Increasing and decreasing quantities by a percent

This lesson develops the concept of percentage increase and decrease. In particular students will develop their understanding of:

• Translating between percentages, decimals, and fractions.
• Representing percent increase and decrease as multiplication.
• Recognizing the relationship between increases and decreases.

The initial activity is to look at calculating percentage changes using a calculator. Students also examine the net result of a 20% decrease in prices, followed by a 25% increase in prices.

The main activity is a collaborative exercise. Students are given ‘money’ cards showing $100, $150, $160, and $200. There are ten cards with either a percentage increase or percentage decrease written inside an arrow. All of the arrows must be placed between the money cards to make true statements.

There are pre-lesson and post-lesson formative assessment tasks. Detailed teacher notes give suggestions on questioning and how to use the resources. Full solutions are given for each of the sections.

This is a concept development lesson from the Mathematics Assessment Resource Service, a collaboration between UC Berkeley and the Shell Centre team at the University of Nottingham. Further information on the collection is given here.