# 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  Year 9 Term 2 and leads on to Indices and Standard Form.

4 Part Lesson
4 Part Lesson
4 Part Lesson
4 Part Lesson
4 Part Lesson
##### Revision Lessons
Extended Learning
##### Proportional Reasoning
Extended Learning
Problem Solving
Revision
Revision
Revision
Revision
##### 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!

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