Foundation plus - Ratio, proportion and rates of change - GCSE Mathematics

Select a course.

arrow_back

Foundation plus - Ratio, proportion and rates of change

infoWhy this? We are teaching this unit so that pupils can use ratio and proportion to solve a wide range of practical problems, including working with rates of change and compound measures such as speed, density and pressure, and interpreting distance–time graphs

scheduleWhy now? We are teaching it now in Year 10 so that pupils can apply proportional reasoning and compound measures across their current GCSE topics and real-life contexts, strengthening their ability to model, interpret and solve multi-step problems involving change over time

A ratio compares two or more quantities, showing how many times one value contains or is contained within the other.
To share a quantity into a given ratio, the total is divided into parts proportional to the values in the ratio.
Direct proportion means that as one quantity increases, the other increases at a constant rate (y = kx).
Inverse proportion means that as one quantity increases, the other decreases so that their product is constant (xy = k).
The difference between two values in a ratio can be used to find the actual values when the total or part of the total is known.
Ratios can be combined or simplified to solve more complex problems involving multiple relationships.
Proportion can be used to scale quantities up or down, such as in recipes.
On a direct proportion graph, the relationship is linear and passes through the origin.
The rate of change in a direct proportion graph is constant and can be deduced from the gradient.
Average speed is calculated as total distance divided by total time.
Density is calculated as mass divided by volume (density = mass/volume).
Pressure is calculated as force divided by area (pressure = force/area).
Distance-time graphs represent how distance changes over time, and their gradients represent speed.

rocket_launchYou must be able to

Share a quantity into a given ratio, including finding individual parts.
Solve worded problems involving direct proportion, including setting up and solving equations.
Solve worded problems involving inverse proportion, including setting up and solving equations.
Solve problems when given the difference between two values in a ratio.
Solve problems by combining two or more different ratios to find unknown values.
Use proportion to solve recipe problems, including scaling quantities up or down.
Deduce rates of change (gradients) from direct proportion graphs.
Calculate average speeds, distances, and times using the formula speed = distance/time.
Calculate density, mass, and volume using the formula density = mass/volume.
Calculate pressure, area, and force using the formula pressure = force/area.
Draw and interpret distance-time graphs, including identifying periods of rest, constant speed, and changes in speed.

Curriculum Portal