Mental maths · methods
Maths skills, step by step
From adding within 10 to multiplying, dividing, fractions, percentages, shapes and data, one step at a time. Each skill has its method, worked examples and answers; then practise it in the game.
Stage 1 · Number sense
- Bonds to 10Know each pair that makes 10 on sight
- Adding within 10Count on 1, 2 or 3; past that, pairs to ten
- Subtracting within 10Ask: what adds on to get there?
- DoublesKnow every double without thinking
- Bonds to 20Look at the ones: reuse the pairs to 10
- Place value to 1000Its place tells you what a digit is worth
Stage 2 · Add & subtract strategies
- Near doublesOne apart: double, then add 1
- Making tenMake 10 first, then add what's left
- Subtracting through tenTake it down to 10, then take the rest
- Adding 9 and 8+9: add 10, take 1 back (+8: take 2)
- Adding and subtracting tensOnes stay put: just add or take the tens
- Two-digit additionLeft to right: tens first, then ones
- Making 100Fill up in steps: to the next 10, then 100
- Giving changeCount up from the price, like a shopkeeper
- Two-digit subtractionTake the tens first, then the ones
- Three-digit + and −Left to right, one place at a time
Stage 3 · Times tables
Stage 4 · Division
Stage 5 · Time & measures
- Metres and centimetresMetres × 100, then add the centimetres
- kg and g, L and mL× 1000; the small unit takes three digits
- Reading a clockLong hand × 5 = minutes; short hand = hour
- The 24-hour clocka.m. stays; p.m. hours add 12
- Time betweenCount in stretches: first to the o'clock
- Perimeter and areaPerimeter = (length + width) × 2
Stage 6 · Big numbers & speed
- Large numbers and roundingLook one place right: 5 or more rounds up
- Squares to 25Ends in 5: tens × next number, then 25
- Two-digit × 11Split the digits, put their sum between
- ×5 by halving×5 is ×10, then halve
- ×25 and ×125×25 is ×100, then halve twice
- Two-digit × one-digitSplit into tens and ones; multiply each, add
- Three-digit × one-digitHundreds, tens, ones: multiply each, add
- Long multiplicationSplit the multiplier into tens and ones
- ×9 and ×99×99 is ×100 take away one lot
- Same tens, ones make 10Tens × the next number, then ones × ones
- Multiplying near 100Front: cross-subtract. Back: gap × gap
Stage 7 · Factors & multiples
Stage 8 · Fractions & decimals
- Adding like fractionsSame bottom: add the tops, then simplify
- Improper fractions and mixed numbersTop ÷ bottom: quotient whole, remainder top
- Decimal place value0.1s, 0.01s, 0.001s: compare place by place
- Adding and subtracting decimalsMatch the places, work as whole numbers
- Adding unlike fractionsSame denominator first: use the L.C.M.
- Fractions of an amountDivide by the bottom, times the top
- Multiplying fractionsTops times tops, bottoms times bottoms
- Dividing fractionsDividing by a fraction: flip it and multiply
- Decimals ×10, ×100, ×1000Each zero moves the point one place right
- Multiplying decimalsMultiply as whole numbers, count the places
- Decimals ÷10, ÷100, ÷1000Each zero moves the point one place left
- Dividing decimalsMake the divisor whole: move both points
- Fractions and decimalsScale the bottom to 10, 100 or 1000
- Percentages, fractions and decimalsA percentage is a fraction out of 100
- Percentages in your headFind 10% first, then double or halve
Stage 9 · Mixed operations
Stage 10 · Percentages & speed
Stage 11 · Shape & space
- DirectionsN up, E right; each step round is 45°
- AnglesLine 180°, point 360°, right angle 90°
- Angles in triangles and quadrilateralsTriangle 180°, quadrilateral 360°
- Area (II)Base × height; a triangle's is half that
- SolidsCount the base's sides, then work it out
- VolumeLength × width × height: easy pair first
- Capacity and volume1 mL = 1 cm³, 1 L = 1000 mL
- CirclesCircumference = 3.14 × diameter