This website is changing

Framework for teaching mathematics

Year 3 

Calculations

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.

Understanding addition and subtraction (p.24-29)

• Extend understanding of the operations of addition and subtraction, read and begin to write the related vocabulary, and continue to recognise that addition can be done in any order.
  Use the +, - and = signs. (p.25,29)
• Extend understanding that more than two numbers can be added; add three or four single-digit numbers mentally, or three or four two-digit numbers with the help of apparatus or pencil and paper. (p.27)
• Extend understanding that subtraction is the inverse of addition. (p.25,29)

Rapid recall of addition and subtraction facts (p.30-31)

• Know by heart:
  all addition and subtraction facts for each number to 20;
  all pairs of multiples of 100 with a total of 1000 (e.g. 300 + 700).
  Derive quickly:
  all pairs of multiples of 5 with a total of 100 (e.g. 35 + 65). (p.31)

Mental calculation strategies (+ and -) (p.32-41)

• Use knowledge that addition can be done in any order to do mental calculations more efficiently. For example:
  put the larger number first and count on;
  add three or four small numbers by putting the largest number first and/or by finding pairs totalling 9, 10 or 11;
  partition into '5 and a bit' when adding 6, 7, 8 or 9
  (e.g. 47 + 8 = 45 + 2 + 5 + 3 = 50 + 5 = 55);
  partition into tens and units, then recombine
  (e.g. 34 + 53 = 30 + 50 + 4 + 3). (p.33)
• Find a small difference by counting up from the smaller to the larger number (e.g. 102 - 97). (p.33)
• Identify near doubles, using doubles already known (e.g. 80 + 81). (p.33)
• Add and subtract mentally a 'near multiple of 10' to or from a two-digit number by adding or subtracting 10, 20, 30 and adjusting. (p.35)
• Use patterns of similar calculations. (p.35)
• Say or write a subtraction statement corresponding to a given addition statement, and vice versa. (p.35)
• Use known number facts and place value to add/subtract mentally. (p.37,39)
• Bridge through a multiple of 10, then adjust. (p.41)

Pencil and paper procedures (+ and -) (p.42-45)

• Use informal pencil and paper methods to support, record or explain HTU ± TU, HTU ± HTU.
  Begin to use column addition and subtraction for HTU ± TU where the calculation cannot easily be done mentally. (p.43,45)

Understanding multiplication and division (p.46-51)

• Understand multiplication as repeated addition.
  Read and begin to write the related vocabulary.
  Extend understanding that multiplication can be done in any order. (p.47)
• Understand division as grouping (repeated subtraction) or sharing. Read and begin to write the related vocabulary.
  Recognise that division is the inverse of multiplication, and that halving is the inverse of doubling. (p.49)
• Begin to find remainders after simple division. (p.51)
• Round up or down after division, depending on the context. (p.51)

Rapid recall of multiplication and division facts (p.52-53)

• Know by heart:
  multiplication facts for the 2, 5 and 10 times-tables.
  Begin to know the 3 and 4 times-tables. (p.53)
• Derive quickly:
  division facts corresponding to the 2, 5 and 10 times-tables;
  doubles of all whole numbers to at least 20 (e.g. 17 + 17 or 17 × 2);
  doubles of multiples of 5 to 100 (e.g. 75 × 2, 90 × 2);
  doubles of multiples of 50 to 500 (e.g. 450 × 2);
  and all the corresponding halves (e.g. 36 ÷ 2, half of 130, 900 ÷ 2). (p.53)

Mental calculation strategies (× and ÷) (p.54-57)

• To multiply by 10/100, shift the digits one/two places to the left. (p.55)
• Use doubling or halving, starting from known facts
  (e.g. 8 × 4 is double 4 × 4). (p.55)
• Say or write a division statement corresponding to a given multiplication statement. (p.55)
• Use known number facts and place value to carry out mentally simple multiplications and divisions. (p.57)

Checking results of calculations (p.58-59)

• Check subtraction with addition, halving with doubling and division with multiplication. (p.59)
• Repeat addition or multiplication in a different order. (p.59)
• Check with an equivalent calculation. (p.59)

NOTE
Key objectives are highlighted in bold type.