Percentages and interest
Term 2 starting in week 9 :: Estimated time: 2 weeks
- Convert and compare fractions, decimals and percentages (review)
- Work out percentages of amounts (with and without a calculator) (review)
- Increase and decrease by a given percentage (review)
- Express one number as a percentage of another (review)
- Calculate simple and compound interest
- Repeated percentage change
- Find the original value after a percentage change (review)
- Solve problems involving growth and decay
- Solve problems involving percentages, ratios and fractions
For higher-attaining pupils:
- Understand iterative processes
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Activities for pupils
Here are some related resources in alphabetical order. Some may only be appropriate for high-attaining learners while others will be useful for those in need of support. Click anywhere in the grey area to access the resource.
Visualise Percentages If you can picture in your mind what a percentage looks like you may be better able to preform mental calculations.
Percentages In Your Head Video It is really useful to have some mental strategies for working out percentages in your head.
Percentages Quiz A multi-level quiz on finding percentages. The lower level questions can be done mentally while the highest level questions require a calculator.
Fractions Decimals Percentages Revise the methods for converting fractions to decimals and percentages.
Fraction Percentage Match the fraction with the equivalent percentage. A drag and drop self marking exercise.
Fraction Percentage Pairs The traditional pairs or Pelmanism game adapted to test knowledge of simple fractions and their equivalent percentages.
Particular Pipes Construct the pipes using a set number of pieces with lengths given as fractions, decimals or percentages.
Express as a Percentage Here are some examples showing how to express one quantity as a percentage of another.
Express as a Percentage This self-marking quiz requires you to work out what one quantity is as a percentage of a second quantity.
Express Percentage Puzzle Drag the numbers into the percentage statements to make them true.
Fractions, Decimals, Percentages An exercise on converting fractions to decimals, decimals to percentages and percentages to fractions.
Number Skills Inventory A checklist of basic numeracy techniques that every pupil should know.
Percentage Change Video When you have mastered working out percentages you can then apply that skill to calculating percentage increase, decrease and reverse percentages.
Percentage Change Test your understanding of using percentages with this self marking quiz about percentage change.
Fractions Decimals Percentages Video A reminder of the quick methods of converting between fractions, decimals and percentages.
Percentage Switch Practise percentage increase and decrease calculations by completing this table.
Interest Practise using the formulas for simple interest and compound interest.
Interest Video Learn about simple interest, compound interest, appreciation and depreciation. This video is to help you do the online, self-marking exercise.
4.3 Billion Dollars Short Futurama clip: Fry's reaction to becoming a billionaire!
Compound Interest Calculator A customised online calculator for quickly finding the solutions to compound interest problems.
Overdraft Charges Do you understand how your bank charges you for taking out an overdraft? Try this self marking quiz.
Iteration Find approximate solutions to equations numerically using iteration.
Two-Step Percentages An exercise in which each problem requires two percentage calculations to find the solution.
Here are some exam-style questions on this topic:
- "(a) In an election, David Linewhip gained 27 552 votes out of a total of 43 715 votes. Write 27 552 as a percentage of 43 715 giving your answer to the nearest integer." ... more
- "Elaine invests £150 000 in a savings account for six years." ... more
- "Winky Lash wants to invest £20 000 for 3 years in a bank. She has the following two choices of banks, both offering compound interest but on different terms:" ... more
- "The value of a boat is £220 000." ... more
- "In 2009 the price of a Big Mac was £2.29." ... more
- "Davy Browning buys a premium skateboard." ... more
- "(a) Davy Browning earns £54000 per year before paying tax.
He pays tax on his earnings at a rate of 18%.
Calculate the amount Davy has after paying tax." ... more - "(a) Audrey, Seymore and Mr Mushnic share potted plants in the ratio Audrey : Seymore : Mr Mushnic = 3 : 4 : 7. Seymore receives 12 plants. Calculate the total number of plants shared." ... more
- "The value of a new car is £22 000." ... more
- "Windthrup bought a car for £9500 which depreciated by 6% in the first year and 3.5% in the second year." ... more
- "Tamara Knight has £5000 to invest." ... more
- "Using \(x_{n+1}=-5-\frac{6}{x_n^2} \)" ... more
- "Zoe invests £5000 in an account for one year. At the end of the year, interest is added to her account." ... more
- "Michael Banks invests £2000 in a savings account for two years. The account pays 2% compound interest per annum." ... more
- "The value of a new house, \(V\), is given by:" ... more
- "Here are the details for two bank accounts." ... more
- "Montague invests £7000 for six years in a bank offering compound interest at \(x%\) per annum." ... more
- "John times how long it takes him to run around Hazelnut Park each Friday afternoon. The last three weeks his times, rounded to the nearest minute are \(p, q \; \text{and} \; r\)." ... more
- "Consider the following cubic equation:
$$x^3-7x-5=0$$
An approximate solution can be found by using the following iterative process.
