Scheme of work: GCSE Higher: Year 9: Term 2: Ratio and Proportion
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
Key Concepts
It is important for students 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.
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.
You’re right about common misconceptions between ratios and fractions – pupils will often confuse the ratio 2 : 3 with the fraction 2/3.
However, I also think that there is a lot of value in pointing out the similarities between ratios and fractions. Equivalent ratios is conceptually very similar to equivalent fractions, and it is worth pointing out those similarities.
Thanks for sharing!
mrmath_admin says:
Hi Dewi
Thanks for the comment. I completely agree about the need to understand a ratio as a proportion. These questions are becoming much more common nowadays in exam papers. Students continue to find them difficult.
It is also common to see ratio and proportion problems linked with the lowest common multiple.
Thanks again
Jonathan
Dewi Williams says:
You’re right about common misconceptions between ratios and fractions – pupils will often confuse the ratio 2 : 3 with the fraction 2/3.
However, I also think that there is a lot of value in pointing out the similarities between ratios and fractions. Equivalent ratios is conceptually very similar to equivalent fractions, and it is worth pointing out those similarities.
Thanks for sharing!
mrmath_admin says:
Hi Dewi
Thanks for the comment. I completely agree about the need to understand a ratio as a proportion. These questions are becoming much more common nowadays in exam papers. Students continue to find them difficult.
It is also common to see ratio and proportion problems linked with the lowest common multiple.
Thanks again
Jonathan