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

Coordinates are a set of values that show an exact position.

An expression contains one or more terms, where each term is separated by an operator.

The probability that an event will occur is the proportion of times the event is expected to happen in a suitably large experiment.

Problem solving with 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

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

Which are of the following are expressions?

The points A, B, C and D are in order on a straight line.  AB : BD = 2 : 7, AC : CD = 15 : 3.  Find the ratio of AB : BC : CD

The points A, B and C are on a straight line.  The coordinates of A are (6, 2).  The coordinates of B are (8, 5).  Given that AB : BC = 1 : 2.  Find the $$x$$ coordinate of C.

The ratio of red to yellow sweets in a bag is 2 : 3.  The ratio of hearts to stars in the bag is 3 : 1.  What is the probability of picking out a red heart?  (Give your answer as a decimal)

The ratio of gravel to water in this fish tank is 1 : 5.  What volume of water is in the tank?

There are red and green counters in a bag in the ratio of 1 : 2.  2 are taken at random, the probability that 2 red counters are taken is $$8\over75$$.  How many green counters are there?

Which of the following are equivalent ratios to 3 : 9?

Point A and B are on a straight line.  The coordinates of point A are (2, 3).  Point B is 2 to the right and 4 below point A.  What are the coordinates of point B?

There are 42 cars and vans in a car park in the ratio of 5 : 2.  How many vans are there?

Bag A contains $$b$$ beads, bag B contains two more than bag A and bag C contains twice as many as bag B.  Which of the following is the correct expression for the number of beads in bag C?

Problem solving with algebraic ratios

Lesson outcome