National Curriculum: Ratio, proportion and rates of change - KS3 - Making Connections
Making connections to other topics within Key Stage 3
Pupils will need to be conversant with a whole range of number topics to support their learning and development within this area. In particular they will need to be secure in multiplication and division operations with fractions, percentages and decimals. They will also need to understand and use inverse operation.
Some aspects of this area will require pupils to use and interpret mathematical relationships both algebraically and graphically. Connections should be made when teaching direct and inverse proportion.
Connections between this area of study should be made when working with similar triangles and other similar shapes as the concept of proportionality is the basis of similarity.
Making connections to this topic in Year 6
In year 6 pupils will have used ratio and proportion in a range of contexts:
- Pupils recognise proportionality in contexts when the relations between quantities are in the same ratio (e.g. similar shapes, recipes).
- Pupils link percentages of 360° to calculating angles of pie charts.
- Pupils consolidate their understanding of ratio when comparing quantities, sizes and scale drawings by solving a variety of problems. They might use the notation a:b to record their work.
- Pupils solve problems involving unequal quantities e.g. ‘for every egg you need three spoonfuls of flour’, ‘35 of the class are boys’. These problems are the foundation for later formal approaches to ratio and proportion.
Cross-curricular and real life connections
- Science: science can provide the context for many basic ratio problems such as NRICH’s Oh Harry!
- Geography: statistics on populations in different parts of Canada at different periods, given as percentages and also allowing calculations of average rates of change
- Art: see proportion wheel for creating art cards of different sizes by reducing pictures in different proportions