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Students learn how to simplify and use equivalent ratios to calculate proportionate amounts. They use this knowledge to model direct and indirect variation problems.

This unit takes place in Term 1 of Year 10 and leads on to indices and standard form.

- 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

- 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

- 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.

- 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.

January 26, 2022

How to find the area of a sector as a fraction of a full circle.