Rates, unit prices and density
Use a ratio table to find the amount "for each one": the price per kilogram, the litres per pound, and the mass of each cubic centimetre.
- UK: Year 8
- France: grade 8
- Germany: grade 3
- Syria: grade 7
- Ukraine: grade 3
- Russia: grade 4
Guide
This studio follows the Key Stage 3 aim to "use compound units such as speed, unit pricing and density to solve problems". (Speed has its own studio with distance–time graphs.) The tool is the ratio table from the proportion studio: some cells come from the problem and your child fills the others.
A rate is how much of one thing there is for each one unit of another: pence per kilogram, litres per pound, grams per cubic centimetre (g/cm³). Every rate can be written both ways round, and its units tell you which way round it is.
Common slips: thinking the cheapest pack is the best buy; switching the rate round halfway through (litres per pound used as pounds per litre); working out density as volume ÷ mass; and dropping units, for example reading 2.5 g/cm³ as 2.5 kg/m³.