keep-together ### Find the mistake **Noor works out the front view of a column of piles. Click the line where her reasoning goes wrong.** ``` 1 The first column has piles of 3, 1 and 2 cubes. 2 Noor draws the front view of that column. 3 She adds the piles, so the column shows 6 squares. 4 The front view is 6 squares tall. ``` Line: {{field-15}} Why is it wrong? {{lines-2}} ::: :::teacher-note **Answer:** line 3 Line 3: a front view shows only the tallest pile in each column, not all of them added up. ::: :::keep-together ### Which drawing **Which drawing tells you exactly how many cubes there are?** ☐ The front view ☐ The side view ☐ The top view with no numbers ☐ A top view with the height written on each pile ::: :::teacher-note **Answer:** A top view with the height written on each pile With a height on every pile, adding the numbers gives the total. ::: :::typical ## Build to a description **Six cubes.** Both views must be 3 squares. **The fewest.** **The most.** **From a top view.** **Nets or drawings.** Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ::: ## Views :::keep-together ### Side view **Look at the stack on the board. How many squares does its side view show?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 3 From the right, the rows give tallest piles 2, 0 and 1: 3 squares. ::: :::keep-together ### Cube count **A top view with heights is 3 1 on the top row and 0 2 on the bottom row. How many cubes are there?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 6 3 + 1 + 0 + 2 = 6 cubes. ::: :::keep-together ### The top view **Which view shows which cells of the base have cubes?** ☐ The side view ☐ The top view ☐ The front view ☐ The isometric drawing ::: :::teacher-note **Answer:** The top view Looking down, the top view shows a square for every occupied cell. ::: :::keep-together ### Review: nets **Review: which of these six-square nets folds into a cube?** ☐ A 2 by 3 block ☐ A straight row of six ☐ A cross: one square above and one below a row of four ☐ A row of three above a row of three ::: :::teacher-note **Answer:** A cross: one square above and one below a row of four Only the cross-shaped net covers all six faces once. ::: ## Make: two designs Write one advantage and one disadvantage of nets and of 3D drawings. Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ## Exit ticket :::keep-together **A front view shows 3 squares. Does the pile have 3 cubes? Why or why not?** {{lines-3}} ::: :::teacher-note **Answer:** Not necessarily. The front view shows only the tallest pile in each column; there could be more cubes behind. :::