# Ratio, Proportion and Rates of Change

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.

##### Prerequisite Knowledge
• 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

##### Key Concepts
• 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.

##### Working mathematically

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.

##### Subject Content

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.

This site uses Akismet to reduce spam. Learn how your comment data is processed.

### Mr Mathematics Blog

#### Mathematics OFSTED Inspection – The Deep Dive

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 […]

#### How to Solve Quadratics by Factorising

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 […]

#### How Write 3 Part Ratios

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 […]