Primary 5 maths · Measurement & time · About 12 minutes
Draw cubes and cuboids on isometric grids
Count along each of the three directions in turn.
Start the interactive lesson →Open practice activity
What you will learn
- Draw cubes and cuboids on isometric grids
Models used: number sentences, stories, diagrams.
Before you start
Count a layer, then stack the layers
One layer is 4 cubes wide and 3 cubes deep. It contains 12 cubes.
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.
A flat square shows one face. An isometric drawing shows width, height and depth together, so the cubes can be counted.
Width 4, height 1, depth 3
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
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
What did the picture help us see?
A third layer gives 36 cubes. Remember the cubes hidden inside.
Worked example: A new example, together
Find the volume of a cuboid 2 cm by 5 cm by 3 cm.
Count along each of the three directions in turn.
Equal layers connect base area and height with total volume.
Each dimension is in centimetres. Count the cubes in one layer, then the equal layers. One layer contains 2 × 5 = 10 unit cubes.
Each dimension is in centimetres. Count the cubes in one layer, then the equal layers. Find the volume of a cuboid 2 cm by 5 cm by 3 cm.
30 cm³
One layer contains 2 × 5 = 10 unit cubes.
Each dimension is in centimetres. Count the cubes in one layer, then the equal layers. There are 3 equal layers.
Each dimension is in centimetres. Count the cubes in one layer, then the equal layers. Count all layers: 10 × 3 = 30.
Each dimension is in centimetres. Count the cubes in one layer, then the equal layers. Check the result against the question we started with.
10 × 3 = 30.
We found 30 cm³. Equal layers connect base area and height with total volume.
Each dimension is in centimetres. Count the cubes in one layer, then the equal layers.
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
- Draw 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.
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