Teaching for mastery in primary maths

In this chapter, pupils are exposed to the concept of length as a measurement through real-life, relatable examples, which will help them to build the foundations of their understanding.

Pupils compare, describe and solve practical problems dealing with length and height. They use language such as “long”, “short”, “tall”, “longer”, “shorter” and “taller” and make statements such as, “The teacher is taller than…” 

Additionally, pupils measure and record lengths and heights using both non-standard and standard measuring equipment. For example, they use bricks or cubes to measure the length of a particular object and may start to use a ruler.

In this chapter, pupils meet the concept of weight (or mass) as a measurement. They use the terms “weight” and “mass” interchangeably.

Once again, pupils are introduced to the concept through real-life, relatable examples and should be encouraged to handle different objects to get a feel for and an understanding of what is meant by weight (or mass). 

Pupils will compare, describe and solve practical problems for weight (or mass). They use language such as “heavy”, “light”, “heavier than” and “lighter than” and make statements such as, “The tennis ball is heavier than the feather”.

Additionally, pupils measure and record weight (or mass) using both non-standard and standard measuring equipment. For example, they use balance scales to determine the weight of an object in cubes. 

In this chapter, pupils are exposed to the concepts of capacity and volume as measurements through real-life, relatable examples, which will help them to build the foundations of their understanding.

Pupils handle and fill a variety of objects, such as jars, bottles, jugs and cups, and compare, describe and solve practical problems involving capacity and volume. They should use language such as “full”, “empty”, “more than” and “less than”, and link to their work on fractions by using language such as “half”, “half-full” and “quarter”.

Additionally, pupils measure and record capacity and volume using non-standard measuring equipment, such as cups.

In this chapter, pupils measure lengths and heights in metres (m) and centimetres (cm) using rulers.

Pupils build on previous learning by using standard equipment and units to measure lengths and heights. They use the standard measurements of metres (m) and centimetres (cm) and measure to the nearest unit. They choose the most appropriate unit to estimate and measure a given length or height in any direction.

As before, pupils use common language to compare lengths and heights and start to put them in order. First introduced in the place value chapters, pupils use symbols such as < , > and = to form comparison statements (eg,  1m > 1cm).

In this chapter, pupils measure weight (or mass) in grams (g) and kilograms (kg).

Pupils build on previous learning by using standard equipment and units to measure weight (or mass). They use the standard measurements of grams (g) and kilograms (kg) and measure to the nearest unit. They choose the most appropriate unit to estimate and measure a given weight (or mass).

As before, pupils use common language such as “heavier than” and “lighter than” to compare the weight (or mass) of particular objects. They also put the weight of several objects in order, including those that are not physically in the classroom (eg, in comparing a pillow and an elephant). 

Continuing on from their work on comparing lengths in the previous chapter, pupils use the symbols < , > and = to form comparison statements (eg, 1kg > 1g). This also reinforces work on place value and ordering.

In this chapter, pupils measure capacity and volume in litres (l) and millilitres (ml) and begin to measure temperature.

Pupils build on previous learning by using standard equipment and units to measure capacity and volume. They use the standard measurements of litres (m) and millilitres (cm) and measure to the nearest unit. They choose the most appropriate unit to estimate and measure a given capacity or volume.

Pupils are introduced to the concept of temperature and start to estimate and measure temperatures in degrees centigrade (°C) using a thermometer.

As before, pupils use common language to compare and order different capacities and volumes. They use symbols such as < , > and = to form comparison statements (eg, 2l > 1l).

In this chapter, pupils add and subtract lengths and measure the perimeter of simple 2D shapes.

Pupils continue to measure and compare lengths. They now use millimetres (mm), as well as centimetres and metres, in real-life contexts and discuss the connection between them. This reinforces work on place value.

Using their existing understanding of addition and subtraction, pupils solve problems in which they add and subtract different lengths. Linked to this, they find the perimeter of simple 2D shapes by measuring the lengths of their sides.

In this chapter, pupils use measurements of length, weight (or mass), capacity and volume in word problems involving addition and subtraction.

Pupils measure and compare lengths, weights, capacities and volumes using standard units of measurement at all times. It is essential that all work on measurement is linked to place value. For example, pupils know that 1,000 millilitres is equal to 1 litre.

Using their existing understanding of addition and subtraction, pupils solve problems in which they add and subtract different lengths, weights, capacities and volumes. Where possible, problems should be presented in authentic, real-life contexts.

In this chapter, pupils find the area of simple shapes by counting squares.

Using concrete examples, pupils meet the concept of area for the first time. They understand that area is the amount of space bounded by a flat 2D object. Pupils find and compare the areas of simple rectilinear shapes by counting squares. 

In this chapter, pupils measure and calculate the perimeter of rectilinear shapes.

Building on their earlier work on perimeter, pupils measure and calculate the perimeter of rectilinear shapes in both centimetres and metres.

When calculating the perimeter, they may be presented with shapes including given measurements on all sides, or of particular sides only.

In this chapter, pupils convert between different units of measure, using concrete objects and visual representations.

In doing so, pupils reinforce their understanding of each measure and explore the links to previous work on place value, multiplication and division. 

Pupils solve problems in which they convert between different units of measure (eg, converting between centimetres and metres to determine whether 146cm is greater or less than 1.4 metres). They see how number work can be applied to measure in authentic contexts.

In this chapter, pupils understand approximate equivalents between metric and common imperial units.

Pupils reinforce their work on the previous chapter by converting between different units of metric measure. They convert between millimetres, centimetres and metres for length, millilitres and litres for capacity and volume and grams and kilograms for weight (or mass).

Although pupils may have an awareness of simple imperial units both in other subjects and in real life, this chapter sees these concepts formalised. They start to understand and use approximate equivalences between metric units and common imperial units, such as inches, pounds and pints.

In order to understand the difference and connection between metric and imperial units of measure, pupils should be given the opportunity to use concrete materials and measuring equipment.

In this chapter, pupils calculate the area of rectangles (including squares) and solve problems that involve measures.

Pupils reinforce work on perimeter and area by measuring and calculating the perimeter of composite rectilinear shapes. They calculate and compare the area of rectangles (including squares) using square centimetres (cm²) and square metres (m²) and estimate the area of irregular shapes.

Using existing knowledge from previous chapters and other topics, pupils solve problems involving length and area with all four operations. These problems may involve decimal notation and scaling.

In this chapter, pupils estimate volume and solve problems involving capacity and volume.

Pupils begin to estimate capacity (eg, using water) and volume (eg, using 1cm³ blocks to build cubes and cuboids). In addition, they solve problems involving capacity and volume using all four operations. In doing so, they apply existing number and calculation skills.

In this chapter, pupils bring together their existing knowledge of length, area and volume to find the area and volume of simple 2D and 3D shapes.

Continuing work on metric and imperial units, pupils solve problems involving the calculation and conversion of units of measure (eg, between miles and kilometres), using decimal notation up to three decimal places where appropriate.

They also use, read, write and convert standard measurements of length, weight and volume from a smaller unit to a larger one (and vice versa), also using decimal notation up to three decimal places. 

Pupils calculate, estimate and compare the volume of cuboids (including cubes) using standard units, including cubic centimetres (cm³) and cubic metres (m³), later extending this to other units, such as cubic millimetres (mm³) and cubic kilometres (km³).

In time, pupils realise that shapes with the same areas can have different perimeters (and vice versa) and start to recognise when it is possible to use formulae in the calculation of the area and volume of shapes.

Pupils build on their previous knowledge to find the area of other shapes, including parallelograms and triangles. They deduce and explain the formulae for these new shapes.