Measurement

KS2

MA-Y5-D005

Converting between metric and common imperial units; calculating perimeter and area of rectangles, triangles and parallelograms; volumes of cuboids; solving problems involving time and money.

National Curriculum context

In Year 5, measurement extends to include some imperial units that remain in common use (miles, pounds, pints, gallons) and approximate metric equivalents. The non-statutory guidance specifies that pupils should use, read and write standard units — including decimal notation — and practise converting between units, developing fluency in using different measurement contexts. Area is extended beyond rectilinear shapes to triangles and parallelograms, connecting to multiplication and division. Volume of a cuboid (length × width × height, measured in cm³) is introduced, connecting three-dimensional thinking to arithmetic. These practical skills connect directly to the number work of the year and provide real-world contexts for decimals, fractions and large number calculations.

Concepts

Clusters

Prerequisites

With difficulty levels

AI Direct: 1

Lesson Clusters

Understand and calculate the volume of cuboids

practice Curated

Only one concept in this domain. Volume of cuboids (V = l × w × h) is the new measurement concept introduced in Year 5.

1 concepts Structure and Function

Volume of cuboids

Teaching Suggestions (1)

Study units and activities that deliver concepts in this domain.

Volume of Cuboids

Mathematics Pattern Seeking

CPA Stage: concrete → pictorial → abstract NC Aim: problem solving

multilink cubes centimetre cubes

isometric drawings of cuboids layered diagrams showing volume as layers of area bar model for comparison problems

Fluency targets: Estimate the volume of cubes and cuboids using standard units (cm³ and m³); Calculate volume by counting unit cubes; Begin to connect volume with multiplication of three dimensions

Volume of cuboids

Prerequisites

Concepts from other domains that pupils should know before this domain.

Area of rectilinear shapes from Measurement

MA-Y4-C013

Domain Vocabulary

11 terms across 1 concepts (11 domain-specific)

Domain-specific (11)

Concept

cm²(noun)

The unit of area equal to a square with sides of one centimetre; abbreviated as cm².

cubic centimetre(noun)

A unit of volume equal to a cube with edges of 1 cm, written as cm³.

cuboid(noun)

A 3-D shape with 6 rectangular faces, 12 edges, and 8 vertices; like a box.

formula(noun)

A mathematical rule expressed using letters and symbols that shows the relationship between quantities.

height(noun)

How tall something is, measured from bottom to top.

length(noun)

How long something is from one end to the other.

space(noun)

The three-dimensional extent in which objects exist; in maths, used when discussing volume, capacity, and 3D shapes.

three-dimensional(adjective)

Having length, width, and height (depth); occupying physical space rather than being flat.

unit cube(noun)

A cube with edges of exactly 1 unit length, used as the standard building block for measuring volume.

volume(noun)

The amount of space a 3-D object takes up, or the amount of liquid in a container.

width(noun)

The measurement of how wide something is, typically the shorter horizontal dimension of a shape.

Concepts (1)

Volume of cuboids

knowledge AI Direct

MA-Y5-C014

Volume is the amount of three-dimensional space a solid occupies, measured in cubic units (cm³, m³). The volume of a cuboid is calculated as length × width × height. In Year 5, pupils build cuboids from unit cubes, estimate volumes, and apply the formula. Mastery means pupils understand volume as a 3-D measurement distinct from area, can calculate the volume of a cuboid using the formula, and use appropriate cubic units.

Teaching guidance

Build cuboids from 1 cm³ cubes: a 3 × 4 × 2 cuboid contains 24 cubes = 24 cm³. Show that this can be seen as 3 layers of 4 × 2 = 8 cubes, or 4 rows of 3 × 2 = 6 cubes — connecting to the commutativity of multiplication. Connect area of the base (length × width) to volume: volume = base area × height. Introduce the unit cm³ (cubic centimetre) as the space a 1 cm × 1 cm × 1 cm cube occupies. Compare cm³ (volume) with cm² (area) to keep units clear.

Vocabulary (11 terms)

cm² T3 — The unit of area equal to a square with sides of one centimetre; abbreviated as cm².

cubic centimetre T3 new — A unit of volume equal to a cube with edges of 1 cm, written as cm³.

cuboid T3 — A 3-D shape with 6 rectangular faces, 12 edges, and 8 vertices; like a box.

formula T3 — A mathematical rule expressed using letters and symbols that shows the relationship between quantities.

height T3 — How tall something is, measured from bottom to top.

length T3 — How long something is from one end to the other.

space T3 new — The three-dimensional extent in which objects exist; in maths, used when discussing volume, capacity, and 3D shapes.

three-dimensional T3 new — Having length, width, and height (depth); occupying physical space rather than being flat.

unit cube T3 new — A cube with edges of exactly 1 unit length, used as the standard building block for measuring volume.

volume T3 — The amount of space a 3-D object takes up, or the amount of liquid in a container.

width T3 — The measurement of how wide something is, typically the shorter horizontal dimension of a shape.

Common misconceptions

Pupils confuse volume (cm³, 3-D) with area (cm², 2-D). They may multiply only two dimensions rather than three. The formula V = l × w × h is sometimes misremembered as V = l + w + h (confusing with perimeter additions). Pupils may not understand that a flat shape has no volume, or that two shapes with the same surface area can have different volumes.

Difficulty levels

Entry

Building cuboids from 1 cm³ cubes and counting the total to find volume.

Example task

Build a cuboid that is 3 cubes long, 2 cubes wide and 2 cubes tall. How many cubes did you use?

Model response: 12 cubes. The volume is 12 cm³.

Developing

Using the formula V = l × w × h to calculate volume of cuboids, and distinguishing volume from area.

Example task

A box is 5 cm long, 4 cm wide and 3 cm tall. What is its volume?

Model response: V = 5 × 4 × 3 = 60 cm³.

Expected

Calculating volume of cuboids in different units, estimating volumes, and finding a missing dimension given the volume.

Example task

A cuboid has volume 120 cm³. Its length is 10 cm and width is 4 cm. What is its height?

Model response: V = l × w × h. 120 = 10 × 4 × h. 120 = 40h. h = 120 ÷ 40 = 3 cm.

CPA Stages

concrete

Building cuboids from unit cubes (1 cm³), counting the cubes to find volume, and exploring how changing dimensions changes volume

Transition: Child predicts the volume before building and explains: 'Volume = length × width × height because it is layers of rectangular arrays'

pictorial

Drawing cuboids on isometric paper with dimensions labelled, calculating volume using the formula, and distinguishing volume (cm³) from area (cm²)

Transition: Child calculates volume from labelled diagrams using the formula and clearly distinguishes volume units (cm³) from area units (cm²)

abstract

Calculating volumes of cuboids from given dimensions without drawing, solving problems involving volume, and working backwards from volume to find a missing dimension

Transition: Child calculates volumes mentally and works backwards from volume to find missing dimensions, connecting cm³ to litres

Delivery rationale

Upper primary maths (Y5) — most pupils at pictorial/abstract stage. AI can deliver with virtual representations.