Represent cubes and cuboids on isometric grids

What you will learn

• Represent cubes and cuboids on isometric grids

Models used: number sentences, stories, tables.

Before you start

• Measure volume using unit cubes cm³ and m³

Count a layer, then stack the layers

One layer is 4 cubes wide and 3 cubes deep. It contains 12 cubes.

1. Count cubes across a layer, then count the layers. Some cubes are hidden.

   One layer is 4 cubes wide and 3 cubes deep. It contains 12 cubes.

   Width 4, height 1, depth 3

2. Count cubes across a layer, then count the layers. Some cubes are hidden.

   Stack a second matching layer. Now there are two lots of 12 cubes.

   Width 4, height 2, depth 3

3. Count cubes across a layer, then count the layers. Some cubes are hidden.

   A third layer gives 36 cubes. Remember the cubes hidden inside.

   12 + 12 + 12 = 36

   Width 4, height 3, depth 3

Worked example: A new example, together

A solid contains 3 equal layers, with 8 unit cubes in each layer. How many unit cubes form the solid?

1. All dimensions refer to the same unit. Read each value with the heading above its column.

   Count along each of the three directions in turn.

   Equal layers connect base area and height with total volume.

   All dimensions refer to the same unit

   Width	Depth	Height / layers
   4	2	3

2. All dimensions refer to the same unit. Read each value with the heading above its column.

   One layer contains 4 × 2 = 8 unit cubes.

   All dimensions refer to the same unit

   Width	Depth	Height / layers
   4	2	3

   A solid contains 3 equal layers, with 8 unit cubes in each layer. How many unit cubes form the solid?

   24 unit cubes

3. All dimensions refer to the same unit. Read each value with the heading above its column.

   There are 3 equal layers.

   All dimensions refer to the same unit

   Width	Depth	Height / layers
   4	2	3

4. All dimensions refer to the same unit. Read each value with the heading above its column.

   Count all layers: 8 × 3 = 24.

   All dimensions refer to the same unit

   Width	Depth	Height / layers
   4	2	3

5. All dimensions refer to the same unit. Read each value with the heading above its column.

   Check the result against the question we started with.

   8 × 3 = 24.

   We found 24 unit cubes. Equal layers connect base area and height with total volume.

   All dimensions refer to the same unit

   Width	Depth	Height / layers
   4	2	3

Common mistakes to discuss

• Drawing what the front looks like. An isometric drawing keeps the depth visible, so each edge length can still be counted.

Check your understanding

• Represent cubes and cuboids on isometric grids
• read and draw a solid so that all three dimensions stay visible
• check the answer against the original quantities and units

Explain your reasoning to an adult, then try a fresh question in the interactive lesson. A result from one attempt is not proof of lasting mastery.