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A piece of cake?
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Fair Sharing
Each child gets half a slice and one third.
Christa
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Fractions, why?
To reason, to calculate, estimate
To understand ratios, decimals, and percents
For everyday life
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Iceberg Metaphor
Informal
Pre-formal
Formal Top of the iceberg
Floatingcapacity
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Learning Trajectory for Fractions
Focuses on concept building.
Text book independent.
A visual representation (and a description)
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Goals of the lesson series
Concept building
Number sense, numeracy: Fractions in daily life
A base for percents and decimals
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Elements of the Learning Trajectory for Fractions
Fraction language
Concept development
Introduction of fraction notation: recognize and understand
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Fraction activitiesSeries ‘Understanding fractions’
Fraction Language:
What can be put on the half-table?How to fold a paper in four equal parts?
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Fraction activitiesSeries ‘Understanding fractions’
Fractions as part-whole and part-amount:
Fair sharing objects (slices of cake)and amounts (pieces of chocolate)
‘How much do you get?’
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Folding activities
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Fair sharing
Share four slices of cake equally amongst six children.Show how you divided the slices.
Write down hoe much each child will get.
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Fraction notation
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Fraction activitiesSeries ‘To simple operations with fractions’
Comparing fractions, introduction of the bar model:
Context of measurement:How many paper strips Is the height of the table?
‘One strip and a little piece of the strip.’
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Fraction activitiesSeries ‘To simple operations with fractions’
Introduction to fraction notation
Recognize, understand, use:
Order a pie
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Fraction activities
Games and applets to support student learning
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Applets
Laundry line
Measuring fractions 1
Measuring fractions 2
http://www.fi.uu.nl/thinklets/
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To be continued …
DME (Digital Math Environment)
Screenprints:
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Different fractions
Result of fair sharing
Part-wole/part-amount
Operator
Measurement
Ratio
Chance
Number
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General goals
Not only knowledge of (rules and systems), but also knowledge about.
Development and use of thinking models.
Reason and generalize.
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Not only formal operations
Give meaning to fractions in different situations
Develop an understanding of the size of fractions
Use fractions in fundamental applications
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…one half plus one
quarter equals three quarters
31 12 4 4
one half plus one quarter equals three
quarters
