ACADEMIC
Calculation
Policy
Calculation Policy
In Lower Key Stage 2, children build on the concrete and conceptual understandings they have gained in Key Stage 1 to develop a real mathematical understanding of the four operations, in particular developing arithmetical competence in relation to larger numbers.
Addition and Subtraction:
Children are taught to use place value and number facts to add and subtract numbers mentally and they will develop a range of strategies to enable them to discard the ‘counting in 1s’ or fingers-based methods of Key Stage 1. In particular, children will learn to add and subtract multiples and near multiples of 10, 100 and 1000, and will become fluent in complementary addition as an accurate means of achieving fast and accurate answers to 3-digit subtractions. Standard written methods for adding larger numbers are taught, learned and consolidated, and written column subtraction is also introduced.
Multiplication and Division:
This key stage is also the period during which all the multiplication and division facts are thoroughly memorised, including all facts up to 12 × 12. Efficient written methods for multiplying or dividing a 2-digit or 3-digit number by a 1-digit number are taught, as are mental strategies for multiplication or division with large but ‘friendly’ numbers, e.g. when dividing by 5 or multiplying by 20.
Fractions:
Children will develop their understanding of fractions, learning to reduce a fraction to its simplest form, as well as finding non-unit fractions of amounts and quantities. The concept of a decimal number is introduced and children consolidate a firm understanding of 1-place decimals, multiplying and dividing whole numbers by 10 and 100.
Mental calculation:
- Know pairs with each total to 20; e.g. 2 + 6 = 8, 12 + 6 = 18, 7 + 8 = 15
- Know pairs of multiples of 10 with a total of 100
- Add any two 2-digit numbers by counting on in 10s and 1s or by using partitioning
- Add multiples and near multiples of 10 and 100
- Perform place-value additions without a struggle; e.g. 300 + 8 + 50 = 358
- Use place value and number facts to add a 1-digit or 2-digit number to a 3-digit number ; e.g. 104 + 56 is 160 since 104 + 50 = 154 and 6 + 4 = 10; 676 + 8 is 684 since 8 = 4 + 4 and ; 76 + 4 + 4 = 84
- Add pairs of ‘friendly’ 3-digit numbers; e.g. 320 + 450
- Begin to add amounts of money using partitioning
Written calculation
- Use expanded column addition to add two or three 3-digit numbers or three 2-digit numbers
- Begin to use compact column addition to add numbers with 3 digits
- Begin to add like fractions; e.g. 3⁄8 + 1⁄8 + 1⁄8
- Recognise fractions that add to 1; e.g. 1⁄4 + 3⁄4 e.g. 3⁄5 + 2⁄5
All:
- Know pairs of numbers which make each total up to 10, and which total 20
- Add two 2-digit numbers by counting on in 10s and 1s; e.g. 56 + 35 is 56 + 30 and then add the 5
- Understand simple place-value additions; e.g. 200 + 40 + 5 = 245
- Use place value to add multiples of 10 or 100
Mental calculation:
- Add any two 2-digit numbers by partitioning or counting on
- Know by heart/quickly derive number bonds to 100 and to £1
- Add to the next 100, £1 and whole number; e.g. 234 + 66 = 300; e.g. 3·4 + 0·6 = 4
- Perform place-value additions without a struggle; e.g. 300 + 8 + 50 + 4000 = 4358
- Add multiples and near multiples of 10, 100 and 1000
- Add £1, 10p, 1p to amounts of money
- Use place value and number facts to add 1-, 2-, 3- and 4-digit numbers where a mental calculation is appropriate; e.g. 4004 + 156 by knowing that 6 + 4 = 10 and that 4004 + 150 = 4154 so the total is 4160
Written calculation
- Column addition for 3-digit and 4-digit numbers
- Add like fractions; e.g. 3⁄5 + 2⁄5 = 7⁄5 = 1 2⁄5
- Be confident with fractions that add to 1 and fraction complements to 1; e.g. 2⁄3 + _ = 1
All:
- Add any 2-digit numbers by partitioning or counting on
- Number bonds to 20
- Know pairs of multiples of 10 with a total of 100
- Add ‘friendly’ larger numbers using knowledge of place value and number facts
- Use expanded column addition to add 3-digit numbers
Mental calculation:
- Know number bonds to 1 and to the next whole number
- Add to the next 10 from a decimal number; e.g. 13.6 + 6.4 = 20
- Add numbers with 2 significant digits only, using mental strategies; e.g. 3.4 + 4.8; e.g. 23 000 + 47 000
- Add 1- or 2-digit multiples of 10, 100, 1000, 10 000 and 100 000; e.g. 8000 + 7000; e.g. 600 000 + 700 000
- Add near multiples of 10, 100, 1000, 10 000 and 100 000 to other numbers; e.g. 82 472 + 30 004
- Add decimal numbers which are near multiples of 1 or 10, including money; e.g. 6.34 + 1.99; e.g. £34.59 + £19.95
- Use place value and number facts to add two or more ‘friendly’ numbers, including money and decimals; e.g. 3 + 8 + 6 + 4 + 7; e.g. 0.6 + 0.7 + 0.4; e.g. 2056 + 44
Written calculation
- Use column addition to add two or three whole numbers with up to 5 digits
- Use column addition to add any pair of 2-place decimal numbers, including amounts of money
- Begin to add related fractions using equivalences; e.g. 1⁄2 + 1⁄6 = 3⁄6 + 1⁄6
- Choose the most efficient method in any given situation
All:
- Add numbers with only 2 digits which are not zeros; e.g. 3.4 + 5.8
- Derive swiftly and without any difficulty number bonds to 100
- Add ‘friendly’ large numbers using knowledge of place value and number facts
- Use expanded column addition to add pairs of 4- and 5-digit numbers
Mental calculation:
- Know by heart number bonds to 100 and use these to derive related facts e.g. 3.46 + 0.54
- Derive, quickly and without difficulty, number bonds to 1000
- Add small and large whole numbers where the use of place value or number facts makes the calculation do-able mentally; e.g. 34 000 + 8000
- Add multiples of powers of 10 and near multiples of the same ; e.g. 6345 + 199
- Add negative numbers in a context such as temperature where the numbers make sense
- Add two 1-place decimal numbers or two
- 2-place decimal numbers less than 1; e.g. 4.5 + 6.3; e.g. 0.74 + 0.33
- Add positive numbers to negative numbers; e.g. Calculate a rise in temperature or continue a sequence beginning with a negative number
Written calculation
- Use column addition to add numbers with up to 5 digits
- Use column addition to add decimal numbers with up to 3 decimal places
- Add mixed numbers and fractions with different denominators
All:
- Derive, swiftly and without difficulty, number bonds to 100
- Use place value and number facts to add ‘friendly’ large or decimal numbers; e.g. 3.4 + 6.6 ; e.g. 26 000 + 54 000
- Use column addition to add numbers with up to 4-digits
- Use column addition to add pairs of 2-place decimal numbers
