Fraction, decimal and percentage equivalence
Term 1 starting in week 10 :: Estimated time: 3 weeks
- Represent tenths and hundredths as diagrams
- Represent tenths and hundredths on number lines
- Interchange between fractional and decimal number lines
- Convert between fractions and decimals - tenths and hundredths
- Convert between fractions and decimals - fifths and quarters
- Convert between fractions and decimals — eighths and thousandths
- Understand the meaning of percentage using a hundred square
- Convert fluently between simple fractions, decimals and percentages
- Use and interpret pie charts
- Represent any fraction as a diagram
- Represent fractions on number lines
- Identify and use simple equivalent fractions
- Understand fractions as division
- Convert fluently being fractions, decimals and percentages
- Explore fractions above one, decimals and percentages
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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.
Equivalent Fractions Video Learn about equivalent fractions and how to express fractions in their lowest terms.
Equivalent Fractions Practise finding equivalent fractions numerically and in fraction diagrams.
Equivalent Fraction Pairs The traditional pairs or Pelmanism game adapted to test knowledge of equivalent fractions.
Visualise Percentages If you can picture in your mind what a percentage looks like you may be better able to preform mental calculations.
Fraction Dissect Draw lines to dissect the rectangles to make the given fractions.
Pie Charts Develop the skills to construct and interpret pie charts in this self-marking set of exercises.
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.
Fractions, Decimals, Percentages An exercise on converting fractions to decimals, decimals to percentages and percentages to fractions.
Fractions Decimals Percentages Video A reminder of the quick methods of converting between fractions, decimals and percentages.
Click on a topic below for suggested lesson Starters, resources and activities from Transum.
- Decimals Working with decimals, for most pupils, presents little difficulty if the pupils have confidence working with whole numbers. The topic of decimals provides an extension to the place value system with the addition of tenths, hundredths, thousandths etc. For many pen and paper multiplication and division calculations the decimal numbers can be considered as whole numbers then the answers adjusted accordingly. So 2.4 x 2.34 can be considered as 24 x 234 ÷ 1000. The numbers are multiplied by ten and one hundred respectively then the answer needs to be divided by the ten and one hundred to compensate. Pupils should use their understanding of place value to round decimal numbers. They should also use decimal numbers in the context of measures and money. This topic also contains activities which encourage pupils to investigate and explore the properties of decimal numbers and gain a better understanding of them.
- 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.
- 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
Fractions Decimals Percentages
Convert fractions to decimals, decimals to percentages and percentages to fractions.
2nd Lesson
PercenTable
Complete the table by calculating common percentages without using a calculator.
3rd Lesson
Estimating Percentages
Estimate the percentages of full circles and rectangles the sectors represent.
4th Lesson
Christmas Eve Snow
Each different letter stands for a different digit. Can you make sense of this word sum?
5th Lesson
Puddings
Complete the calculations with the weights of the puddings
6th Lesson
Christmas Bells
If all the bells ring together at noon, at what time will they next all ring together? This problem requires the use of LCM.
7th Lesson
Christmas Presents
Work out the total cost of five Christmas presents from the information given.
8th Lesson
Cracker Joke
Answer the mental arithmetic questions then convert the answers to letters to find the joke.
9th Lesson
Twelve Days
A Maths puzzle based on the 12 Days of Christmas song.
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.
