Fractions and percentages
Term 2 starting in week 7 :: Estimated time: 3 weeks
- Convert fluently between key fractions, decimals and percentages (review)
- Calculate key fractions, decimals and percentages of an amount without a calculator (review)
- Calculate fractions, decimals and percentages of an amount using calculator methods (review)
- Convert between decimals and percentages greater than 100%
- Percentage decrease with a multiplier
- Calculate percentage increase and decrease using a multiplier
- Express one number as a fraction or a percentage of another without a calculator
- Express one number as a fraction or a percentage of another using calculator methods
- Work with percentage change
- Choose appropriate methods to solve percentage problems
For higher-attaining pupils:
- Find the original amount given the percentage less than 100%
- Find the original amount given the percentage greater than 100%
- Choose appropriate methods to solve complex percentage problems
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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.
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.
Two-Step Percentages An exercise in which each problem requires two percentage calculations to find the solution.
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.
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
One Ninth
Investigate three fractions which add together to give one ninth.
2nd Lesson
High Interest
Calculating percentages through practice problems highlighting mental maths skills,
3rd Lesson
Loopy Lake
Match the fractions to their decimal equivalents and join them with lines that do not cross.
4th Lesson
Kim's Game 3
This is the Maths version of the traditional memory game. Memorise 10 mathematical facts then recall them as they disappear from view.
5th Lesson
Structured Settlement
Without a calculator match a a pie slice to a calculation to an answer.
6th Lesson
Table Legs
Learn an unusual times table from the strategic finger moving up and down the 'Table Leg'!
7th Lesson
Odd One Out
From the numbers given, find the one that is the odd one out.
8th Lesson
Know Weigh
Find the weight of one cuboid (by division) of each colour then add your answers together.
9th Lesson
Team Age
Work out who is in which team from the information given.
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.
