# Percentages

Students need to be able to solve problems using multiplicative reasoning. This requires students to understand the connections between percentages, fractions and decimals and to be able to interpret percentages and percentage change to solve problems. This resource package contains a range of activities to enable students to become fluent in dealing with percentages and be required to reason mathematically in order to solve problems.

Visit the secondary mathematics webpage to access all lists.

### Problem Solved

The resource Problems Involving Percentages begins by asking students to find a single multiplier which will reduce a number by 15%. Further questions ask students to explain how they will know when they have the correct answer, and to compare different methods and say which method they prefer and why. Students are asked to investigate what happens when a price is increased by 15% and then decreased by 15%. The resource contains seventeen pages of questions, prompts, situations to explore and problems to solve involving percentage change.

### Using Percentages to Increase Quantities N7

This resource is designed to enable students to make links between percentages, decimals and fractions, represent percentage increase and decrease as multiplication and recognise the inverse relationship between increases and decreases. Students are given pairs of values and cards with statements such as down by 50%, up by 20% and have to link the amounts using the cards. A second set of cards contains statements such as 'down by a quarter' and another set of statements such as x1.2. Students have to link the values using all three sets of cards.

### Fractions, Decimals and Percentages

This range of resources is designed for use as teacher inspiration when planning lessons.

The resource Decimals, Percentages and Money contains an activity designed to enable students to make connections between word problems involving money and their mathematical representations. Students are given a set of cards containing calculations and another set of cards containing worded problems. Students are required to match the calculation with the solution.

The resource Percentages Encouraging Reasoning is designed to enable students to explore different methods of working with percentages. Students are presented with three problems involving percentage change and are expected to solve the problems using different methods then comment upon each method.

### Arithmetic: Fractions and Percentages

The textbook Arithmetic: Fractions and Percentages begins with a revision of performing calculations using fractions. The next section considers how to convert between fractions and percentages, followed by how to find a percentage of an amount. This work forms essential revision required to be able to progress to the section exploring how to increase and decrease quantities by a percentage. The section contains explanations, examples and exercises showing methods using fractions and methods using multipliers. The text continues with a section requiring students to find the percentage increase or percentage decrease in different contexts and concludes with a section exploring reverse percentage calculations.

The activities file contains five activities: a task revising the basics of calculating using fractions, an activity called investments in which percentages are used to calculate interest on investments, a task called Percentage Opinion in which the class give their opinion as to whether they agree with certain statements and are required to make posters showing the percentage of the class who agreed with each statement and VAT Problems requiring students to find VAT at a rate of 17.5%

### Is It Fair?

This activity asks students to explore whether the electoral system is fair. The first activity considers election results showing the percentage of the vote each party received with the percentage of the seats in parliament they received. The discrepancy leads to a further two activities, the first of which is to consider how voters are divided into constituencies. The final task explores the electoral system and asks students to explore different ways of counting votes. The topic provides an opportunity for work on inverse proportion, conversion calculations, compound percentage change and information handling skills.

### Percentages

Designed to improve confidence in mathematics, these resources from the Centre for Innovation in Mathematics Teaching, focus on percentages and were developed particularly for primary teachers and those non-specialists who teach mathematics in the lower secondary years.

These resources are useful as inspiration when planning lessons and contain worked examples, focused exercises to practice skills and offer extension and topic related tests. The topics covered are: fractions and percentages of quantities, quantities as percentages, percentage increase and decrease, compound interest and depreciation, reverse percentage problems, VAT problems, and annual percentage rate.

### Percentages

This interactive excel file from The Virtual Textbook begins with finding percentages of amounts without using a calculator. There are various options to allow for different degrees of difficulty of the questions posed. Answers can be revealed and new sets of questions generated.

The second sheet has similar sets of questions but calculators are expected to be used. The next sheet helps the student recognise the multiplier as a decimal. The remaining interactive sheets encourage the student to use the multiplier to find either the original amount or the final value after a percentage change.

There are a further seven sheets of questions which may be suitable for classroom use. The questions on VAT use the figure of 17½%