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Foundation - 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 context-based problems, including working with fractions, percentages and compound measures such as speed, density and pressure

scheduleWhy now? We are teaching it now in Year 10 so that pupils secure these essential proportional reasoning skills in time to support later GCSE topics and real-life application questions that appear across the rest of the course

neurologyYou need to know

  • A ratio can be expressed as a fraction (e.g., 3:4 as ¾) or as a percentage (e.g., 3:4 as 75% to 100%).
  • The sum of the parts in a ratio represents the total number of equal shares.
  • To share a quantity in a given ratio, the total is divided into parts according to the ratio.
  • In direct proportion, as one quantity increases, the other increases at a constant rate.
  • In inverse proportion, as one quantity increases, the other decreases so that their product remains constant.
  • Fractions can represent parts of a whole and can be used to solve ratio problems.
  • The difference between two values in a ratio can be used to determine the actual values when the ratio is known.
  • Two or more ratios can be combined by finding equivalent ratios with a common term.
  • Recipes use proportion to scale quantities up or down.
  • On a direct proportion graph, the rate of change is constant and represented by the gradient.
  • Average speed is calculated as total distance divided by total time.
  • Density is calculated as mass divided by volume.
  • Pressure is calculated as force divided by area.

rocket_launchYou must be able to

  • Write a ratio as a fraction or a percentage.
  • Share a given quantity into a specified ratio.
  • Use a known quantity and a ratio to find a missing quantity.
  • Identify and use fractions within ratio problems.
  • 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 where the difference between two values in a ratio is given, to find the actual values.
  • Combine two or more different ratios to solve problems, including finding a common term.
  • Use proportion to solve recipe problems, including scaling quantities up or down.
  • Deduce rates of change from direct proportion graphs, including calculating and interpreting gradients.
  • Calculate average speed, distance, or time given two of the three values.
  • Calculate density, mass, or volume given two of the three values.
  • Calculate pressure, area, or force given two of the three values.


Revision Quiz

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