Everyday maths

These are the topics that come up between about years five and seven: place value, rounding, long division, prime factors, Roman numerals, the unitary method, and simple interest. What they have in common is that the method is the point. Nobody is marked on knowing that 9,452 divided by 7 is 1,350 remainder 2; they are marked on the working that gets there.

• Divisibility Which numbers divide in exactly, and the rule that tells you without dividing.
• Long division The quotient, the remainder, and every step of the working in between.
• Number in words Any number written out, in both the international and Indian systems.
• Place value What each digit of a number is worth, and where it sits.
• Prime factors Break a number into the primes it is made of, in index form as well.
• Profit & loss Profit or loss from cost and selling price, as an amount and as a percentage.
• Roman numerals Numbers to Roman numerals and back, with the pieces it was built from.
• Rounding Round to any place, and see which digit decided it.
• Simple interest Interest on the original sum only, with compound shown beside it for comparison.
• Times table The full table for any number, as far up as you need it.
• Unitary method Find what one costs, then find what any number costs.

The sums you already know how to do and would rather not do twice to check. Each one shows its working.

• Average Paste a list of numbers and get every kind of average at once.
• Decimal to fraction Any terminating decimal as a fraction in lowest terms.
• Exponents Any number to any power, with its squares, cubes and roots.
• Fractions Add, subtract, multiply or divide two fractions, simplified.
• GCF & LCM The greatest common factor and lowest common multiple of two numbers.
• Percentage What is X% of Y, X is what percent of Y, and the change between two numbers.
• Ratio Simplify a ratio, or scale one up to find the missing value.

Areas and volumes for every common shape, each with the formula written out beside the answer.

• Area Area of a rectangle, circle or triangle, in several units, with the formula.
• Circle Radius, diameter, circumference and area — give any one, get the rest.
• Perimeter The distance round a rectangle, square, circle or triangle.
• Pythagoras Find the missing side of a right-angled triangle.
• Slope Slope, distance and midpoint between two points.
• Triangle Area and all three angles from three sides — no height needed.
• Volume Volume and surface area of a cube, box, cylinder, sphere, cone or pyramid.

Metric to imperial and back, using exact conversion factors rather than the rounded ones people memorise.

• Angles Degrees, radians, gradians and turns.
• Length Millimetres, centimetres, metres, inches, feet and yards.
• Speed mph, km/h, metres per second, knots and feet per second.
• Temperature Celsius, Fahrenheit and Kelvin — the one conversion that is not a factor.
• Time units Seconds, minutes, hours, days, weeks and years.
• Unit converter Length, weight, area and volume, converted with exact factors.
• Weight Kilograms, grams, pounds, tonnes and both kinds of ton.

Date arithmetic that accounts for leap years and month lengths, which is exactly why it is worth not doing in your head.

• Age Exact age in years, months and days, and when the next birthday falls.
• Countdown How long until a date, in days, weeks, months and working days.
• Add to a date What date falls a given number of days, weeks or months away.
• Days between dates Days, weeks, months and working days between any two dates.
• Time duration Add up hours and minutes without a calculator getting it wrong.
• Working days Business days between two dates, weekends excluded.