# Percentage Change

Students are required to solve problems which involve percentage change, including examples of percentage increase and decrease and problems in which the original value is to be found after a percentage change has taken place. Other problems include simple interest in financial mathematics and examples of repeated growth such as compound interest. This resource package provides a variety of activities to provide students with the opportunity to develop and practise these skills.

Visit the secondary mathematics webpage to access all lists.

### Using Percentages to Increase Quantities N7

The aims of this resource are to:

• Make links between percentages, decimals and fractions

• Represent percentage increase and decrease as multiplication

• Recognise the inverse relationship between increases and decreases.

Students are presented with the problem that prices decreased by 33% then increased by 50% and are asked to explain what the overall effect will be. Students are then encouraged to work in groups to explore inverse percentages - that is, the relationship between increasing by a percentage and the percentage decrease required to return to the original value. Students are asked to explain what they understand by increasing a price by 10% in words, as a decimal multiplier and as a fraction multiplier.

### Percentages

This resource contains eleven instant maths ideas, ideal for use as starters, extension questions or probing questions to assess understanding. There are a number of suggestions of questions from a variety of areas such as: if the base of a rectangle is increased by 10% and the area is unchanged, by what percentage is the width decreased? This question is ideal for use with the first resource in this list.

The resource contains a student worksheet exploring percentage increase and percentage decrease requiring students to calculate percentage increases and decreases and also work backwards given, for example, the new price and the percentage increase students are required to find the original price.

### Percentages

This resource was developed for use by teachers when planning. Each section offers an overview of a particular aspect of percentages, the key issues as well as highlighting some common misconceptions. Worked examples are provided to support learning and are followed by focused exercises to practice skills. Activities to reinforce learning and offer extension opportunities are also supplied, as are topic related tests.

Topics covered appropriate for this list are percentage increase, percentage decrease, compound interest and depreciation, reverse percentage problems and annual percentage rates.

### New National Curriculum Mathematics 8

Chapter three, **Proportional change**, beginning on page 64 of the pdf, asks students to explore how to calculate the original value after a percentage change has occurred. The initial suggestion is to use trial and improvement techniques before exploring methods using multipliers. The text contains discussion points, explanations, examples and exercises.

Repeated proportional change is explored in the next section, beginning once again with a number of discussion points for students to explore. Examples to consider include an increase followed by an increase and an increase followed by a decrease. Page 71 contains a number of puzzles which could be used as probing questions to assess understanding. The chapter concludes with a review section containing examples of questions found on examination papers.

### The Applied Maths Pack

This resource contains a variety of activities in which students are required to apply mathematics to explore and solve everyday problems. Activities appropriate to this topic are:

**Hire purchase of a car** on page 72 of the pdf in which students are asked to compare different deals offered when buying a car

**Investment** on page 78 in which students explore the best way to invest an inheritance

**Development of index of performance shares** on page 84 in which students consider proportional change of shares.

### Financial Maths

This collection of 18 resources contains a range of activities all designed to enable students to use and apply financial mathematics in unfamiliar contexts. Activities include:

**Exponential Growth and Decay**, which explores compound interest for savings and depreciation of assets.

**Simple compound interest **introduces the concept of simple and compound interest and its effect, studnets use an Excel spreadsheet to calculate and compare the interest amounts accrued.

**Stocks and shares** requires students to calculate simple percentage change; calculating new stock market prices for a variety of fictional shares based on daily percentage changes.

**Working with percentages **asks students to explore financial calculations involving percentage increase and decrease both individually, in combination and in reverse.