Exploration of part-whole relationships involving known simple fractions (halves and quarters).
Focusing on comparing sizes of fractions - involving intuitive ideas on equivalent fractions.
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Resources |
Vocabulary |
An apple
A knife
A glass
Equal sized strips of A3 paper
String
Share an apple notesheet – one per pair (optional)
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half, quarter, three
quarters, third, equal parts
parts, part, whole,
denominator, numerator |
Organisation |
Near ability pairs on mixed ability tables
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Whole class Preparation (about 10 mins) |
How could we cut this apple into halves? Invite suggestions and agree the best methods, then cut the apple.
Draw apple halves on the board. How do we know that these are halves?
How would you write half in figures?
How could we cut the apple into quarters? What is important to remember about each part? Remind them that each part must be equal.
How do we write a quarter? What do the two numbers mean to you?
Discuss the fact that 1⁄4 shows 1 divided into four equal parts.
Explore the language the children use to describe fractions, e.g. a half is 1 out of 2 or 1 divided into two; a third one out of 3 or 1 divided by 3.
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Paired work (10 mins) |
Display a glass of apple juice, a £1 coin and a book. Give out the notesheet.
In pairs record how you would find:
a half then a quarter of a glass of apple juice
a half then a quarter of £1
a half then a quarter of a book.
Are there different methods for doing this? Check with others on your table. Which methods could guarantee finding a half or a quarter? Which do you find easier? Why?
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Class sharing (about 10 mins) |
Children report back on how they worked out these problems.
Emphasis the idea of a quarter being half of a half.
How would you find three quarters of £1? Ask children to demonstrate notation on board. Discuss its meaning. 1⁄4 + 1⁄4 + 1⁄4. Which part of the fraction are you adding? The ones. Why?
Write 1⁄2 + 1⁄4 on the board. How does this work?
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Paired work (about 10 mins) |
Give out two strips of paper each.
How would you find a third of a strip?
How many parts will the strip be divided into?
What about the sizes of these parts?
Is one third bigger or smaller than one half? How do you know? What about two thirds?
If you fold each strip in half again, how many sections do you think you will have?
Given pairs of fractions, children justify and prove which one is bigger, for example, look at five sixths and seven eighths or three quarters and four fifths.
Given other pairs of fractions, children show when they add to more or less than one.
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Class sharing (about 10 mins) |
Children report back on their findings and demonstrate their answers using strips of paper. Record them on the board.
A challenge: Would it be possible for half my daughter’s pocket money to be less than one third of my sons?
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