Finding the Best Buy Using Ratio

June 21, 2023

Differentiated Learning Objectives

• All students should use ratio notation to find the cost of a single unit.
• Using ratio notation, most students should find the best value of two or more offers.
• Some students should solve real-life problems to find the best value for different offers.

Links to Lesson Resources (Members Only)

Starter/Introduction

At the start of the lesson, there are nine different ratios, one of which is the odd one out. If students struggle to get started, encourage them to simply the ratios whenever possible. This way, they will realise that eight of them can be paired, with the odd one out left over.

 Prompts / Questions to consider

• Can the ratios be simplified?
• Are any ratios equivalent?

Finding the Best Buy Using Ratio

When finding the best buy using ratio for two or more offers, students need to translate the information into a ratio in the form quantity : price. It is often easier to convert costs given in pounds to pence as this avoids dividing with decimals. Students should be encouraged to use calculators throughout the lesson.

Work through the first example as demonstrated in the video below. For the second question involving pens, students could be asked to discuss in pairs a suitable number of pens that would be common to both offers. Encourage, students to consider the most efficient method using either the lowest common multiple, highest common factor or the cost of a single pen. Students could then attempt question c on mini-whiteboards with the teacher feeding back after each question.

 Prompts / Questions to consider

• How can we write the ratio? For example, Apples : Cost or Pens : Cost
• What is the easiest number of apples we can use to compare both offers?
• What does the cost tell us about the Best Buy?

After working through the questions on the first slide students could attempt the questions below either on their own or with a peer. After feeding back the solutions, students should attempt the questions on the worksheet provided.

 Prompts / Questions to consider

• What are the two units that make up the ratio?
• How can we find a common number of grams to compare the different offers?

Plenary

The plenary challenges students to find the volume of two cereal boxes before working out which size offers the best value for money. This activity takes approximately 8 minutes, with students working together on mini-whiteboards. It may be necessary to remind students how to find the volume of a cuboid.

 Prompts / Questions to consider

• What are the stages to solving this problem?
• How can we find a common volume to see which size packet offers the best value?

Differentiation

Questions 4, 5 and 6 on the worksheet challenge students to connect Best Buy problems to speed, exchange rates and percentages.

Additional Resources

Ages 11 - 13

Best Buys

How to calculate the best buy using ratio notation.