Key facts:

Fractions have a significant role in our everyday life. Fractions are numerical quantities that denote parts of a whole. There are four key concepts and operations within fractions that are addition, subtraction, multiplication, division and finding a fraction of a quantity. Children are required to have basic numerical skills before they are taught fractions. Consequently whilst working with fractions they will develop further mathematical skills that are crucial in other areas of mathematics as well as in cross curricular subjects. There are various effective methodologies that the teaching research agencies emphasize for teachers to use in teaching fractions to young children. These methods would support the learners to have a better understanding and the teachers to achieve the requirements of the national curriculum.Given a fraction such as , the integer at the bottom of the fraction explicitly 4 is the denominator. This represents how many parts the whole is divided into. The integer on top namely 1 is the numerator which corresponds to the number of parts that are being used. There are three forms of fractions; one of which is proper fraction that has a smaller numerator than the denominator for example . Another form is an improper fraction which consists of a numerator that is larger or equal to the denominator such as 12/6. The last form of fractions is mixed number fraction which includes a whole number and a fraction together, an example of this type is 2 . One of the fundamental facts is that a fraction with the same numerator and denominator is equivalent to one whole. Another significant fact is that two or more fractions may have different numerators and denominators; nonetheless they have the same value. These fractions are identified as equivalent fractions. To comparing fractions: If two fractions have the same denominators, the fraction with the largest numerator is the larger fraction. The key terms and facts stated above provide a foundation for young people to understand the key operations; addition, subtraction, multiplication and division of fractions. To complete an addition/subtraction operation of proper/improper fractions, it is necessary that the denominators of the fractions are equal. The procedure is then followed by adding/subtracting the numerators only and writing the result above the common denominator. However if the given fractions consist of unlike denominators, they must be converted to their equivalent fractions so that they all share a common denominator. This is achieved by finding lowest common multiple of the denominators and. Addition/subtraction of fractions that are in mixed number form, must be converted to improper fractions, and followed by the processes specified above. Multiplication of fractions is less challenging as it can be completed despite the fractions not having common denominators. In this process the numerators are multiplied together, their product is placed at the top of the solution fraction. Similarly the product of the denominators is placed at the bottom. Division of fractions is calculated by changing the operation sign to multiplication and multiplying the first fraction to the reciprocal of the second.Young people will need to have numerous skills before fractions are introduced to them. These skills include basic number skills such as multiplication and division of numbers and are required in simplifying or finding equivalent fraction. This directs me to my next point that young people will develop numerous useful skills through the course of working with fractions. One of these skills includes being able to find common multiples of two or more integers. Another skill they would attain is finding greatest common divisor of two or more integers.Fractions are initially introduced to young people at key stage 1; this includes children from ages five to seven years. During this stage pupils are enforced to be able to identify and name as one of two equal parts, 1/3 as one of three and as one of four equal parts. They are also expected to be able to distinguish, find, name and write simple fractions such as , , 2/4, of a length, shape, set of objects or quantity. As well as that they should develop the ability to write simple fractions of a quantity, identify which one is greater or smaller and the equivalence of simple fractions. By the end of key stage 2, pupils of ages 8-11 years are expected to be able to compare, order fractions as well as solving worded problems. Additionally they are expected to convert improper fractions to mixed number fractions and vice versa. Moreover, they are required to solve addition/subtraction of proper, improper and mixed fractions that have equal or different denominators. Writing patterns of equivalent fractions reduce factions to lowest terms and finding a fraction of a quantity is also taught during key stage 2. Furthermore, multiplication and division of simple pairs of proper fractions, reducing a fraction in its simplest form as well as recognize equivalences between simple fractions, decimals and percentages. Key stage 3 is the core stage as young people should have developed all the skills and knowledge that are necessary within fractions. During this period teachers are ought to teach ordering complex fractions, multiplying/dividing complex fractions of different forms and writing one number as a fraction of another. Additionally, converting fractions to decimals/percentages, relating ratios with fractions and determining the number of times a number can be divided by another should also be taught at this phase. During key stage 4, pupils of ages 13-16 years are expected to use the application of fractions in other core topic of mathematics namely in handling data, algebraic expression, etc.The national curriculum is designed as such that it allows the knowledge of young people to grow and widen gradually yet effectively. However research shows that many children find fractions challenging and remain struggling to understand the major concepts of fractions at secondary school. This may be due to lack of effective teaching. It is reasonable that every child learns differently never the less they have enough similarities for teachers to find a teaching method that is suitable for all of them to learn effectively. One of the effective procedures of teaching is using a variety of methods such as providing practical activities or possibly a quiz. This keeps maintains both the interest and focus of young people, which is vital as children tend to lose interest easily due to having a short duration of concentration. Fractions should be taught by doing concrete examples by using objects that are familiar to the children i.e. pizza. Once the student feels confident then drawing pictures would be another interactive method. This helps young people to visualize and improve their understanding of key concepts such as equivalent fractions. Getting young people involved by playing interactive games helps motivate them to learn. The Teaching and Learning Research Programme shows children learn faster by using technology. In addition, providing multiple examples helps to build up their understanding. Teaching at a steady pace is another important aspect of teaching, as its crucial to give young people time to think and take sufficient notes. A further effective teaching method is that teachers should not introduce new concepts, until young people having good understand of the fundamentals. Fractions are crucial in mathematics as they are used in other topics across the discipline, including probability, percentages, decimals, vectors, handling data, algebraic equations and many more. Other than Mathematics, fractions are used in many cross curricular subjects. In Music, fractions are used to show the beat length of notes. Similarly different measures of beat can be formed by using notes that have fraction values which would sum up to the value of the measure. Likewise in Physical Education, fractions are used in different forms in sports. They are used to record scores or time games. An example of this is football; its played in two forty-five minute halves. In Food Technology, many food recipes are not a whole measurement, they are a fraction. Therefore individuals should have the skills to multiply and divide fractions if they want to cook for more or less people. Moreover in science subjects such as Physics- Fractions used in Radioactive decay and half-life fractions are used to calculate amount of time required for a quantity to fall to half its value. In Chemistry, fractions are used to balance chemical equations.Fractions should be taught by doing concrete examples of objects thats familiar to the children i.e. pizza. Once the student feels comfortable then drawing pictures would be another option. This helps the students visualize which will assist them in understanding the concepts. Let them play games. If the student doesnt understand the basic foundation of fractions they will struggle even in simple task such as adding fractions. Fraction are important as we use them not only in Mathematics but in other core subjects an in our every day life.

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