" ... more - "Ramin buys a car for £25,000. The value of the car decreases by 20% in the first year." ... more
- "Ruby invests a certain amount of money in a bank account that pays a nominal annual interest rate of 6.7%, compounded quarterly." ... more
Here are some Advanced Starters on this statement:
- Double or Half?
At ten percent change per day is doubling achieved faster than halving? more - Hundred and Fifty Percent
Divide 110 into two parts so that the larger part is 150% of the smaller part. more - Rich or Poor?
An interesting outcome of percentage increase and decrease more - Square Root of 1%
What is the square root of one percent? more
Click on a topic below for suggested lesson Starters, resources and activities from Transum.
- Fractions A fraction is a part of a number. Fractions are either vulgar or decimal. Vulgar fractions can be proper, improper or mixed. Equivalent fractions have the same value. Pupils, at all stages of their learning, should practise using fractions. From dealing with halves, the most basic fraction, to manipulating algebraic fractions containing surds, this topic is always relevant. Proficiency also depends on reasonable numeracy skills particularly the multiplication tables and finding the lowest common multiple of two numbers. Pupils also need to be able to convert vulgar fractions to decimals and percentages and vice versa. Be wary of teaching the 'rules' for manipulation fractions by rote. Pupils need to understand the reason why and the time-honoured key to understanding starts with the imaginary pizza and the much-used fraction wall.
- Money For many pupils the ability to understand financial transactions is a skill they thank their mathematics teacher for. Understanding the use of money is a real, practical application of mathematics in the real world and is just as important today as ever it was. When it comes to managing our money and avoiding costly mistakes it is well worthwhile to strive to become an expert. There are key aspects of personal finance the pupils should understand as the get older and more independent in their lives and the activities provided here provide resources for a small part of their learning process.
- Percentages Percentages provide a useful and common way to express a part of a quantity. The word is derived from the Latin per centum meaning “by the hundred”. Although percentages are usually used to express numbers between zero and one, any ratio can be expressed as a percentage. Pupils begin working with common percentages such as 50%, 25% and 10% and practise estimating percentages to get a better understanding of the concept. They then learn how to convert percentages to decimals and vulgar fractions and vice versa. More advanced problem solving may include percentage change and how it is applied in real life to discounts and interest. A study of the use of percentages in the media can provide many discussion points and can provide a stimulus for classroom display work.
- Sequences A pattern of numbers following a rule is called a sequence. There are many different types of sequence and this topic introduces pupils to some of them. The most basic sequences of numbers is formed by adding a constant to a term to get the next term of the sequence. This rule can be expressed as a linear equation and the terms of the sequence when plotted as a series of coordinates forms a straight line. More complex sequences are investigated where the rule is not a linear function. Other well-known sequences includes the Fibonacci sequence where the rule for obtaining the next term depends on the previous two terms. Sequences can be derived from shapes and patterns. A growing patterns of squares or triangles formed from toothpicks is often used to show linear sequences in a very practical way. Diagrams representing sequences provides interesting display material for the classroom. Typically pupils are challenged to find the next term of a given sequence but a deeper understanding is needed to find intermediate terms, 100th term or the nth term of a sequence.
Lesson Starters
Here are some suggestions for whole-class, projectable resources which can be used at the beginnings of each lesson in this block.
1st Lesson
Fractions Decimals Percentages
Convert fractions to decimals, decimals to percentages and percentages to fractions.
2nd Lesson
High Interest
Calculating percentages through practice problems highlighting mental maths skills,
3rd Lesson
Sid's Schemes
Work out which is the best scheme for Sid to choose for his summer bonus. One scheme involves a common misconception about percentages.
4th Lesson
Structured Settlement
Without a calculator match a a pie slice to a calculation to an answer.
5th Lesson
Estimating Percentages
Estimate the percentages of full circles and rectangles the sectors represent.
6th Lesson
Refreshing Revision
It is called Refreshing Revision because every time you refresh the page you get different revision questions.
Some of the Starters above are to reinforce concepts learnt, others are to introduce new ideas while others are on unrelated topics designed for retrieval practice or and opportunity to develop problem-solving skills.
