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Framework for teaching mathematics

Year 5 

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.

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

• Derive quickly or continue to derive quickly:
  decimals that total 1 (e.g. 0.2 + 0.8) or 10 (e.g. 6.2 + 3.8);
  all two-digit pairs that total 100 (e.g. 43 + 57);
  all pairs of multiples of 50 with a total of 1000 (e.g. 350 + 650).
  (p.39)

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

• Find differences by counting up through next multiple of 10, 100 or 1000, e.g. calculate mentally a difference such as 8006 - 2993. (p.41)
  Autumn Unit 11
• Partition into H, T and U, adding the most significant digits first. (p.41)
  Autumn Unit 11
• Identify near doubles, such as 1.5 + 1.6. (p.41)
  Spring Unit 9
• Add or subtract the nearest multiple of 10 or 100, then adjust. (p.41)
  Spring Unit 9
• Develop further the relationship between addition and subtraction. (p.43)
• Add several numbers (e.g. four or five single digits, or multiples of 10 such as 40 + 50 + 80). (p.43)
  Spring Unit 9
• Use known number facts and place value for mental addition and subtraction (e.g. 470 + 380, 810 - 380, 7.4 + 9.8, 9.2 - 8.6). (p.45,47)

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

• Use informal pencil and paper methods to support, record or explain additions and subtractions. Extend written methods to:
  column addition/subtraction of two integers less than 10000;
  Autumn Unit 11, Spring Unit 9
  addition of more than two integers less than 10000;
  addition or subtraction of a pair of decimal fractions, both with one or both with two decimal places (e.g. £29.78 + £53.34). (p.49,51)
  Autumn Unit 11, Spring Unit 10

Understanding multiplication and division (p.52-57)

• Understand the effect of and relationships between the four operations, and the principles (not the names) of the arithmetic laws as they apply to multiplication.
  Autumn Unit 2
  Begin to use brackets. (p.53,55)
  Spring Unit 2
• Begin to express a quotient as a fraction, or as a decimal when dividing a whole number by 2, 4, 5 or 10, or when dividing £.p.
  Round up or down after division, depending on the context. (p.57)
  Summer Unit 2

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

• Know by heart all multiplication facts up to 10 × 10. (p.59)
• Derive quickly or continue to derive quickly:
  division facts corresponding to tables up to 10 × 10;
  doubles of all whole numbers 1 to 100 (e.g. 78 × 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)

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

• Use doubling or halving, starting from known facts. For example:
  double/halve any two-digit number by doubling/halving the tens first;
  double one number and halve the other;
  to multiply by 25, multiply by 100 then divide by 4;
  find the ×16 table facts by doubling the ×8 table;
  find sixths by halving thirds. (p.61)
  Autumn Unit 2 , Spring Unit 2
• Use factors (e.g. 8 × 12 = 8 × 4 × 3). (p.61)
  Spring Unit 3
• Use closely related facts (e.g. multiply by 19 or 21 by multiplying by 20 and adjusting; develop the ×12 table from the ×10 and ×2 tables). (p.63)
  Spring Unit 3
• Partition (e.g. 47 × 6 = (40 × 6) + (7 × 6)). (p.63)
  Spring Unit 3
• Use the relationship between multiplication and division. (p.63)
  Spring Unit 3, Summer Unit 3
• Use known facts and place value to multiply and divide mentally. (p.65)
  Spring Unit 3, Summer Unit 3

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 2, Autumn Unit 3
  Extend written methods to:
  short multiplication of HTU or U.t by U;
  long multiplication of TU by TU;
  short division of HTU by U (with integer remainder). (p.67,69)
  Summer Unit 3

Using a calculator (p.70-71)

• Develop calculator skills and use a calculator effectively. (p.71)
  Autumn Unit 1, Autumn Unit 3, Autumn Unit 5, Spring Unit 1, Summer Unit 1, Summer Unit 5

Checking results of calculations (p.72-73)

• Check with the inverse operation when using a calculator. (p.73)
  Autumn Unit 3, Autumn Unit 11, Spring Unit 2
• Check the sum of several numbers by adding in the reverse order. (p.73)
• Check with an equivalent calculation. (p.73)
  Spring Unit 2
• Estimate by approximating (round to nearest 10 or 100),
  then check result. (p.73)
  Autumn Unit 3
• Use knowledge of sums and differences of odd/even numbers. (p.73)

NOTE
Key objectives are highlighted in bold type.