Modelling Direct Proportion

Modelling Direct Proportion Learning Objectives:

By the end of the lesson:

  • All students should be able to use the constant of proportionality to describe how two measurements are in direct proportion.
  • Most students should be able to model two units that are in direct proportion using the constant of proportionality.
  • Some students should be able identify whether two units are in direct proportion using the constant of proportionality.


The starter is used to introduce the term direct proportion and the symbol α.  I ask the class to work in pairs to match together measurements that increase or decrease at the same rate.  This takes about five minutes before I ask students to present their work on mini whiteboards.

When feeding back to the class the matched pairs are shown using the proportionality symbol, for instance, Test Score ∝ Time spent revising.

Modelling Direct Proportion

I explain in this lesson we are going to derive a formula to model two measure two measurements that are in direct proportion.  The model will involve a value we call the Constant of Proportionality (k).  The value of k describes the rate at which two measurements increase or decrease together.  We will use this model to calculate one value when the other measurement is known.

As you can see in the video below, I work through the first two questions with the class and ask them to attempt the third question on mini-whiteboards so I can assess their understanding.

I use the interactive Excel file to demonstrate additional examples if they are needed. You can download this question and answer generator here.

When the class are ready, I ask them to work independently through the questions on the third slide and then the worksheet.


Modelling Direct Proportion

The plenary challenges students to apply what they have learned to a real-life situation.  After a few minutes if students are struggling to make progress, I help them to set up the formula. This way they can still attempt parts b and c. The extension is to rearrange the formula to calculate the weight when given the extension.

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About Mr Mathematics

My name is Jonathan Robinson and I passionate about teaching mathematics. I am currently Head of Maths in the South East of England and have been teaching for over 15 years. I am proud to have helped teachers all over the world to continue to engage and inspire their students with my lessons.

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