Number
Decimals
Teaching for mastery in
primary maths
Contents
Number: Decimals
Introduction3
01. Introduction to decimals4
02. Four operations with decimals 5
03. Calculating with decimals 6
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Number: Decimals
Introduction
Throughout these chapters, pupils extend their understanding of the number system to
include tenths, hundredths and thousandths.
Previously, pupils worked with numbers and parts of numbers smaller than one when
learning about fractions. In this topic, pupils will learn that tenths, hundredths and
thousandths can also be represented using decimal notation. They will realise that a given
number or proportion may be represented using either decimal or fraction notation, and
make connections between the two.
Money and other measures such as length, weight and volume offer useful contexts
through which pupils can solve problems using decimals. However, pupils should also
work with decimals in more abstract contexts, including those in which they are not able to
think of the digits after the decimal point as representing centimetres, millilitres or pence,
but instead as tenths, hundredths and thousandths of the whole.
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Chapter 1:
Introduction to decimals
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.
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Chapter 2:
Four operations with decimals
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 onedigit 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 = 241⁄2 = 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.
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Chapter 3:
Calculating with decimals
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.
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