Calculations

34-37 Understanding addition and subtraction

Consolidate understanding of relationship between + and -.Understand the principles (not the names) of the commutative and associative laws as they apply or not to addition and subtraction. (p.34,36)

38-39 Rapid recall of addition and subtraction facts

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)

Missing number problems PrimaryResources 'Missing Numbers' Addition pyramid, possible extension of rearranging numbers to create largest total PrimaryResources 'Bricks' Number bonds - to 5, 10, 100 or set your own Ambleside 'NumberBond Machine'

40-47 Mental calculation strategies (+ and -)

Find a small difference by counting up (e.g. 5003 - 4996). (p.40)
Count on or back in repeated steps of 1, 10 or 100. (p.40)
Partition into tens and units, adding the tens first. (p.40)
Identify near doubles, using known doubles (e.g. 150 + 160). (p.40)
Add or subtract the nearest multiple of 10, then adjust. (p.40)
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.Add three two-digit multiples of 10, such as 40 + 70 + 50. (p.42)	Addition activity. Use levels easy and medium. (Can be used for problem solving activities by rearranging base numbers to make largest total)	Ambleside 'Callum Addition Pyramid'
Use known number facts and place value to add or subtract mentally, including any pair of two-digit whole numbers. (p.44,46)	Addition pyramid, possible extension of rearranging numbers to create largest total	Primary Resources 'Bricks 2'

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

Use informal pencil and paper methods to support, record or explain additions/subtractions. 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)

52-57 Understanding multiplication and division

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

58-59 Rapid recall of multiplication and division facts

Know by heart:multiplication facts for 2, 3, 4, 5 and 10 times-tables. (p.58)	Positioning numbers on an empty 100 square Useful for highlighting numbers Primary Games ‘Billy Bug' Use as a physical counting stick. Very easy to cover / uncover numbers / multiples Primary Resources 'Counting Stick' Practice at identifying multiplication facts in rather fun way. Children individually or on whiteboard during mental and oral starter Primary Resources Moon Maths Activity allowing practice of recognition of chosen multiples. Short starter or short individual practice. Grid Club 'Alien Tables'
Begin to know:multiplication facts for 6, 7, 8 and 9 times-tables. (p.58)	Positioning numbers on an empty 100 squareUseful for highlighting numbers Primary Games ‘Billy Bug' Use as a physical counting stick. Very easy to cover / uncover numbers / multiples Primary Resources 'Counting Stick' Practice at identifying multiplication facts in rather fun way. Children individually or on whiteboard during mental and oral starter Primary Resources Moon Maths Activity allowing practice of recognition of chosen multiples. Short starter or short individual practice. Grid Club 'Alien Tables'
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. (p.58)	Interactive number square. Highlight numbers, change start number, change number of columns, show multiples and primes. VERY versatile. Change column width to discuss different arrays	Standards/numeracy 'NumberGrid'

60-65 Mental calulation strategies (mult and div)

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)
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)
Partition (e.g. 23 × 4 = (20 × 4) + (3 × 4)). (p.62)
Use the relationship between multiplication and division. (p.62)
Use known number facts and place value to multiply and divide integers, including by 10 and then 100 (whole-number answers). (p.64)

66-69 Pencil and paper procedures (mult and div)

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

72-73 Checking results of calculations

Check with the inverse operation. (p.72)
Check the sum of several numbers by adding in reverse order. (p.72)
Check with an equivalent calculation. (p.72)
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)

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