Modelling Variations

Students learn how to model variations of direct and indirect proportions by setting up an equation.  They learn how to solve this equation to find k, the constant of proportionality.  As learning progresses students illustrate these linear and non-linear using graphs.

This unit takes place in Year 10 Term 6 and follows on from Ratio and Proportion.

Modelling Variations Lessons
Revision Lessons
Prerequisite Knowledge
  • Use ratio notation, including reduction to simplest form
  • Express a multiplicative relationship between two quantities as a ratio
  • Understand and use proportion as equality of ratios
  • Relate ratios to fractions
  • Express the division of a quantity into two parts as a ratio
  • Apply ratio to real contexts and problems (such as those involving conversion, comparison, scaling, mixing, concentrations)
  • Understand and use proportion as equality of ratios
Success Criteria
  • Understand that X is inversely proportional to Y is equivalent to X is proportional to 1/Y;
  • Solve problems involving direct and inverse proportion, including graphical and algebraic representations
  • Construct and interpret equations that describe direct and inverse proportion.
Key Concepts
  • The symbol ∝ is used to represent ‘is proportional to’.
  • Direct proportion and varies directly both include y ∝  x, y ∝ x2 and y ∝ x3
  • Indirect proportion and varies inversely both include y ∝ 1/x
  • k is used as the constant of proportionality
  • Students need to be able to associate the graphical representations with the various proportions.
Common Misconceptions
  • Students often struggle with writing the correct proportional formula from the written description. Writing indirect proportions is particularly difficult for most students.
  • Modelling the variation as a formula with the correct value of k is key to accessing this topic.
  • When students do write the correct formula they are often unable to correctly manipulate it to calculate unknown values.

Leave a Reply

Your email address will not be published. Required fields are marked *

You may use these HTML tags and attributes:

<a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <cite> <code> <del datetime=""> <em> <i> <q cite=""> <s> <strike> <strong>

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Mr Mathematics Blog

Literacy in Mathematics – Creating Problem Solvers

Last year my school had a OFSTED trial inspection. Whilst the maths team recieved favourable feedback the inspectors noted a need for a focus on whole school literacy. Because of this I was asked to demonstrate how we develop student’s literacy in mathematics. Literacy in Mathematics By developing student’s literacy in mathematics we aim to […]

Angles in Polygons

There are two key learning points when solving problems with angles in polygons.  The first is to understand why all the exterior angles of a polygon have a sum of 360°.  The second is to understand the interior and exterior angles appear on the same straight line. Students can be told these two facts and […]

Getting Ready for a New School Year

When getting ready for a new school year I have a list of priorities to work through. Knowing my team have all the information and resources they need to teach their students gives me confidence we will start the term in the best possible way.  Mathematics Teaching and Learning Folder All teachers receive a folder […]