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Framework for teaching mathematics

Year 5 

Numbers and the number system

Yearly teaching programmes, shown below, are taken from the relevant section of the Framework for teaching mathematics: Reception to Year 6. The numbers, in brackets, are page references to the relevant supplement of examples in the Framework which you can download by clicking on an icon in the `Downloads box on the left of this page.

Links to Unit Plans which cover specific teaching objectives are indicated by the link to Unit Plans pointer.

Place value, ordering and rounding (p.2-15)

  • Read and write whole numbers in figures and words, and know what each digit represents.
    (For decimals, see page 29.) (p.3)
    link to Unit Plans Autumn Unit 1
  • Multiply and divide any positive integer up to 10000 by 10 or 100 and understand the effect
    (e.g. 9900 ÷ 10, 737 ÷ 10, 2060 ÷ 100). (p.7)
    link to Unit Plans Autumn Unit 1
  • Use the vocabulary of comparing and ordering numbers, including symbols such as <, >, , , =. Give one or more numbers lying between two given numbers. Order a set of integers less than 1 million.
    (For decimals, see page 29.) (p.9)
    link to Unit Plans Autumn Unit 1, Spring Unit 1
  • Use the vocabulary of estimation and approximation.
    Make and justify estimates of large numbers, and estimate simple proportions such as one third, seven tenths.
    Round any integer up to 10000 to the nearest 10, 100 or 1000.
    (For rounding decimals, see page 31.) (p.11,13)
    link to Unit Plans Summer Unit 1
  • Order a given set of positive and negative integers
    (e.g. on a number line, on a temperature scale).
    link to Unit Plans Spring Unit 1
    Calculate a temperature rise or fall across 0°C. (p.15)
    link to Unit Plans Summer Unit 1

Properties of numbers and number sequences (p.16-21)

  • Recognise and extend number sequences formed by counting from any number in steps of constant size, extending beyond zero when counting back. For example:
    count on in steps of 25 to 1000, and then back;
    count on or back in steps of 0.1, 0.2, 0.3... (p.17)
    link to Unit Plans Autumn Unit 12, Spring Unit 11
  • Make general statements about odd or even numbers, including the outcome of sums and differences. (p.19)
  • Recognise multiples of 6, 7, 8, 9, up to the 10th multiple.
    Know and apply tests of divisibility by 2, 4, 5, 10 or 100. (p.19)
    link to Unit Plans Autumn Unit 12, Spring Unit 11
  • Know squares of numbers to at least 10 × 10. (p.21)
    link to Unit Plans Autumn Unit 12
  • Find all the pairs of factors of any number up to 100. (p.21)
    link to Unit Plans Autumn Unit 12

Fractions, decimals and percentages, ratio and proportion (p.22-33)

  • Use fraction notation, including mixed numbers, and the vocabulary numerator and denominator.
    Change an improper fraction to a mixed number (e.g. change 13/10 to 13/10).
    Recognise when two simple fractions are equivalent, including relating hundredths to tenths (e.g. 70/100 = 7/10). (p.23)
    link to Unit Plans Autumn Unit 4
  • Order a set of fractions such as 2, 23/4, 13/4, 21/2, 11/2, and position them on a number line. (p.23)
    link to Unit Plans Autumn Unit 4, Spring Unit 4
  • Relate fractions to division, and use division to find simple fractions, including tenths and hundredths, of numbers and quantities (e.g. 3/4 of 12, 1/10 of 50, 1/100 of £3). (p.25)

    link to Unit Plans Spring Unit 4, Summer Unit 4, Summer Unit 5
  • Solve simple problems using ideas of ratio and proportion ('one for every...' and 'one in every...'). (p.27)
    link to Unit Plans Autumn Unit 5, Summer Unit 5
  • Use decimal notation for tenths and hundredths.
    Know what each digit represents in a number with up to two decimal places.
    link to Unit Plans Autumn Unit 5
    Order a set of numbers or measurements with the same number of decimal places. (p.29)
    link to Unit Plans Spring Unit 4
  • Round a number with one or two decimal places to the nearest integer. (p.31)
    link to Unit Plans Spring Unit 4
  • Relate fractions to their decimal representations: that is, recognise the equivalence between the decimal and fraction forms of one half, one quarter, three quarters and tenths and hundredths (e.g. 7/10 = 0.7, 27/100 = 0.27). (p.31)

    link to Unit Plans Autumn Unit 5, Summer Unit 4
  • Begin to understand percentage as the number of parts in every 100, and find simple percentages of small whole-number quantities (e.g. 25% of £8).
    Express one half, one quarter, three quarters, and tenths and hundredths, as percentages (e.g. know that 3/4 = 75%). (p.33)
    link to Unit Plans Autumn Unit 5, Summer Unit 4

NOTE
Key objectives are highlighted in bold type.