What are the models used to teach fractions?
- area model
- length model
- set model
When are fractions first introduced in the FP?
Grade 2
(term 2 and 3 gets introduced typically)
Fractions
Parts of a whole
Concepts related to fractions learners must understand by the end of primary school
- Equal parts and fair sharing
- Numbers of parts have special names (e.g. quarters, halves)
- If the number of fractional parts increases, the size of each part becomes smaller
- Denominator
- Equivalent fractions
Denominator
The number by which the whole was divided to form the fractional parts
Equivalent fractions
Different ways to refer to the same amount
What can be used to teach the length model?
- Fraction wall
- Cuisenaire rods
- Strips of paper
What can be used to teach the area model?
- Folded paper
- Real-life objects such as pizzas, sandwiches, cakes
- clay
Which model is most difficult for learners to use? Why?
Set models
It is more complex to think of collections as part of a whole or a larger collection
What should teachers do when introducing fractions?
- Use fractional language before introducing symbols
- provide learners with many opportunities to practice sharing
- constantly refer back to the whole and number of divisions
- count in fractions
Is it necessary for FP learners to know the terminology “numerator” and “denominator”?
No
How could one explain the numerator and denominator to learners in the FP?
The top number shows how many pieces/parts there are
The bottom number shows the size of the whole/how many pieces make up the whole
What is another name for the area model?
Regional model
Why do learners struggle with fractions?
- Lack sufficient experience in fair sharing
- Lack sufficient concrete experience in handling parts of a whole
- 1st time thinking about values between 0 and 1
- the vocabulary of fractions is not familiar/used often
- fractions are taught too early without opportunities for concrete conceptualization
What is the suggested approach for teaching fractions?
- Practise sharing wholes into equal and non-equal parts
- Introduce fraction names for different parts (names before symbols!)
- Practise finding equivalent fractions
The way we write fractions is called a…
Common convention
When can fraction symbols be introduced?
When learners have become fluent in partitioning and naming fractions
Why should more than one area model be used?
If one model is overused, learners tend to think they can only share that model
What experience do learners come with when learning about fractions? How does this influence the starting point?
Learners are familiar with sharing objects between people. Leftovers if there are any should be further divided
What confusions might learners have with fractions?
- difficulty adding fractions (adds both the numerators and denominators)
- difficulty reading fractions
- assuming a fraction name refers to a specific shape
Why should one avoid using the language “two over three” etc?
- Results in miscalculations
- Does not allow learners to understand the size of fractions or compare them accurately
Why might the learner make the mistake of adding both the numerator and denominator?
- insufficient experience counting in fractions
- moved too quickly to using fractional symbols before using the language
How could a teacher help a child to correct the mistake of adding both the numerator and denominator?
- counting in fractions with the child
- providing fraction bars/circles for the learner to shade when adding
- encouraging the child to read the problem aloud (e.g. two eighths add three eighths)
- modeland use correct fractional language
How can teachers avoid a learner misunderstanding a fraction name as referring only to a certain shape?
- expose learners to many different fractional models
- give learners experience partitioning many different shapes not only circles, squares or rectangles
