Mathematics
Cambridge Primary Mathematics
Curriculum outline
Cambridge Primary combines a worldclass curriculum with highquality support for teachers and integrated assessment. The curriculum is dedicated to helping schools develop learners who are confident, responsible, reflective, innovative and engaged. Cambridge Primary has curriculum frameworks for English (including English as a Second Language), Mathematics and Science which have been designed to engage learners in an active and creative learning journey.
The curriculum frameworks for each subject for Cambridge Primary are organised into six stages. They reflect the teaching target for each year group and provide comprehensive learning objectives. For Cambridge Primary Mathematics, the curriculum is presented in five content areas or ‘strands’. These are further subdivided into ‘substrands’. The strands and substrands are:
Number
 Numbers and the number system
 Calculation – Mental strategies, Addition and subtraction, Multiplication and division
Geometry
 Shapes and geometric reasoning
 Position and movement
Measure
 Money (until stage 3)
 Length, mass and capacity
 Time
 Area and perimeter (from stage 4)
Handling data
 Organising, categorising and representing data
 Probability (from stage 5)
Problem solving
 Using techniques and skills in solving mathematical problems
 Using understanding and strategies in solving problems (from stage 4)
The first four content areas are all underpinned by Problem solving , which describes using techniques and skills and the application of understanding and strategies in solving problems. Mental strategies are also a key part of the Number content.

This curriculum focuses on principles, patterns, systems, functions and relationships so that learners can apply their mathematical knowledge develop a holistic understanding of the subject.
The Cambridge Primary Mathematics curriculum framework provides a solid foundation upon which the later stages of education can be built.
Cambridge Primary offers an optional testing structure to assess learner performance and report progress for both learners and parents. These assessments provide an international benchmark that enables teachers to identify learner strengths and weaknesses for individuals and class groups and develop further teaching and learning support using the information from the test results.
Cambridge Primary Progression Tests are available to schools registered for Cambridge Primary for stages 3–6. These tests are marked by teachers and come with full mark schemes and marking guidance. At the end of Cambridge Primary, schools can also offer Cambridge Primary Checkpoint, a diagnostic test which offers comprehensive feedback at the end of the Cambridge Primary stage.


Stage 1
Strand: Number
Substrand: Numbers and the number system
 Recite numbers in order (forwards from 1 to 100, backwards from 20 to 0)
 Read and write numerals from 0 to 20
 Count objects up to 20, recognising conservation of number
 Count on in tens from zero or a singledigit number to 100 or just over
 Count on in twos, beginning to recognise odd/even numbers to 20 as ‘every other number’
 Begin partitioning twodigit numbers into tens and ones and reverse
 Within the range 0 to 30, say the number that is 1 or 10 more or less than any given number
 Use more or less to compare two numbers, and give a number which lies between them
 Order numbers to at least 20, positioning on a number line; use ordinal numbers
 Use the = sign to represent equality
 Give a sensible estimate of some objects that can be checked by counting, e.g. to 30
 Find halves of small numbers and shapes by folding, and recognise which shapes are halved.

Strand: Number
Substrand: Calculation
Mental strategies
 Know all number pairs to 10 and record the related addition/subtraction facts
 Begin to know number pairs to 6, 7, 8, 9 and 10
 Add more than two small numbers, spotting pairs to 10, e.g. 4 + 3 + 6 = 10 + 3
 Begin using pairs to 10 to bridge 10 when adding/ subtracting, e.g. 8 + 3, add 2, then 1
 Know doubles to at least double 5
 Find near doubles using doubles already known, e.g. 5 + 6
 Begin to recognise multiples of 2 and 10.
Addition and subtraction
 Understand addition as counting on and combining two sets; record related addition sentences
 Understand subtraction as counting back and ‘take away’; record related subtraction sentences
 Understand difference as ‘how many more to make?’
 Add/subtract a singledigit number by counting on/back
 Find two more or less than a number to 20, recording the jumps on a number line
 Relate counting on and back in tens to finding 10 more/less than a number (< 100)
 Begin to use the +, – and = signs to record calculations in number sentences
 Understand that changing the order of addition does not change the total
 Add a pair of numbers by putting the larger number first and counting on
 Recognise the use of a sign such as £ to represent an unknown, e.g. 6 + £ = 10
 Begin to add single and twodigit numbers.
Multiplication and division
 Double any singledigit number
 Find halves of even numbers of objects up to 10
 Try to share numbers to 10 to find which are even and which are odd
 Share objects into two equal groups in a context.

