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 and follows on from Ratio and Proportion.

Modelling Variations 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Your email address will not be published.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

Solving Inequalities using a Number Line

Students should be able to represent the solutions to an inequality on a number line, using set notation or as a list of integer values.  Here’s how I teach using the balance method for solving inequalities using a number line. Matching inequalities, Number sets and Number Lines At the start of the lesson students recap […]

Practical Tips for Using Mini-Whiteboards in a Mathematics Lesson

In this blog I will share some practical tips for using mini-whiteboards in a mathematics lesson.  I use mini-whiteboards nearly every lesson because they help the students show me the progress they are making.  When I understand what the misconceptions are I am able to address them in subsequent examples as part of my feedback.  […]

Showing Progress during a Mathematics Lesson

Demonstrating student progression during a mathematics lesson is about understanding the learning objective and breaking that down into explicit success criteria. Using Success Criteria Take, for example, a lesson on calculating the area of compound rectilinear shapes. The intended learning objective was written on the main whiteboard. Success criteria were used to break down the individual […]