How to Teach Fractions

ProblemFractions = one of the most difficult

concepts for children to grasp Notation of fractions Formal vocabulary Learners may be able to draw and

label fractions correctly, but not be able to put them in order of size, or use them to solve problems.

Do not behave like ‘normal’ numbers

How to Teach FractionsIt is important that learners think

about relationships between fractions, rather than just trying to memorize methods for processing them.

FACTUAL

FACTUALCONCECPTUAL

We should move towards a more holistic approach when teaching

fractions.

Teachers’ MistakesSyntactic vs. Semantic emphasis

◦Technical procedures instead of understanding/meaning

Adult- vs. Student- centered approach◦Ignore ‘prefactional’ knowledge◦Adult concepts are very different from

children’s

Confusing representation

Multiple RepresentationsStudents given multiple

explanations can have…◦Greater conceptual understanding◦Transfer knowledge to tasks not

directly taught to them

Different Interpretations for the Fraction ¾ (Lamon, 2001)

Interpretation Example

Part/Whole 3 out of 4 equal parts of a whole or a set of objects

Measure ¾ means a distance of 3 (1/4 units) from 0 on the number line

Operator ¾ of something, stretching or shrinking

Quotient 3 divided by 4, ¾ is the amount each person receives

Ratio 3 parts cement to 4 parts sand

Provide exposure to other types of interpretations Ignoring other ideas leaves incomplete understanding

Multiple RepresentationsLearners need to be familiar with multiple representations of fractions, andshould always be given more than one representation.

1/3 of the class are boys.

Multiple RepresentationsUse a variety of mediums to

illustrate the same fractionSharing CakesClockManipulatives

Multiple RepresentationsWhat fraction of the hats are red?

Multiple RepresentationsWhat fraction of the circles are

blue?

Multiple RepresentationsPictorial representations of a particular

fraction may be of different sizes and different shapes. For example, don’t always use shaded sections of circles.

When you divide things into fractions it doesn't matter how you do this as long as the parts are all equal in size.

Multiple Representations

Multiple RepresentationsUse manipulatives when

introducing fractions. Practice cutting different shapes

into fractions.

How to teach FractionsStudents learn more if they

actually enjoy the activity, have a chance to discuss what they do, explain their work, and reach a shared understanding.

Conceptual Understanding

Making connectionsIntegrate into other math topicssolving money problemssharing a billcomparing pricescalculating journey times

Making ConncetionsCookingchecking the weight of

ingredients

Making ConnectionsInterpreting data in pictograms

and bar chartsUsing a metre ruleMeasuring a roomComparing each other’s heights

Making ConnectionsAsk learners to think of some

fractions they encounter in an everyday context

Classifying FractionClassifying different

representations of fractions, or statements about them, can be a very effective method of encouraging learners to reflect on and discuss their properties

Evaluating statements about fractionsLearners are given some

generalisations about fractions, perhaps printed out on separate cards, and are asked to choose whether they consider these to be ‘always’, ‘sometimes’ or ‘never’ true, and to justify their choices, with examples and convincing explanation.

Links outside the classroomMany learners do not use their

understanding of fractions outside the classroom, and are unwilling or unable to transfer it to ‘real life’ problems.

Encourage children to give names to the fractions they see in everyday life.

Did your family have meatloaf for dinner last night? How many pieces was it cut into? How many pieces did you eat?

Encourage kids to share.

Links outside the classroom

Links outside the classroomThe proportions of the human

body provide links with art, and with dressmaking/tailoring.

Artists assume the eyes are half-way down the face, the nose half-way between the eyes and the chin.

Fraction Quotes A man is like a fraction whose

numerator is what he is and whose denominator is what he thinks of himself. The larger the denominator, the smaller the fraction.

—Leo Tolstoy“We live but a fraction of our

lives”— Henry David Thoreau

GamesFraction War Game Show (Jeopardy)FairytalesFraction Blackjack