Decimals and fractions

Activities to try

1. 1

   Split the £3.20 bar: a quarter as division

   Why it works: Finding a fraction of an amount is a division: a quarter of £3.20 is £3.20 shared into 4 equal parts, which is 80p.

   1. Take a bar representing £3.20 and split it into four equal parts.
   2. Read what one part is worth and label it (80p / £0.80).
   3. Write the matching calculation: ¼ of £3.20 = £3.20 ÷ 4 = 80p.
   4. Check by adding or multiplying back: 80p × 4 = £3.20.
   5. State in your own words why 'a quarter of' means dividing by 4.
2. 2

   Cut the rope: align the point before subtracting

   Why it works: Decimals with different numbers of decimal places must be aligned on the decimal point before subtracting, because columns must match in place value; writing 2.5 as 2.50 is a helpful way to make the empty hundredths column visible.

   1. Start with a 2.5 m rope marked on a ruler or number line.
   2. Cut off 0.75 m and predict the remaining length before calculating.
   3. Rewrite 2.5 as 2.50 so both numbers have the same number of decimal places.
   4. Stack 2.50 above 0.75 with the decimal points lined up vertically, then subtract with borrowing.
   5. Read the remaining length (1.75 m) and check it against your prediction on the ruler.
3. 3

   One mass, two notations: 3/10 of 1 kg

   Why it works: A quantity can be written as a fraction, as grams, or as a decimal of a kilogram, and converting fluently in both directions depends on anchoring 1 kg = 1000 g.

   1. Anchor the fact 1 kg = 1000 g, e.g. on a double number line (kg on one side, g on the other).
   2. Find 3/10 of 1000 g = 300 g.
   3. Express the same mass as a decimal of a kilogram: 300 g = 0.3 kg.
   4. Convert back the other way too: 0.3 kg = 300 g.
   5. Explain why 300 g and 0.3 kg are two notations for the same amount.