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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.

July 6, 2019

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 […]

June 30, 2019

The method of how to solve quadratics by factorising is now part of the foundational knowledge students aiming for higher exam grades are expected to have. Here is an example of such a question. Solve x2 + 7x – 18 = 0 In my experience of teaching and marking exam papers students often struggle with […]

June 24, 2019

When learning how to write 3-part ratios students need to understand how ratios can be made equivalent. The start of the lesson reminds students by asking which of six ratios is the odd one out. This is presented to the class as they come into the lesson. Writing Equivalent Ratios A few students immediately go […]