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# Views of a solid

Angles and shapes · Solids

<!-- Speaker note: 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). About 40 minutes (Predict and Run 10 min · Investigate 10 min · Modify 10 min · Practise and Make 10 min). -->

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## Today

**We are learning to** a pile of cubes can be drawn in 3D or as top, front and side views. A front or side view shows only the tallest pile in each column; a top view with numbers shows every pile.

- 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.

<!-- Speaker note: Before class: Do the Run board yourself first. Build a small pile from linking cubes to hold up. The one idea: a view shows only what you can see from one side, so the front and side views show the tallest pile in each column and hide the rest. The common mistake is adding the piles (Noor's mistake). The board's rows run from the back (top of the grid) to the front. The front view looks from the front; the side view looks from the right. The top view puts the back row at the top. The view orientation is the hinge for this node: students who mix up front and side cannot compare representations. -->

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## Why it matters

> An architect shows a building from above, from the front and from the side. Why not just one drawing?

<!-- Speaker note: An **isometric drawing** shows a solid in 3D on isometric (triangle) paper. **Views** are flat drawings seen from one side: the **top** view (also called the plan), the **front** view and the **side** view (together called elevations). A view shows what you can see; cubes hidden behind others do not show. -->

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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

**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

<!-- Speaker note: What happens: No. A front view shows the tallest pile in each column; cubes behind it, or lower down, are hidden. Take two or three predictions before anyone runs it. -->

<!-- Speaker note: Teacher: ask what could be hiding behind the front pile. -->

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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%2Fviews%2Fstep-2&code=widget%3A+views%0Asize%3A+3%0Amax%3A+4%0Astart%3A+2%2C1%2C0%3B+0%2C1%2C0%3B+0%2C0%2C3%0A&fresh=1}}

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

<!-- Speaker note: Press a cell in the grid to add a cube to that pile. After the tallest, it goes back to 0. -->

<!-- Speaker note: Teacher: ask students to say which view they think will change before they press. -->

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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. A front view shows the tallest pile in each column; cubes behind it, or lower down, are hidden.

<!-- 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>

## 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: 3

<!-- Speaker note: The tallest pile is 3, so the front view shows 3 squares for that column. -->

<!-- Speaker note: Teacher: ask Noor's question again with a column of 1, 3, 1. -->

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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

**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.
```

* Answer: line 3

<!-- Speaker note: Line 3: a front view shows only the tallest pile in each column, not all of them added up. -->

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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>

## 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

* Answer: A top view with the height written on each pile

<!-- Speaker note: With a height on every pile, adding the numbers gives the total. -->

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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>

## Build to a description



- **Six cubes:** Both views must be 3 squares.
- **The fewest:** 
- **The most:** 
- **From a top view:** 
- **Nets or drawings:** 

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

<!-- Speaker note: What this step is for: Building to a description uses the views to reason about hidden cubes: the fewest, the most, and the trade-offs of each drawing. Hints, in order: Piles of 1 cube only. / Use six of the nine cells, with at least one in every row and every column. / The top view has 4 squares, so 4 piles. / The tallest pile is 3, so every pile can be at most 3. / Press a cell until its number matches. / The numbers are back row 2 1 0, middle row 0 3 0, front row 0 0 1. For students who need more support: Use a real pile of linking cubes and look at it from each side before using the board. For early finishers: Two different piles can have the same top, front and side views. Can you find a pair? The hard part, on purpose: Knowing which side is which. Turn a real pile of cubes round on the desk beside the board; the side view is seen from the right. When students get stuck: A student adds all the piles to find a view. Ask: If you stand at the front, which cubes can you see in one column? Fix: Only the tallest pile. Lower piles are hidden behind it. / A student confuses front and side views. Ask: Which way are you looking? Which row is nearest you? Fix: Front looks from the front row; side looks from the right. / A student thinks the isometric drawing shows every cube. Ask: Can you see the cube hidden behind the tall pile? Fix: No drawing from one direction shows everything; the top view with numbers is the exception. -->

<!-- Speaker note: Teacher: ask for the fewest cubes first, then the most. -->

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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>

## Views

{{embed: https://studio.learningwaypoints.com/tutorials/_playground-board/index.html?id=deck%2Fmaths%2Fangles%2Fviews%2Fstep-5&code=widget%3A+views%0Asize%3A+3%0Amax%3A+4%0Astart%3A+2%2C0%2C0%3B+0%2C0%2C0%3B+1%2C1%2C1%0A&fresh=1}}

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

<!-- Speaker note: What this step is for: Reading views and counting cubes, mixed; adding the piles is the planted slip; the cube net review keeps nets 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>

## Side view

**Look at the stack on the board. How many squares does its side view show?**

* Answer: 3

<!-- Speaker note: From the right, the rows give tallest piles 2, 0 and 1: 3 squares. -->

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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>

## 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: 6

<!-- Speaker note: 3 + 1 + 0 + 2 = 6 cubes. -->

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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 top view

**Which view shows which cells of the base have cubes?**

- The side view
- The top view
- The front view
- The isometric drawing

* Answer: The top view

<!-- Speaker note: Looking down, the top view shows a square for every occupied cell. -->

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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: 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

* Answer: A cross: one square above and one below a row of four

<!-- Speaker note: Only the cross-shaped net covers all six faces 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>

## Make: two designs

Write one advantage and one disadvantage of nets and of 3D drawings.

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

<!-- Speaker note: What this step is for: Building a solid whose three views match, then judging nets against drawings, brings the lesson's representations together. Hints, in order: A top view of 5 squares needs 5 piles. / Some piles must be 2 cubes tall, or the front and side views are too small. -->

<!-- Speaker note: Teacher: ask which drawing they would give a builder. -->

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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 front view shows 3 squares. Does the pile have 3 cubes? Why or why not?**

* Not necessarily. The front view shows only the tallest pile in each column; there could be more cubes behind.

<!-- 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 completes AC9M7SP01. Where it leads: building solids from their views, and surface area and volume of prisms (Measurement); drawing in perspective in Year 8. -->