Ratio and Proportion

August 23, 2016

Students learn how to simplify and use equivalent ratios to calculate proportionate amounts.  They use this knowledge to model direct and indirect variation problems.

This unit takes place in Term 1 of Year 10 and leads on to indices and standard form.

Ratio and Proportion Lessons
Number: Interactive Lessons
3 Part Ratios
4 Part Lesson
3 Part Ratios
Students learn how to solve problems involving 3-part ratios.
Number: Interactive Lessons
Proportion and Recipes
4 Part Lesson
Proportion and Recipes
Students learn how to use proportion and ratio notation to adjust recipes for different amounts.
Number: Interactive Lessons
Simplifying Ratios
4 Part Lesson
Simplifying Ratios
Students learn how to simplify ratios using the highest common factor.
Number: Interactive Lessons
Sharing to a Ratio
4 Part Lesson
Sharing to a Ratio
Students learn how to share an amount according to a ratio.
Number: Interactive Lessons
Proportional Reasoning
4 Part Lesson
Proportional Reasoning
Students learn how to work with proportional amounts using ratio notation.
Number: Interactive Lessons
Modelling Inverse Proportion
4 Part Lesson
Modelling Inverse Proportion
Students learn how to model inverse proportion problems using the constant of variation
Number: Interactive Lessons
Direct Linear Proportion
4 Part Lesson
Direct Linear Proportion
Students learn how to model variables in direct proportion using the constant of proportionality.
Additional Resources
Number: Interactive Lessons
Proportional Reasoning
Extended Learning
Proportional Reasoning
Additional practice modelling proportional amounts using ratio notation.
Number: Interactive Lessons
Simplifying Ratios
Extended Learning
Simplifying Ratios
Students gain additional practice writing ratios in their simplest form.
Number: Interactive Lessons
Problem Solving with Ratio
Problem Solving
Ratio
Problem Solving with Ratio. There are five problems that link to money, fractions and probability.
Number: Interactive Lessons
Revising Direct Proportion
Revision
Direct Proportion
Revision lesson on direct proportion for exam students.
Number: Interactive Lessons
Revising Best Value
Revision
Best Value Ratio Problems
Revision lesson on best value for exam students.
Number: Interactive Lessons
Revising Calculating Exchange Rates
Revision
Calculating Exchange Rates
Revision lesson on exchange rates for exam students.
Number: Interactive Lessons
Revising Sharing to a Ratio
Revision
Sharing to a Ratio
Revision lesson on sharing to a ratio for exam students.
Number: Free Resources
Revising Equivalent Ratios
Revision
Equivalent Ratios
Revision lesson on equivalent ratios for exam students.
Prerequisite Knowledge
  • solve problems involving the relative sizes of two quantities where missing values can be found by using integer multiplication and division facts
  • solve problems involving the calculation of percentages
  • solve problems involving unequal sharing and grouping using knowledge of fractions and multiples
Success Criteria
  • 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
  • solve problems involving direct and inverse proportion, including graphical and algebraic representations
  • understand that X is inversely proportional to Y is equivalent to X is proportional to 1/Y
  • construct and interpret equations that describe direct and inverse proportion
Key Concepts
  • It is important for students to visualise equivalent and ratios by categorising objects and breaking them down into smaller groups.
  • It is important to apply equivalent ratios when solving problems involving proportion. Including the use of the unitary method.
  • To share amount given a ratio it is necessary to find the value of a single share.
  • When two or more measurements increase at a linear rate they are in direct proportion. Inverse proportion is when one increases at the same rate the other decreases.
  • The constant of proportionality, k, is used to define the rate at which two or more measures change.
  • Recognising the graphical representations of direct and indirect proportion is vital to understanding the relationship between two measurements.
Common Misconceptions
  • Ratios amounts are often confused with fractions involving the same digits. For instance 2 : 3 is confused with 2⁄3 or 1 : 2 = 1⁄2.
  • When solving problems involving proportion students tend to struggle with forming a ratio. For instance, 3 apples cost 45p would form the ratio apples : cost.
  • When writing ratios into the form 1 : n students incorrectly assume that n has to be an integer or greater than 1.

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