Exploring fractions, decimals, percentages and misconceptions

For underpinning the following Functional Maths coverage & range statements:• Understand and use simple fractions • Understand and use equivalences between (common) fractions, decimals and percentages

Objectives• Recognise and use equivalent forms• Read, write, order and compare in words and figures common

fractions and mixed numbers• Recognise equivalencies between common fractions, decimals and

percentages and use these to find parts of whole number quantities • Use fractions to order and compare amounts or quantities• Identify equivalencies between fractions, decimals & percentages• State when fractions, percentages and decimals are used in real life.

Julie Beaumont 2

Functional MathsExploring Fractions, Decimals,

Percentages and Misconceptions.

Functional MathsExploring Fractions, Decimals,

Percentages and Misconceptions.

Week 4

3

Session Outcomes:• Be able to read, write, order and

compare common fractions.• To identify equivalences between

fractions, decimals and percent.• To identify the relationship between

fractions, decimals and percent.• To explore misconceptions of fractions.• Calculate sums using decimals.• Calculate percentages.

4

Converting between fractions, decimals and %:

A same value can be written in differentforms. For example:

½ 0.5 50%To convert a fraction into a decimal, divide the top of the fraction by the bottom of the fraction:

e.g. ½ = 1÷2 = 0.5

To convert a decimal into a percentage, multiply by 100:

e.g. 0.5 x 100 = 50%

Is the same as:

Is the same as:

5

Converting between fractions, decimals and %:

Place the fraction, decimal and % cards into the correct blank spaces on the grid.

Fraction

Decimal

%

½ 0.5

¼ 25%

0.20

1/10 10%

0.75 75%

3/9

100%

6

Fraction Decimal %

½ 0.5

¼ 25%

0.20

1/10 10%

0.75 75%

3/9

100%

7

Why use fractions, decimals and %?

When might we use fractions:

• When telling the time (e.g. ¼ past).• In shop sales (e.g. a 1/3 off, ½ price).• When measuring (e.g. ½ a metre).

• When dividing (e.g. 1 pizza divided between 6 people).

• In recipes (e.g. half a dozen).

When might we use decimals:

• When working with money.• To show probability, or the likelihood

of something happening.• To show how many whole and part

numbers there are to a value (e.g. 3.25 means 3 whole numbers and one quarter of a whole number).

When might we use %:

• Shops use percentages in sales.• Banks use them for loan rates,

mortgages, savings accounts..• Weather forecasts use them to tell us the chances of rain. • To calculate VAT and income tax.

When working in business we may choose between fractions, decimals and %s to make a sale item look more appealing to customers. For example, 20% off may sound more appealing than 1/5 off a sale item, even though they are really the same amount!

8

Sharing Amounts

9

Misconceptions of Fractions:

1. Can a fraction be bigger than one whole?

2. Is it possible to have three halves of one object?

3. Are fractions anything to do with division?

4. A fraction is a small piece of a whole.

10

5. You cannot have a fraction that is bigger than one.

6. Five is less than six so 1/5 must be smaller than 1/6.

7. Decimals and fractions are completely different types of numbers.

Misconceptions of Fractions:

Helen Holt 11

8. Every fraction can be written as a decimal.

9. Every percentage can be written as a decimal and a fraction?

10.If you add the same number to the top and bottom number of a fraction, the fraction gets bigger in value.

Misconceptions of Fractions:

12

Where can we find fractions?

Take a look at this article. Notice how fractions are used to explain and analyse the results of the survey.

13

Fraction Decimal %

½ 0.5 50%

¼ 0.25 25%

1/5 0.20 20%

1/10 0.1 10%

3/4 0.75 75%

3/9 0.333 33.3%

1/1 1.00 100%