Stage 3
Strand: Number
Substrand: Numbers and the number system
 Recite numbers 100 to 200 and beyond
 Read and write numbers to at least 1000
 Count on and back in ones, tens and hundreds from two and threedigit numbers
 Count on and back in steps of 2, 3, 4 and 5 to at least 50
 Understand what each digit represents in threedigit numbers and partition into hundreds, tens and units
 Find 1, 10, 100 more/less than two and threedigit numbers
 Multiply twodigit numbers by 10 and understand the effect
 Round twodigit numbers to the nearest 10 and round threedigit numbers to the nearest 100
 Place a threedigit number on a number line marked off in multiples of 100
 Place a threedigit number on a number line marked off in multiples of 10
 Compare threedigit numbers, use < and > signs, and find a number in between
 Order two and threedigit numbers
 Give a sensible estimate of a number as a range (e.g. 30 to 50) by grouping in tens
 Find half of odd and even numbers to 40, using notation such as 13 1/2

 Understand and use fraction notation, recognising that fractions are several parts of one whole, e.g. 3/4 is three quarters and 2/3 is two thirds
 Recognise equivalence between 1/2 , 2/4 , 4/8, 5/10 using diagrams
 Recognise simple mixed fractions, e.g. 1 1/2 and 2 1/4
 Order simple or mixed fractions on a number line, e.g. using the knowledge that 1/2 comes half way between 1/4 and 3/4 , and that 1 1/2 comes half way between 1 and 2
 Begin to relate finding fractions to division
 Find halves, thirds, quarters and tenths of shapes and numbers (whole number answers).

Stage 3 continued
Strand: Number
Substrand: Numbers and the number system
Mental strategies
 Know addition and subtraction facts for all numbers to 20
 Know the following addition and subtraction facts:
 multiples of 100 with a total of 1000
 multiples of 5 with a total of 100
 Know multiplication/division facts for 2x, 3x, 5x and 10x tables
 Begin to know 4x table
 Recognise two and threedigit multiples of 2, 5 and 10
 Work out quickly the doubles of numbers 1 to 20 and derive the related halves
 Work out quickly the doubles of multiples of 5 (< 100) and derive the related halves
 Work out quickly the doubles of multiples of 50 to 500.
Addition and subtraction
 Add and subtract 10 and multiples of 10 to and from two and threedigit numbers
 Add 100 and multiples of 100 to threedigit numbers
 Use the = sign to represent equality, e.g. 75 + 25 = 95 + 5
 Add several small numbers
 Find complements to 100, solving number equations such as 78 + £ = 100
 Add and subtract pairs of twodigit numbers
 Add threedigit and twodigit numbers using notes to support
 Reorder an addition to help with the calculation, e.g. 41 + 54, by adding 40 to 54, then 1
 Add/subtract singledigit numbers to/from threedigit numbers
 Find 20, 30, … 90, 100, 200, 300 more/less than threedigit numbers.

Multiplication and division
 Understand the relationship between halving and doubling
 Understand the effect of multiplying twodigit numbers by 10
 Multiply singledigit numbers and divide twodigit numbers by 2, 3, 4, 5, 6, 9 and 10
 Multiply teens numbers by 3 and 5
 Begin to divide twodigit numbers just beyond 10x tables, e.g. 60 / 5, 33 / 3
 Understand that division can leave a remainder (initially as ‘some left over’)
 Understand and apply the idea that multiplication is commutative
 Understand the relationship between multiplication and division and write connected facts.

