Mathematics
Number and place value
Work confidently to 1,000,000: name place values (units, tens, hundreds, thousands, ten-thousands, hundred-thousands), write numbers in words and expanded form, compare with < and >, and round to the nearest 10, 100 or 1000. Multiplication tables to 10 and the standard written methods for multiplication and division (including two-digit divisors) are assumed knowledge.
Fractions, decimals and percentages
- Equivalent fractions: multiply or divide numerator and denominator by the same number.
- Add or subtract only after equalising denominators: 2/3 + 1/4 = 8/12 + 3/12 = 11/12. Never add denominators.
- A decimal is a fraction over 10, 100 or 1000; money is written to two decimal places.
- Percent means "out of 100": 25% of 80 = 80 ÷ 4 = 20.
Measurement
- Length: 10 mm = 1 cm, 100 cm = 1 m, 1000 m = 1 km.
- Mass: 1000 mg = 1 g, 1000 g = 1 kg. Capacity: 1000 ml = 1 l.
- Time: 60 seconds = 1 minute, 60 minutes = 1 hour. In 24-hour time add 12 to afternoon hours (3.30 p.m. = 15:30).
- Perimeter is the distance around a shape; area of a rectangle = length × breadth, given in square units.
Worked example
A 12-litre tank is filled with a 750 ml bottle. How many bottles are needed?
Reasoning: the units differ, so convert first - 12 l = 12,000 ml. Then divide: 12,000 ÷ 750 = 16. Answer: 16 bottles. Checking backwards, 16 × 750 = 12,000 ml = 12 l, which matches.
Traps that cost marks
- Subtracting or dividing with mixed units (litres with millilitres, kilograms with grams) before converting.
- Writing area in cm instead of cm².
- Borrowing 10 instead of 60 in time subtraction (10:15 − 9:40 = 35 minutes).
- Confusing "how many more" with "how many times".
- Stopping after the first step of a two-step word problem.