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

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

An equation is used to show 2 expressions that are equal to each other.

Writing equations from 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

Algebraic 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

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 7 : 5.  Which of the following are correct equations linking adults and children?

$$8x-2y = 3x+5y$$.  What is the ratio of $$x:y$$?

Which of the following is the correct way of writing the ratio 1 to 2?

There are 36 cans of drink and bags of sweets in a vending machine. The ratio of cans : bags is 2 : 1. 4 of each are sold.  What is the ratio of cans : bags now? (In its simplest form)

There are 56 vehicles in a car park.  The ratio of cars : vans is 5 : 2.  4 more vans enter the car park.  What is the ratio of cars : vans now?  (Give your answer in its simplest form)

The ratio of adults to children at an athletics club is 8 : 5.  8 adults leave, the ratio is now 4 : 3.  How many children are members of the club?

3 bags contain counters in the ratio 6 : 3 : 5. Some counters are taken out of 1 bag and put into the other 2. The ratio of counters is now 6 : 5 : 10.  What is the minimum number of counters removed?

The ratio of the number of £1 coins to £2 in Sam’s money box is 3 : 2.  Their gran gives them 6 more £1 coins, the ratio is now 2 : 1.  How much money was in Sam’s money box originally?

Writing equations from ratios

Lesson outcome