Framework for teaching mathematics

Year 4 

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.

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

Understanding addition and subtraction (p.34-37)

• Consolidate understanding of relationship between + and -.
  Autumn Unit 2, Autumn Unit 12, Summer Unit 12
  Understand the principles (not the names) of the commutative and associative laws as they apply or not to addition and subtraction. (p.34,36)
  Autumn Unit 2, Spring Unit 2, Summer Unit 2, Summer Unit 8
  

Rapid recall of addition and subtraction facts (p.38-39)

• Consolidate knowing by heart:
  addition and subtraction facts for all numbers to 20.
  Derive quickly:
  all number pairs that total 100 (e.g. 62 + 38, 75 + 25, 40 + 60);
  all pairs of multiples of 50 with a total of 1000 (e.g. 850 + 150). (p.38)

Mental calculation strategies (+ and -) (p.40-47)

• Find a small difference by counting up (e.g. 5003 - 4996). (p.40)
  Autumn Unit 12
  
• Count on or back in repeated steps of 1, 10 or 100. (p.40)
  Autumn Unit 2
  
• Partition into tens and units, adding the tens first. (p.40)
  Spring Unit 2
  
• Identify near doubles, using known doubles (e.g. 150 + 160). (p.40)
  Autumn Unit 2
  
• Add or subtract the nearest multiple of 10, then adjust. (p.40)
  Spring Unit 2, Summer Unit 2
  
• Continue to use the relationship between addition and subtraction. (p.42)
• Add 3 or 4 small numbers, finding pairs totalling 10, or 9 or 11.
  Autumn Unit 3, Spring Unit 2
  Add three two-digit multiples of 10, such as 40 + 70 + 50. (p.42)
  Spring Unit 2
  
• Use known number facts and place value to add or subtract mentally, including any pair of two-digit whole numbers. (p.44,46)
  Spring Unit 2, Summer Unit 2, Summer Unit 8, Summer Unit 10, Summer Unit 12
  

Pencil and paper procedures (+ and -) (p.48-51)

• Use informal pencil and paper methods to support, record or explain additions/subtractions.
  Autumn Unit 2, Spring Unit 3, Spring 10
  Develop and refine written methods for:
  column addition and subtraction of two whole numbers less than 1000, and addition of more than two such numbers;
  money calculations (for example, £7.85 ± £3.49). (p.48,50)
  Autumn Unit 3, Autumn Unit 12, Spring Unit 3 Summer Unit 2, Summer Unit 3, Summer Unit 12
  

Understanding multiplication and division (p.52-57)

• Extend understanding of the operations of × and ÷, and their relationship to each other and to + and -.
  Autumn Unit 9, Spring Unit 9
  Understand the principles (not the names) of the commutative, associative and distributive laws as they apply to multiplication. (p.52,54)
  Spring Unit 9
  
• Find remainders after division.
  Divide a whole number of pounds by 2, 4, 5 or 10 to give £.p.
  Spring Unit 9
  Round up or down after division, depending on the context. (p.56)
  Summer Unit 9
  

Rapid recall of multiplication and division facts (p.58-59)

• Know by heart:
  multiplication facts for 2, 3, 4, 5 and 10 times-tables. (p.58)
  Spring Unit 9
  
• Begin to know:
  multiplication facts for 6, 7, 8 and 9 times-tables. (p.58)
  Summer Unit 10
  
• Derive quickly:
  division facts corresponding to 2, 3, 4, 5 and 10 times-tables;
  doubles of all whole numbers to 50 (e.g. 38 + 38, or 38 × 2);
  doubles of multiples of 10 to 500 (e.g. 460 × 2);
  doubles of multiples of 100 to 5000 (e.g. 3400 × 2);
  and the corresponding halves (e.g. 74 ÷ 2, ¹/₂ of 420, half of 3800). (p.58)
  Spring Unit 9, Summer Unit 9, Summer Unit 10
  

Mental calculation strategies (× and ÷) (p.60-65)

• Use doubling or halving, starting from known facts. For example:
  double/halve two-digit numbers by doubling/halving the tens first;
  to multiply by 4, double, then double again;
  to multiply by 5, multiply by 10 then halve;
  to multiply by 20, multiply by 10 then double;
  find the 8 times-table facts by doubling the 4 times-table;
  find quarters by halving halves. (p.60)
  Autumn Unit 9, Summer Unit 9
  
• Use closely related facts (e.g. to multiply by 9 or 11, multiply by 10 and adjust; develop the ×6 table from the ×4 and ×2 tables). (p.62)
  Spring Unit 9
  
• Partition (e.g. 23 × 4 = (20 × 4) + (3 × 4)). (p.62)
• Use the relationship between multiplication and division. (p.62)
  Summer Unit 9
  
• Use known number facts and place value to multiply and divide integers, including by 10 and then 100 (whole-number answers). (p.64)

Pencil and paper procedures (× and ÷) (p.66-69)

• Approximate first. Use informal pencil and paper methods to support, record or explain multiplications and divisions.
  Autumn Unit 9
  Develop and refine written methods for TU × U, TU ÷ U. (p.66,68)
  Autumn Unit 9, Summer Unit 10

Checking results of calculations (p.72-73)

• Check with the inverse operation. (p.72)
  Spring Unit 10
  
• Check the sum of several numbers by adding in reverse order. (p.72)
• Check with an equivalent calculation. (p.72)
  Autumn Unit 10, Spring Unit 5
  
• Estimate and check by approximating (round to nearest 10 or 100). (p.72)
• Use knowledge of sums or differences of odd/even numbers. (p.72)
  Summer Unit 3
  

NOTE
Key objectives are highlighted in bold type.