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- Work interchangeably with terminating decimals and their corresponding fractions.
- Define percentage as ‘number of parts per hundred’, interpret percentages and percentage changes as a fraction or a decimal
- Interpret fractions and percentages as operators

- If the ratio between two things is the same they are in direct proportion.
- To divide an amount in a given ratio find the value of one share by finding the total number of shares, then divide the amount by the total number of shares.
- To compare values work out the cost per unit or number of units per pound or penny. This takes the form of 1 : n.
- A common misconception is to write the ratio of 2 : 3 as 2/3. Emphasise the need to consider the total number of shares when writing a ratio as an equivalent fraction or percentage.

Develop fluency

- Consolidate their numerical and mathematical capability from key stage 2 and extend

their understanding of the number system - Select and use appropriate calculation strategies to solve increasingly complex problems

Reason mathematically

- Extend their understanding of the number system; make connections between number

relationships, and their algebraic and graphical representations - Extend and formalise their knowledge of ratio and proportion in working with measures

and geometry, and in formulating proportional relations algebraically

Solve problems

- Develop their mathematical knowledge, in part through solving problems and evaluating

the outcomes, including multi-step problems - Select appropriate concepts, methods and techniques to apply to unfamiliar and non-routine problems.

Ratio, proportion and rates of change

- Change freely between related standard units [for example time, length, area, volume/capacity, mass]
- Use scale factors, scale diagrams and maps
- Express one quantity as a fraction of another, where the fraction is less than 1 and greater than 1
- Use ratio notation, including reduction to simplest form
- Divide a given quantity into two parts in a given part:part or part:whole ratio; express the division of a quantity into two parts as a ratio
- Understand that a multiplicative relationship between two quantities can be expressed as a ratio or a fraction
- Relate the language of ratios and the associated calculations to the arithmetic of fractions
- Solve problems involving direct and inverse proportion, including graphical and algebraic representations
- Use compound units such as speed, unit pricing and density to solve problems.

May 19, 2017

As we prepare to say goodbye to our exam classes I thought it would be helpful to share some ideas about planning ahead in the summer term with your maths department. Tidy your classrooms and staffroom With all the revision work that has been going on over the past few months you probably have loads of […]

April 12, 2017

Many problems involve three-dimensional objects or spaces. Pythagoras Theorem in 3D Shapes can be used as much with these problems as those in plane shapes. Knowing when to use Pythagoras Theorem The starter recaps applying Pythagoras Theorem as part of a larger problem involving the perimeter of a trapezium and square. The aim of this […]

March 27, 2017

Drawing frequency trees for GCSE maths is a new topic and appears on both the higher and foundation curriculum. I’ve taught this lesson a couple of times, once to Year 10 and once to Year 11 and I have to say the kids really enjoy it. What is a frequency tree? Frequency trees can be […]