Solving Problems with Percentages

August 23, 2016

Students learn how to convert between fractions, decimals and percentages and how to write one number as a percentage of another. They use this knowledge to calculate a repeated percentage change and reverse percentages.

This unit takes place in Term 1 of Year 10 and follows on from working with fractions and decimals.

Solving Problems with Percentages Lessons

Fractions, Decimals and Percentages

Writing a Percentage

Percentage Increase

Percentage Decrease

Calculating a Repeated Percentage Change

Reverse Percentages

Compound Interest

Compound Decrease

Prerequisite Knowledge

Multiply and divide by powers of ten
Recognise the per cent symbol (%)
Understand that per cent relates to ‘number of parts per hundred’
Write one number as a fraction of another
Calculate equivalent fractions

Success Criteria

Define percentage as ‘number of parts per hundred
Interpret fractions and percentages as operators
Interpret percentages as a fraction or a decimal
Interpret percentages changes as a fraction or a decimal
Interpret percentage changes multiplicatively
Express one quantity as a percentage of another
Compare two quantities using percentages
Work with percentages greater than 100%;
Solve problems involving percentage change
Solve problems involving percentage increase/decrease
Solve problems involving original value problems
Solve problems involving simple interest including in financial mathematics
Set up, solve and interpret the answers in growth and decay problems, including compound interest and work with general iterative processes.

Key Concepts

Use the place value table to illustrate the equivalence between fractions, decimals and percentages.
To calculate a percentage of an amount without calculator students need to be able to calculate 10% of any number by dividing by 10.
To calculate a percentage of an amount with a calculator students should be able to convert percentages to decimals mentally and use the percentage function.
Equivalent ratios are useful for calculating the original amount after a percentage change.
To calculate the multiplier for a percentage change students need to understand 100% as the original amount. E.g., 10% decrease represents 10% less than 100% = 0.9.
Students need to have a secure understanding of the difference between simple and compound interest.

Common Misconceptions

Students often consider percentages to limited to 100%. A key learning point is to understand how percentages can exceed 100%.
Students sometimes confuse 70% with a magnitude of 70 rather than 0.7.
Students can confuse 65% with 1/65 rather than 65/100.
Compound interest is often confused with simple interest, i.e., 10% compound interest = 110% × 110% = 1.1² not 220% (2.2).

Mr Mathematics Blog

Showing Progress during a Mathematics Lesson

April 17, 2019

Demonstrating student progression during a mathematics lesson is about understanding the learning objective and breaking that down into explicit success criteria. Using Success Criteria Take, for example, a lesson on calculating the area of compound rectilinear shapes. The intended learning objective was written on the main whiteboard. Success criteria were used to break down the individual […]

Plotting and Interpreting Conversion Graphs

March 26, 2019

Plotting and interpreting conversion graphs requires linking together several mathematical techniques. Recent U.K. examiner reports indicate there are several common misconceptions when plotting and interpreting conversion graphs. These include: drawing non-linear scales on the x or y axis, using the incorrect units when converting between imperial and metric measurements, taking inaccurate readings from either axis not […]

Calculating the Volume of a Pyramid

March 10, 2019

When calculating the volume of a pyramid we can substitute the values of the length, width and perpendicular height into the formula V = 1/3 lwh. In my experience this is often provided for the students with little explanation as to why a volume of a pyramid is exactly one third the volume of a […]