Measure volume using unit cubes cm³ and m³

What you will learn

• Measure volume using unit cubes cm³ and m³

Models used: number sentences, stories, tables.

Before you start

• Find areas and perimeters of composite rectilinear figures

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.

   Hidden cubes occupy space too. Base area counts one layer; height tells how many unit layers fill the solid or liquid depth.

   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 4 equal layers, with 16 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.

   Separate base dimensions, layer size and number of layers. Check what is known and what is missing.

   Equal layers connect base area and height with total volume.

   All dimensions refer to the same unit

   Width	Depth	Height / layers
   4	4	4

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

   One layer contains 4 × 4 = 16 unit cubes.

   All dimensions refer to the same unit

   Width	Depth	Height / layers
   4	4	4

   A solid contains 4 equal layers, with 16 unit cubes in each layer. How many unit cubes form the solid?

   64 unit cubes

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

   One layer contains 4 × 4 = 16 unit cubes.

   All dimensions refer to the same unit

   Width	Depth	Height / layers
   4	4	4

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

   There are 4 equal layers.

   All dimensions refer to the same unit

   Width	Depth	Height / layers
   4	4	4

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

   Count all layers: 16 × 4 = 64.

   All dimensions refer to the same unit

   Width	Depth	Height / layers
   4	4	4

6. 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.

   16 × 4 = 64.

   We found 64 unit cubes. Equal layers connect base area and height with total volume.

   All dimensions refer to the same unit

   Width	Depth	Height / layers
   4	4	4

Common mistakes to discuss

• Counting only the cubes on show. Hidden cubes fill the solid too. Count one layer, then multiply by the number of layers.

Check your understanding

• Measure volume using unit cubes cm³ and m³
• explain volume or a missing dimension through equal layers
• 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.