Ratio and Proportion

Scheme of work: GCSE Foundation: Year 10: Term 1:

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 the 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

  • Students need to visualise equivalents 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

  • Ratio 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.

Ratio and Proportion Resources

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