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Students learn how to model variations of direct and indirect proportions by setting up an equation. They learn how to solve this equation to find k, the constant of proportionality. As learning progresses students illustrate these linear and non-linear using graphs.

This unit takes place in Year 10 Term 6 and follows on from Ratio and Proportion.

- 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

- Understand that X is inversely proportional to Y is equivalent to X is proportional to 1/Y;
- Solve problems involving direct and inverse proportion, including graphical and algebraic representations
- Construct and interpret equations that describe direct and inverse proportion.

- The symbol ∝ is used to represent ‘is proportional to’.
- Direct proportion and varies directly both include y ∝ x, y ∝ x
^{2}and y ∝ x^{3} - Indirect proportion and varies inversely both include y ∝ 1/x
- k is used as the constant of proportionality
- Students need to be able to associate the graphical representations with the various proportions.

- Students often struggle with writing the correct proportional formula from the written description. Writing indirect proportions is particularly difficult for most students.
- Modelling the variation as a formula with the correct value of k is key to accessing this topic.
- When students do write the correct formula they are often unable to correctly manipulate it to calculate unknown values.

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 […]