# The UK School Curriculum

The statutory programme of study for mathematics at Key Stages 1 and 2

The attainment targets for mathematics are:

• Ma2 Number and algebra
• Ma3 Shape, space and measures
• Ma4 Handling data

Teachers should expect attainment at a given level to be demonstrated through activities in which the mathematics from the different attainment targets is at, or very close to, the same level.

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## Key Stage 1

### Ma2 Number

1. Using and applying number
Problem solving
a. approach problems involving number, and data presented in a variety of forms, in order to identify what they need to do
b. develop flexible approaches to problem solving and look for ways to overcome difficulties
c. make decisions about which operations and problem-solving strategies to use
d. organise and check their work
Communicating
e. use the correct language, symbols and vocabulary associated with number and data
f. communicate in spoken, pictorial and written form, at first using informal language and recording, then mathematical language and symbols
Reasoning
g. present results in an organised way
h. understand a general statement and investigate whether particular cases match it
i. explain their methods and reasoning when solving problems involving number and data.
2. Numbers and the number system
Counting
a. count reliably up to 20 objects at first and recognise that if the objects are rearranged the number stays the same; be familiar with the numbers 11 to 20; gradually extend counting to 100 and beyond
Number patterns and sequences
b. create and describe number patterns; explore and record patterns related to addition and subtraction, and then patterns of multiples of 2, 5 and 10 explaining the patterns and using them to make predictions; recognise sequences, including odd and even numbers to 30 then beyond; recognise the relationship between halving and doubling
The number system
c. read and write numbers to 20 at first and then to 100 or beyond; understand and use the vocabulary of comparing and ordering these numbers; recognise that the position of a digit gives its value and know what each digit represents, including zero as a place-holder; order a set of one and two-digit numbers and position them on a number line and hundred-square; round any two-digit number to the nearest 10.
3. Calculations
Number operations and the relationships between them
a. understand addition and use related vocabulary; recognise that addition can be done in any order; understand subtraction as both 'take away' and 'difference' and use the related vocabulary; recognise that subtraction is the inverse of addition; give the subtraction corresponding to an addition and vice versa; use the symbol '=' to represent equality; solve simple missing number problems [for example, 6 = 2 + ? ]
b. understand multiplication as repeated addition; understand that halving is the inverse of doubling and find one half and one quarter of shapes and small numbers of objects; begin to understand division as grouping (repeated subtraction); use vocabulary associated with multiplication and division
Mental methods
c. develop rapid recall of number facts: know addition and subtraction facts to 10 and use these to derive facts with totals to 20, know multiplication facts for the x2 and x10 multiplication tables and derive corresponding division facts, know doubles of numbers to 10 and halves of even numbers to 20
d. develop a range of mental methods for finding, from known facts, those that they cannot recall, including adding 10 to any single-digit number, then adding and subtracting a multiple of 10 to or from a two-digit number; develop a variety of methods for adding and subtracting, including making use of the facts that addition can be done in any order and that subtraction is the inverse of addition
e. carry out simple calculations of the form 40 + 30 = ?, 40 + ? = 100, 56 - ? = 10; record calculations in a number sentence, using the symbols +, -, x , ÷ and = correctly [for example, 7 + 2 = 9] .
4. Solving numerical problems
a. choose sensible calculation methods to solve whole-number problems (including problems involving money or measures), drawing on their understanding of the operations
b. check that their answers are reasonable and explain their methods or reasoning.
5. Processing, representing and interpreting data
a. solve a relevant problem by using simple lists, tables and charts to sort, classify and organise information
b. discuss what they have done and explain their results.

Knowledge, skills and understanding
a. practical activity, exploration and discussion
b. using mathematical ideas in practical activities, then recording these using objects, pictures, diagrams, words, numbers and symbols
c. using mental images of numbers and their relationships to support the development of mental calculation strategies
f. exploring and using a variety of resources and materials, including ICT

## Key Stage 2

### Ma2 Number and algebra

1. Using and applying number
Problem solving
a. make connections in mathematics and appreciate the need to use numerical skills and knowledge when solving problems in other parts of the mathematics curriculum
b. break down a more complex problem or calculation into simpler steps before attempting a solution; identify the information needed to carry out the tasks
c. select and use appropriate mathematical equipment, including ICT
d. find different ways of approaching a problem in order to overcome any difficulties
Communicating
g. use notation diagrams and symbols correctly within a given problem
Reasoning
k. search for pattern in their results; develop logical thinking and explain their reasoning.
2. Numbers and the number system
Number patterns and sequences
b. recognise and describe number patterns, including two- and three-digit multiples of 2, 5 or 10, recognising their patterns and using these to make predictions; make general statements, using words to describe a functional relationship, and test these; recognise prime numbers to 20 and square numbers up to 10 x 10; find factor pairs and all the prime factors of any two-digit integer
Integers
c. read, write and order whole numbers, recognising that the position of a digit gives its value; use correctly the symbols <, >, =; multiply and divide any integer by 10 or 100 then extend to multiplying and dividing by 1000; round integers to the nearest 10 or 100 and then 1000; order a set of negative integers, explaining methods and reasoning; multiply and divide decimals by 10 or 100
Fractions, percentages and ratio
d. understand unit fractions [for example, one-third or one-eighth] then fractions that are several parts of one whole [for example, two-thirds or five-eighths], locate them on a number line and use them to find fractions of shapes and quantities
e. understand simple equivalent fractions and simplify fractions by cancelling common factors; compare and order simple fractions by converting them to fractions with a common denominator, explaining their methods and reasoning
g. recognise approximate proportions of a whole and use simple fractions and percentages to describe them, explaining their methods and reasoning
3. Calculations
Mental methods
e. work out what they need to add to any two-digit number to make 100, then add or subtract any pair of two-digit whole numbers; handle particular cases of three-digit and four-digit additions and subtractions by using compensation or other methods [for example, 3000 - 1997, 4560 + 998]
f. recall multiplication facts to 10 x 10 and use them to derive quickly the corresponding division facts
Written methods
i. use written methods to add and subtract positive integers less than 1000, then up to 10000, then add and subtract numbers involving decimals; use approximations and other strategies to check that their answers are reasonable
4. Solving numerical problems
e. read and plot coordinates in the first quadrant, then in all four quadrants [for example, plot the vertices of a rectangle, or a graph of the multiples of 3].

### Ma3 Shape, space and measures

3. Understanding properties of position and movement
c. identify and draw 2D shapes in different orientations on grids; locate and draw shapes using coordinates in the first quadrant, then in all four quadrants [for example, use coordinates to locate position in a computer game] .

### Ma4 Handling data

1. Using and applying handling data
Problem solving
c. identify the data necessary to solve a given problem
Communicating
f. decide how best to organise and present findings
2. Processing, representing and interpreting data
b. interpret tables, lists and charts used in everyday life; construct and interpret frequency tables, including tables for grouped discrete data
c. represent and interpret discrete data using graphs and diagrams, including pictograms, bar charts and line graphs, then interpret a wider range of graphs and diagrams, using ICT where appropriate