Stage 5
Strand: Number
Substrand: Numbers and the number system
 Count on and back in steps of constant size, extending beyond zero
 Know what each digit represents in five and sixdigit numbers
 Partition any number up to one million into thousands, hundreds, tens and units
 Use decimal notation for tenths and hundredths and understand what each digit represents
 Multiply and divide any number from 1 to 10 000 by 10 or 100 and understand the effect
 Round fourdigit numbers to the nearest 10, 100 or 1000
 Round a number with one or two decimal places to the nearest whole number
 Order and compare numbers up to a million using the > and < signs
 Order and compare negative and positive numbers on a number line and temperature scale
 Calculate a rise or fall in temperature
 Order numbers with one or two decimal places and compare using the > and < signs
 Recognise and extend number sequences.
 Recognise odd and even numbers and multiples of 5, 10, 25, 50 and 100 up to 1000
 Make general statements about sums, differences and multiples of odd and even numbers.

 Recognise equivalence between: 1/2, 1/4 , and 1/8 ; 1/3 and 1/6 ; 1/5 and 1/10
 Recognise equivalence between the decimal and fraction forms of halves, tenths and hundredths and use this to help order fractions, e.g. 0.6 is more than 50 percent and less than 7/10
 Change an improper fraction to a mixed number, e.g. 4/7 to 1 3/4 ; order mixed numbers and place between whole numbers on a number line
 Relate finding fractions to division and use to find simple fractions of quantities
 Understand percentage as the number of parts in every 100 and find simple percentages of quantities
 Express halves, tenths and hundredths as percentages
 Use fractions to describe and estimate a simple proportion, e.g. 1/5 of the beads are yellow
 Use ratio to solve problems, e.g. to adapt a recipe for 6 people to one for 3 or 12 people.
Strand: Number
Substrand: Calculation
Mental strategies
 Know by heart pairs of oneplace decimals with a total of 1, e.g. 0.8 + 0.2
 Derive quickly pairs of decimals with a total of 10, and with a total of 1
 Know multiplication and division facts for the 2x to 10x tables
 Know and apply tests of divisibility by 2, 5, 10 and 100
 Recognise multiples of 6, 7, 8 and 9 up to the 10th multiple
 Know squares of all numbers to 10 x 10
 Find factors of twodigit numbers
 Count on or back in thousands, hundreds, tens and ones to add or subtract
 Add or subtract near multiples of 10 or 100, e.g. 4387 – 299

Stage 5 continued
 Use appropriate strategies to add or subtract pairs of two and threedigit numbers and numbers with one decimal place, using jottings where necessary
 Calculate differences between near multiples of 1000, e.g. 5026 – 4998, or near multiples of 1, e.g. 3.2 – 2.6
 Multiply multiples of 10 to 90, and multiples of 100 to 900, by a singledigit number
 Multiply by 19 or 21 by multiplying by 20 and adjusting
 Multiply by 25 by multiplying by 100 and dividing by 4
 Use factors to multiply, e.g. multiply by 3, then double to multiply by 6
 Double any number up to 100 and halve even numbers to 200, and use this to double and halve numbers with one or two decimal places, e.g. double 3.4 and half of 8.6
 Double multiples of 10 to 1000 and multiples of 100 to 10 000, e.g. double 360 or double 3600, and derive the corresponding halves.
Addition and subtraction
 Find the total of more than three two or threedigit numbers using a written method
 Add or subtract any pair of three and/or fourdigit numbers, with the same number of decimal places, including amounts of money.

Multiplication and division
 Multiply or divide threedigit numbers by singledigit numbers
 Multiply twodigit numbers by twodigit numbers
 Multiply twodigit numbers with one decimal place by singledigit numbers, e.g. 3.6 x 7
 Divide threedigit numbers by singledigit numbers, including those with a remainder (answers no greater than 30)
 Start expressing remainders as a fraction of the divisor when dividing twodigit numbers by singledigit numbers
 Decide whether to group (using multiplication facts and multiples of the divisor) or to share (halving and quartering) to solve divisions
 Decide whether to round an answer up or down after division, depending on the context
 Begin to use brackets to order operations and understand the relationship between the four operations and how the laws of arithmetic apply to multiplication.
