Mathematics key stage 1

Statutory content 

Teaching should ensure that appropriate connections are made between the sections on 'number' and 'shape, space and measures'.

Explanatory notes

During key stage 1 pupils develop their knowledge and understanding of mathematics through practical activity, exploration and discussion. They learn to count, read, write and order numbers to 100 and beyond. They develop a range of mental calculation skills and use these confidently in different settings. They learn about shape and space through practical activity which builds on their understanding of their immediate environment. They begin to grasp mathematical language, using it to talk about their methods and explain their reasoning when solving problems.

The mathematics programmes of study and the primary framework for mathematics are fully aligned. The framework provides a detailed basis for implementing the statutory requirements of the programme of study for key stage 1 in mathematics.

Building on the early learning goals

Pupils' prior experience of mathematics includes:

  • counting and using numbers to at least 10 in familiar contexts
  • recognising numerals 1 to 9
  • talking about and creating simple patterns
  • beginning to understand addition as combining two groups of objects and subtraction as 'taking away'
  • describing the shape and size of solid and flat shapes
  • using everyday words to describe position
  • using early mathematical ideas to solve practical problems.

 

Note about sections

There is no separate section of the programme of study numbered Ma1 that corresponds to the first attainment target, using and applying mathematics. Teaching requirements relating to this attainment target are included within the other sections of the programme of study.

Knowledge, skills and understanding

Using and applying number

1. Pupils should be taught to:

Problem solving

  1. approach problems involving number, and data presented in a variety of forms, in order to identify what they need to do
  2. develop flexible approaches to problem solving and look for ways to overcome difficulties
  3. make decisions about which operations and problem-solving strategies to use
  4. organise and check their work

Communicating

  1. use the correct language, symbols and vocabulary associated with number and data
  2. communicate in spoken, pictorial and written form, at first using informal language and recording, then mathematical language and symbols

Reasoning

  1. present results in an organised way
  2. understand a general statement and investigate whether particular cases match it
  3. explain their methods and reasoning when solving problems involving number and data.

Numbers and the number system

2. Pupils should be taught to:

Counting

  1. 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

  1. 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

  1. 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.

Calculations

3. Pupils should be taught to:

Number operations and the relationships between them

  1. 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 + ? ]
  2. 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

  1. 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
  2. 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
  3. carry out simple calculations of the form 40 + 30 = ?, 40 + ? = 100, 56 - ? = 10; record calculations in a number sentence, using the symbols +, -, x , รท and = correctly [for example, 7 + 2 = 9] .

Solving numerical problems

4. Pupils should be taught to:

  1. choose sensible calculation methods to solve whole-number problems (including problems involving money or measures), drawing on their understanding of the operations
  2. check that their answers are reasonable and explain their methods or reasoning.

Processing, representing and interpreting data

5. Pupils should be taught to:

  1. solve a relevant problem by using simple lists, tables and charts to sort, classify and organise information
  2. discuss what they have done and explain their results.

Explanatory notes

Note for 1e, 1f

Cross reference to English

En1 Speaking and listening: Speaking

1. To speak clearly, fluently and confidently to different people, pupils should be taught to:

b. choose words with precision

c. organise what they say

En3 Writing: Composition

1. Pupils should be taught to:

c. put their ideas into sentences

Note for 1f

ICT opportunity

Pupils could use ICT to communicate results using appropriate mathematical symbols.

Note for 1i

Explaining methods is an important foundation for reasoning and proof in later key stages.

Note for 5

This provides a basis for pupils' understanding of handling data in later key stages.

This content relates to the 1999 programmes of study and attainment targets.