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Students learn how to use ratio notation to solve problems ranging from interpreting the scale of a map to calculating a speed, distance or time.

This unit takes place in Term 3 of Year 8 and follows on from multiplying and dividing with fractions.

- 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.

June 8, 2018

To introduce teaching reciprocals of numbers and terms I begin the lesson explaining that everything has an opposite. The opposite of shutting a door is to open it. The opposite of saying hello is to say goodbye. Numbers have opposites too we call them reciprocals. Teaching Reciprocals of Numbers and Terms To start the lesson […]

May 11, 2018

When I teach how to find the surface area of cylinders I like to add a constant level of challenge and enjoyment to the lesson. Rather than repetitively calculating the surface area of a cylinder I introduce more complex cylindrical shapes. How to find the Surface Area of Cylinders To find the surface area of […]

April 15, 2018

Inspiring students to enjoy maths and feel the success that comes with attempting a difficult challenge is why I teach. The feeling of success is addictive. The more students experience it the more they want it and the further out of their comfort zone they are willing to go to get more of it. Teaching […]