Framework for teaching mathematics

Year 6 

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 pointer

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

• Multiply and divide decimals mentally by 10 or 100, and integers by 1000, and explain the effect.
  Autumn Unit 1, Summer Unit 1, Summer Unit 8
  (For more on place value with decimals, see page 29.) (p.7)
• Use the vocabulary of estimation and approximation.
  Consolidate rounding an integer to the nearest 10, 100 or 1000.
  Spring Unit 1
  (For rounding decimals, see page 31.) (p.11,13)
• Find the difference between a positive and a negative integer, or two negative integers, in a context such as temperature or the number line, and order a set of positive and negative integers. (p.15)
  Spring Unit 1

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

• Recognise and extend number sequences, such as the sequence of square numbers, or the sequence of triangular numbers 1, 3, 6, 10, 15
  Count on in steps of 0.1, 0.2, 0.25, 0.5, and then back. (p.17)
  Autumn Unit 12
• Make general statements about odd or even numbers, including the outcome of products. (p.19)
  Spring Unit 11
• Recognise multiples up to 10 × 10. Know and apply simple tests of divisibility. Find simple common multiples. (p.19)
  Spring Unit 11
• Recognise squares of numbers to at least 12 × 12. (p.21)
• Recognise prime numbers to at least 20.
  Spring Unit 11
  Factorise numbers to 100 into prime factors. (p.21)
  Spring Unit 11, Summer Unit 9

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

• Change a fraction such as ³³/₈ to the equivalent mixed number 4¹/₈, and vice versa.
  Spring Unit 5 Part 1
  Recognise relationships between fractions: for example, that ¹/₁₀ is ten times ¹/₁₀₀, and ¹/₁₆ is half of ¹/₈.
  
  Reduce a fraction to its simplest form by cancelling common factors in the numerator and denominator. (p.23)
  Autumn Unit 4, Summer Unit 1, Summer Unit 10
• Order fractions such as ²/₃, ³/₄ and ⁵/₆ by converting them to fractions with a common denominator, and position them on a number line. (p.23)
  Spring Unit 5 Part 1
• Use a fraction as an 'operator' to find fractions, including tenths and hundredths, of numbers or quantities
  (e.g. ⁵/₈ of 32, ⁷/₁₀ of 40, ⁹/₁₀₀ of 400 centimetres). (p.25)
  
  Spring Unit 5 Part 1, Summer Unit 1, Summer Unit 10
• Solve simple problems involving ratio and proportion. (p.27)
  Autumn Unit 5, Autumn Unit 10, Summer Unit 5, Summer Unit 8, Summer Unit 10
• Use decimal notation for tenths and hundredths in calculations, and tenths, hundredths and thousandths when recording measurements.
  Know what each digit represents in a number with up to three decimal places.
  Autumn Unit 4
  Give a decimal fraction lying between two others (e.g. between 3.4 and 3.5).
  Order a mixed set of numbers or measurements with up to three decimal places. (p.29)
  Spring Unit 1, Summer Unit 1,
• Round a number with two decimal places to the nearest tenth or to the nearest whole number. (p.31)
  Autumn Unit 5, Spring Unit 1, Summer Unit 1
• Recognise the equivalence between the decimal and fraction forms of one half, one quarter, three quarters, one eighth and tenths, hundredths and thousandths
  (e.g. ⁷⁰⁰/₁₀₀₀ = ⁷⁰/₁₀₀ = ⁷/₁₀ = 0.7).
  
  Autumn Unit 4, Autumn Unit 5
  Begin to convert a fraction to a decimal using division. (p.31)
  Spring Unit 5 Part 1
• Understand percentage as the number of parts in every 100.
  Autumn Unit 4, Summer Unit 1, Summer Unit 8
  Express simple fractions such as one half, one quarter, three quarters, one third, two thirds, and tenths and hundredths, as percentages (e.g. know that ¹/₃ = 33¹/₃%).
  
  Spring Unit 5 Part 1
  Find simple percentages of small whole-number quantities (e.g. find 10% of £500, then 20%, 40% and 80% by doubling). (p.33)
  Autumn 4, Spring Unit 5 Part 1, Summer Unit 1

NOTE
Key objectives are highlighted in bold type.