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Framework for teaching mathematics

Year 6 

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

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

• Consolidate all strategies from previous year, including:
  find a difference by counting up;
  add or subtract the nearest multiple of 10, 100 or 1000, then adjust;
  use the relationship between addition and subtraction;
  add several numbers. (p.41,43)
  Autumn Unit 11, Summer Unit 2
• Use known number facts and place value to consolidate mental addition/subtraction (e.g. 470 + 380, 810 - 380, 7.4 + 9.8, 9.2 - 8.6). (p.45,47)
  Spring Unit 7

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

• Use informal pencil and paper methods to support, record or explain additions and subtractions.
  Autumn Unit 11
  Extend written methods to column addition and subtraction of numbers involving decimals. (p.49,51)
  Autumn Unit 11, Spring Unit 7, Summer Unit 2, Summer Unit 7

Understanding multiplication and division (p.52-57)

• Understand and use the relationships between the four operations, and the principles (not the names) of the arithmetic laws.
  Use brackets. (p.53,55)
  Spring Unit 3
• Express a quotient as a fraction or as a decimal rounded to one decimal place. Divide £.p by a two-digit number to give £.p.
  Spring Unit 2
  Round up or down after division, depending on the context. (p.57)
  Autumn Unit 3,
  Spring Unit 2

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

• Consolidate knowing by heart:
  multiplication facts up to 10 × 10. (p.59)
• Derive quickly:
  division facts corresponding to tables up to 10 × 10;
  squares of multiples of 10 to 100 (e.g. 60 × 60);
  doubles of two-digit numbers (e.g. 3.8 × 2, 0.76 × 2);
  doubles of multiples of 10 to 1000 (e.g. 670 × 2);
  doubles of multiples of 100 to 10000 (e.g. 6500 × 2);
  and the corresponding halves. (p.59)
  Summer Unit 2, Summer Unit 6

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

• Use related facts and doubling or halving. For example:
  double or halve the most significant digit first;
  to multiply by 25, multiply by 100 then divide by 4;
  double one number and halve the other;
  find the ×24 table by doubling the ×6 table twice. (p.61)
  Autumn Unit 2
• Use factors (e.g. 35 × 18 = 35 × 6 × 3). (p.61)
  Spring Unit 3
• Use closely related facts: for example, multiply by 49 or 51 by multiplying by 50 and adjusting.
  Develop the ×17 table by adding facts from the ×10 and ×7 tables. (p.63)
  Spring Unit 3
• Partition (e.g. 87 × 6 = (80 × 6) + (7 × 6); 3.4 × 3 = (3 × 3) + (0.4 × 3)). (p.63)
• Use the relationship between multiplication and division. (p.63)
  Autumn Unit 2, Spring Unit 2
• Use known number facts and place value to consolidate mental multiplication and division. (p.65)
  Spring Unit 2

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

• Approximate first.
  Autumn Unit 2
  Use informal pencil and paper methods to support, record or explain multiplications and divisions.
  Autumn Unit 3
  Extend written methods to:
  multiplication of ThHTU × U (short multiplication);
  short multiplication of numbers involving decimals;
  long multiplication of a three-digit by a two-digit integer;
  short division of TU or HTU by U (mixed-number answer);
  division of HTU by TU (long division, whole-number answer);
  short division of numbers involving decimals. (p.67,69)
  Autumn Unit 3, Spring Unit 3, Summer Unit 9

Using a calculator (p.70-71)

• Develop calculator skills and use a calculator effectively. (p.71)
  Autumn Unit 3, Autumn Unit 6 Part 2, Spring Unit 1, Spring Unit 2, Spring Unit 4, Spring Unit 5 Part 1, Spring Unit 7, Summer Unit 2, Summer Unit 9

Checking results of calculations (p.72-73)

• Check with the inverse operation when using a calculator. (p.73)
  Autumn Unit 6 Part 2, Autumn Unit 11, Spring Unit 7
• Check the sum of several numbers by adding in reverse order. (p.73)
  Spring Unit 7
• Check with an equivalent calculation. (p.73)
  Autumn Unit 6 Part 2, Spring Unit 4
• Estimate by approximating (round to nearest 10, 100 or 1000), then check result. (p.73)
  Spring Unit 7
• Use knowledge of sums, differences, products of odd/even numbers. (p.73)
• Use tests of divisibility. (p.73)

NOTE
Key objectives are highlighted in bold type.