Fraction multiplication Multiply the numerators and the denominators.

Here a teacher would be trying to emphasise that we cannot always successfully describe quantity by counting. But just more time is not sufficient to improve understanding; the emphasis of instruction should also shift from the development of algorithms for performing operations on fractions to the development of a quantitative understanding of fractions.

Fraction Lengths is slightly more challenging, as the denominators are not always multiples of the same number. This will aid them in developing a more robust grasp of the concept of a fraction. An important realization students need to make is that there is a direct relationship between two quantities.

This might be achieved through questions inviting learners to describe the same fraction in different ways or by identifying problems with equal answers.

In developing a sound understanding of the part-whole concept of fractions, it is necessary for teachers to present situations of fair sharing, where the child is expected to reason out the consequences of different actions.

When it comes to calculation of fractions, the danger is that we introduce rules to be memorised and suddenly the conceptual development appears no longer to be valued. Realize you can learn. Indefinite wholes - where the extent of the whole is not clear, for example we do not know how long the pattern extends in either direction in the image below: If you think through pictures, you will easily see the need for multiplying or dividing both the numerator and denominator by the same number.

After a while, some students might discover the rule about the common denominator, or what kind of pieces the fractions will need split into. Of course this is a gradual process, but greatly helped by you modeling appropriate language wherever possible and drawing attention to good use of specific vocabulary by children themselves.

They need to understand that the dividend is the number of parts in each share, while the divisor refers to the fraction name of the share. Partitioning Even young children can partition regions or composite units approximately equally among two or three recipients. For example, this video shows a visual method for equivalent fractions: As opposed to an individual playing competitively against another individual when neither will want to give away their strategy!

Fraction addition - different denominators First find a common denominator by taking the least common multiple of the denominators. Throughout the paper I will discuss how we can use these simpler topics as a starting point in the uphill battle to understanding this extremely difficult concept.

Learners have to make a decision about the best table to stand at if the chocolate on it is shared between everyone at that table. One of the first problems will be how to count things.

Ok, so he returns 3 cows and we jump 6, from -3 to 3?

They can even have fun splitting the pieces further or conversely merging pieces together.Learning about fractions is one of the most difficult tasks for middle and junior high school children. The results of the third National Assessment of Educational Progress (NAEP) show an apparent lack of understanding of fractions by nine-.

Paper 2: Understanding whole numbers By Terezinha Nunes and Peter Bryant, University of Oxford Key understandings in mathematics learning A review commissioned by the Nuffield Foundation.

The idea of equivalence is a key one to introduce as children's understanding of fractions develops. Not only are learners encouraged to find families of fractions that are equivalent, but also to recognise decimal equivalents of fractions.

Tucker: Fractions and Units in Everyday Life 77 more complicated, intuition cannot be counted on to develop an understanding in a person’s mind of what fractions are, much less how to calculate with them. • Some ideas to help your students construct their own understanding of fractions.

• Some ideas to help your students talk about fractions. This unit links to the teaching requirements of the NCF () and NCFTE () outlined in Resource 1. Understanding what’s really going on behind the math is surely a key to really doing math well (and discovering that math is actually fun).

Pi is more than circumference divided by diameter.

It’s a measurement of the curvature of space.

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