Proportionality means when variables are in proportion if they have a constant multiplicative relationship.

A ratio shows the relative sizes of 2 or more values and allows you to compare a part with another part in a whole.

Algebraic ratios

Maths

Checking and securing understanding of simplifying and unitising ratios

Checking and securing understanding of equivalent ratios

Checking and securing understanding of sharing in a ratio

Checking and securing understanding of converting between ratios, percentages and fractions

Checking and securing understanding of real world ratios

Combining ratios

Changing ratios

Writing equations from ratios

Problem solving with algebraic ratios

In the compound measures unit, pupils will be exploring the multiplicative relationship between different compound measures. Ratio will be one of the ways in which this is explored and the skills from this unit will aid understanding.

The ratio unit will cover comparing fractions, percentages and ratios and being able to move fluently between them. The percentages unit ensured pupils had the opportunity to work with finding the percentage of an amount and the opportunity to calculate interest.

In this unit pupils will learn how to combine ratios, interpret algebraic ratios, and investigate quantity changes and their effect on ratios.

Ratio

To factorise is to express a term as the {{}} of its factors.

Which of these are equivalent ratios to the ratio 3 : 5

Given that $$2x-7$$ : $$6-3x$$ is equivalent to 3 : 5 which of the following equations are also true.

Work out the value of $$x$$ given that $$7 : 10 + x = 2 : x$$ 

Given that $$x>0$$ Work out the value of $$x$$ given that $$3x+1 : x+3 = 2x+4 : x+2$$ 

Given that $$x>0$$ Work out the value of $$x$$ given that $$x : 2x+7= 2x+5 : 10x+13$$ Give your answer as a decimal.

A numerical coefficient is a constant {{ }} of the variables in a term. 

What is the equation of $$y$$ in terms of $$x$$? 

Match each ratio of $$x$$ : $$y$$ to the correct equation of $$y$$ in terms of $$x$$.

The ratio of adults to children at a running club is 8 : 5.  Which of the following are correct equations linking adults and children?

$$4x-6y = 3x-2y$$.  What is the ratio of $$x:y$$?

Algebraic ratios

Lesson outcome