E3-L2 Fractions and misconceptions

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Exploring fractions and
misconceptions
May 2011. Kindly contributed by Helen Holt, Lincoln College.
Search for Helen on www.skillsworkshop.org
Visit the download page for this resource to find detailed teaching notes,
curriculum links and related resources.
Curriculum links
For underpinning the following Functional Maths coverage & range
statements:
Entry 3 Understand and use simple fractions
Level 2 (Level 1) Understand and use equivalences between (common)
fractions, decimals and percentages
Also covers many Adult Numeracy curriculum elements including
N2/E3.1 Read, write and understand common fractions
N2/E3.2 Recognise and use equivalent forms
N2/L1.1 Read, write, order and compare in words and figures common
fractions and mixed numbers
N2/L1.3 Recognise equivalencies between common fractions, decimals and
percentages and use these to find parts of whole number quantities
N2/L2.1 Use fractions to order and compare amounts or quantities
N2/L2.2 Identify equivalencies between fractions, decimals & percentages
Teaching notes
Slides 8-9: You may want to
provide printed grids for students
to fill in or re-usable laminated
grids and cards. A completed grid
is provided on slide 16 – this can
be copied into a Word document
etc. as needed.
Slides 12-14 are for general
discussion – not necessarily all at
the same time! Adapt to suit your
own learner group.
Week 4
Functional Maths
Exploring Fractions and Misconceptions.
Helen Holt
2
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.
Helen Holt
3
What are fractions?
• Fractions, decimals and percent are different
ways of representing an amount.
• I.e. We could say 50% of something, or ½ or 0.5.
These are all the same quantity.
• Fractions are about sharing. You may like to think
of them as ‘parts of a whole’.
Helen Holt
4
What are fractions?
• A fraction describes part of a
whole when the whole is cut
into equal parts.
• This pizza has been cut into
three equal parts. We call
these thirds. A third is
written as:
• Think about two slices. Two
slices is two thirds:
Helen Holt
5
Writing fractions?
• Look at the pictures below. How many
parts are these shapes divided into?
Represent these shapes as fractions.
Helen Holt
6
Converting between fractions,
decimals and %:
A same value can be written in different
forms. For example:
½
Is the
same as:
0.5
Is the
same as:
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%
Helen Holt
7
Converting between fractions,
decimals and %:
Place the fraction,
decimal and %
cards into the
correct blank
spaces on the grid.
Fraction
Decimal
½
¼
0.5
%
25%
0.20
1/10
0.75
10%
75%
3/9
100%
Helen Holt
8
Fraction
Decimal
½
0.5
¼
%
25%
0.20
1/10
10%
0.75
75%
3/9
100%
Helen Holt
9
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!
Helen Holt
10
Sharing Amounts
Helen Holt
11
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.
Helen Holt
12
Misconceptions of Fractions:
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.
Helen Holt
13
Misconceptions of Fractions:
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.
Helen Holt
14
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.
Helen Holt
15
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%
Helen Holt
16
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