Ratio and Proportion

Simplifying Ratios

Proportional Reasoning

Sharing to a Ratio

Proportion and Recipes

Direct Linear Proportion

3-Part Ratios

Inverse Proportion

Equivalent Ratios

Sharing to a Ratio

Calculating Exchange Rates

Best Value Ratio Problems

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
• 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

• 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.
• 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

• 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.