Ratio and Proportion

Students learn how to simplify and use equivalent ratios to calculate proportionate amounts.  They use this knowledge to share an amount using a ratio.

This unit takes place in  and leads on to Indices and Standard Form.

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

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.

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.

2 thoughts on “Ratio and Proportion”

1. Dewi Williamssays:

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!

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Mr Mathematics Blog

Angles in Polygons

There are two key learning points when solving problems with angles in polygons.  The first is to understand why all the exterior angles of a polygon have a sum of 360°.  The second is to understand the interior and exterior angles appear on the same straight line. Students can be told these two facts and […]

Getting Ready for a New School Year

When getting ready for a new school year I have a list of priorities to work through. Knowing my team have all the information and resources they need to teach their students gives me confidence we will start the term in the best possible way.  Mathematics Teaching and Learning Folder All teachers receive a folder […]

Mathematics OFSTED Inspection – The Deep Dive

Earlier this week, my school took part in a trial OFSTED inspection as part of getting ready for the new inspection framework in September 2019. This involved three Lead Inspectors visiting our school over the course of two days. The first day involved a ‘deep dive’ by each of the Lead Inspectors into Mathematics, English […]