Teaching for mastery in primary maths

In this chapter, pupils are formally introduced to decimal notation.

To start, pupils are introduced to tenths and hundredths of a whole and relate decimal notation to the division of whole number by 10 and 100. Pupils make connections between fraction and decimal representations, realising that a given number or proportion may be expressed either way. They also find the effect of dividing a one- or two-digit number by 10 and 100, identifying the value of the digits in the answer as ones, tenths and hundredths.

Pupils learn decimal notation and the language associated with it, including in the context of measurements, and recognise and write decimal equivalents of any number with tenths or hundredths. They go on to order decimal amounts and quantities expressed to the same number of decimal places and make comparisons between them. Additionally, they represent numbers with one or two decimal places in several ways, such as on number lines.

By working with concrete manipulatives and pictorial representations of tenths and hundredths, pupils come to recognise and write decimal equivalents to ¹⁄4, ¹⁄2 and ³⁄4. They use fractions-related language and concepts to help them make connections between fraction and decimal notation.

Later, pupils round decimals with one decimal place to the nearest whole number and compare numbers with up to two decimal places. Pupils connect hundredths to tenths and place value and decimal measure. They build on their understanding of place value and decimal notation to record metric measures, including money and solve simple measure and money problems involving fractions and decimals to two decimal places. They also estimate, compare and calculate different measures, including money in pounds and pence.

In this chapter, pupils convert between fractions and decimals and calculate with decimals.

Building on work from the previous chapter, pupils read, write, order and compare numbers with up to three decimal places. They recognise and use thousandths and relate them to tenths and hundredths, as well as decimal equivalents and measures.

Pupils round decimals with two decimal places to the nearest whole number and to one decimal place. They say, read and write decimal fractions and related tenths, hundredths and thousandths accurately, and read and write decimal numbers as fractions (eg, 0.71 = ⁷¹⁄100).

Linked with previous work on addition and subtraction, pupils count using decimals and fractions above and below zero. They mentally add and subtract tenths, as well as one-digit whole numbers and tenths. They practise adding and subtracting decimals, as well as whole numbers with decimals, decimals with different numbers of decimal places and also complements of 1 (eg, 0.83 + 0.17 = 1). Pupils recognise and describe linear number sequences involving fractions and decimals (eg, 3 , 3¹⁄2, 4, 4¹⁄2...) and find the term-to-term rule in words (eg, add ¹⁄2).

Pupils multiply and divide whole numbers and those with decimals by 10, 100 and 1,000. In doing so, they interpret non-integer answers to division problems and express them in different ways according to the context. Answers are expressed as fractions, as numbers with remainders and as decimals (eg, 98 ÷ 4 = ⁹⁸⁄4 = 24 r2 = 24 ¹⁄2 = 24.5 ≈ 25).

By the end of this chapter, pupils use all four operations to solve length, mass, volume or money problems using decimal notation. They go beyond the measurement and money models of decimals to solve number puzzles involving decimals. As a result of their extensive work on place value in previous topics, pupils check the reasonableness of their answers confidently.

In this chapter, pupils extend calculation work to include numbers with up to three decimal places.

Pupils develop confidence in working with numbers with up to three decimal places. They represent them with objects and diagrams, identifying the value of each digit. Using their understanding of decimal place value, they solve problems requiring answers to be rounded to specified degrees of accuracy.

Building on work from the previous chapter, pupils now multiply numbers with up to three decimal places by 10, 100 or 1,000 and multiply one-digit numbers with up to two decimal places by whole numbers. Additionally, they divide numbers by 10, 100 or 1,000 to find answers with up to three decimal places. They use written division methods to find answers with up to two decimal places.

Later, pupils also recall and use equivalences between simple fractions, decimals and percentages in a variety of contexts, using representations to facilitate understanding.

They use their knowledge of decimals across the curriculum in a wide variety of mathematical and real-life contexts.