Ratio, Proportion and Rates of Change

Students learn how to use ratio notation to solve problems ranging from interpreting the scale of a map to calculating a speed, distance or time.

This unit takes place in Term 3 of Year 8 and follows on from multiplying and dividing with fractions.


Ratio, Proportion and Rates of Change Lessons
4 Part Lesson
Best Buys
4 Part Lesson
Inverse Proportion
4 Part Lesson
Direct Proportion and Exchange Rates
4 Part Lesson
Sharing in a Given Ratio
4 Part Lesson
Writing Ratios in their Simplest Form
4 Part Lesson
Scale Drawings
4 Part Lesson
Ratio and Equivalent Proportions
4 Part Lesson
Calculating Speed, Distance and Time
Additional Resources
Extended Learning
Speed, Distance and Time
Extended Learning
Proportional Reasoning
Extended Learning
Simplifying Ratios
Problem Solving
Ratio
Revision
Direct Proportion
Revision
Best Value Ratio Problems
Revision
Calculating Exchange Rates
Revision
Sharing to a Ratio
Revision
Equivalent Ratios
Prerequisite Knowledge
  • Work interchangeably with terminating decimals and their corresponding fractions.
  • Define percentage as ‘number of parts per hundred’, interpret percentages and percentage changes as a fraction or a decimal
  • Interpret fractions and percentages as operators
Key Concepts
  • If the ratio between two things is the same they are in direct proportion.
  • To divide an amount in a given ratio find the value of one share by finding the total number of shares, then divide the amount by the total number of shares.
  • To compare values work out the cost per unit or number of units per pound or penny.  This takes the form of 1 : n.
  • A common misconception is to write the ratio of 2 : 3 as 2/3.  Emphasise the need to consider the total number of shares when writing a ratio as an equivalent fraction or percentage.
Working mathematically

Develop fluency

  • Consolidate their numerical and mathematical capability from key stage 2 and extend
    their understanding of the number system
  • Select and use appropriate calculation strategies to solve increasingly complex problems

Reason mathematically

  • Extend their understanding of the number system; make connections between number
    relationships, and their algebraic and graphical representations
  • Extend and formalise their knowledge of ratio and proportion in working with measures
    and geometry, and in formulating proportional relations algebraically

Solve problems

  • Develop their mathematical knowledge, in part through solving problems and evaluating
    the outcomes, including multi-step problems
  • Select appropriate concepts, methods and techniques to apply to unfamiliar and non-routine problems.
Subject Content

Ratio, proportion and rates of change

  • Change freely between related standard units [for example time, length, area, volume/capacity, mass]
  • Use scale factors, scale diagrams and maps
  • Express one quantity as a fraction of another, where the fraction is less than 1 and greater than 1
  • Use ratio notation, including reduction to simplest form
  • Divide a given quantity into two parts in a given part:part or part:whole ratio; express the division of a quantity into two parts as a ratio
  • Understand that a multiplicative relationship between two quantities can be expressed as a ratio or a fraction
  • Relate the language of ratios and the associated calculations to the arithmetic of fractions
  • Solve problems involving direct and inverse proportion, including graphical and algebraic representations
  • Use compound units such as speed, unit pricing and density to solve problems.

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