Parents and Carers

Bigger number on top, units under units. Add each column from the right. When a column makes 10 or more, the ten is carried and written above the next digit of the top number.

Always take the bottom digit from the top one. If the top digit is too small, exchange: take 1 from the next column, cross out and rewrite the digits above.

A common mistake is taking the smaller digit from the bigger one in every column.

For take-aways like 1000 − 364, or working out change, we count on from the smaller number in friendly hops, then add the hops.

Split each number into tens and units, multiply each pair in a grid, then add everything in the grid.

Bigger number on top. Multiply each digit from the right; carries go above the top number. For a two-digit number there is one row for the units and one for the tens (with a 0 placed first), then the rows are added.

The digits move: left to multiply, right to divide (1 place for 10, 2 for 100, 3 for 1000). We avoid "just add a zero", because it doesn't work for decimals: 6.4 × 1000 = 6400, not 6.4000.

Split the number up: × 400 is × 4 then × 100, and ÷ 80 is ÷ 8 then ÷ 10.

To multiply or divide by a bigger number, we split it into factors: × 24 is × 8 then × 3, and ÷ 24 is ÷ 8 then ÷ 3. Doubling twice is × 4; halving twice is ÷ 4.

Divide each digit from the left, carrying the remainder to the next digit. If it doesn't divide exactly, we put a decimal point, add zeros and keep dividing, then round if it doesn't stop. A remainder is only used when the question needs one (such as how many minibuses).

Ignore the points and multiply the whole numbers (with a chimney sum if needed), then count the decimal places in the question and put that many back.

Multiply both numbers by 10, 100 or 1000 so you are dividing by a whole number. The answer stays the same. Then use a bus stop.

Pupils first add and subtract negative numbers with yellow (+1) and red (−1) tiles. A yellow and a red tile make a zero pair, which can be removed.

Split the number into any factor pair and keep splitting until every branch ends in a prime. Then write the primes as a product, using powers.

We find the highest common factor by listing factors, not with Venn diagrams.

Brackets, Orders (powers), Divide and Multiply (left to right), Add and Subtract (left to right).

Divide by the bottom number, then multiply by the top number. A bar model shows why.

Build the percentage from blocks you know: 10% (÷ 10), 5% (half of 10%), 1% (÷ 100), 25% (÷ 4) and 50% (half).

Write the percentage as a fraction out of 100 and multiply: 17% of £240 is 17 ÷ 100 × 240.

One table for each option, working down to a unit value (the cost of 1 gram, or 1 pound in euros). An arrow shows the × or ÷ step. Then a sentence that quotes the numbers.

Cover the one you want to find with a finger to see the formula. Write the formula, put the numbers in, then work it out with units.

Count on to the next o'clock, then whole hours, then the minutes left, and add the pieces.

In S2, pupils use π = 3.14 so they can work without the π button. In S3, they use the π button on the calculator, as in National 5.

Tiles show that only matching terms can be collected: x-tiles with x-tiles, and number tiles with number tiles.

An equation is like a balance. Do the same to both sides to keep it level, writing what you did beside each line.

When comparing, pupils say what the numbers show and quote them: "Class A did better on average, because 68 > 62." For spread, we say more varied or less varied.

S3 worked examples show where marks would be given in a National 5 style question. A mark is usually given for substituting into a formula, not for just writing the formula down.