Understanding of Fraction and its TLM

Today we discussed about fraction and it’s TLM. Fraction has been remained challenging topic for both students and teachers. It was seen anyone can do operations on fraction easily but making its visuals produced difficulties. E.g. – gives ½ when ask for 1/3. We mostly see two whole number in one fraction number like 2/3, we see 2 as numerator and 3 as denominator, and here we lost the quantity sense of fraction number which is an important phenomenon in dealing with fractions. It take time to develop meaning of fraction numbers.

In counting we have definite interval between two numbers but it is not in decimal/fractions. Here we go for measurement.  Dealing with fractions multiplying and division relatively easy than addition/subtraction. 

We can use term Ordered pairs for fraction. Numerators and denominators in a definite order make a pair that is fraction.

Fraction can be shown on number line and each fraction has a definite point on number line.

One meaning of fraction is represent a part of a whole. Whole can be a thing or group of things. It is necessary in any condition to represent in fraction that it’s all part must be equal.

In a proper fraction numerator is smaller than denominator and in improper fraction numerator is always greater than denominator. Improper fraction can be also written in the form a whole and a part, In this case it is changed in mixed fraction. Each proper and improper fraction has many equivalent fractions.

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CIRCLE         SQUARE           STRIPS

We can make three type of material (TLM) by using circle, square and strips for Fractions (Ordered pairs). Circle roll, no other type of material roll, children can enjoy seeing whole while roll. On the other hand square model is advantageous for multiplication and for division chocolate-chip model can be useful.  Fraction T.L.M must be proportional while in whole number T.L.M can be both proportional and non-proportional.

We make circles for ½,1/3,1/4,/1/5,1/6,1/8,1/9,1/10 not for 1/7 because of these have divisibility property with 360.We make it one set on Ivory sheet and 1 set on card board.

Ivory sheet material along with card board use to understand it in both ways as part of whole and equal part from the whole as following-

                                                                     With Ivory sheet

                                                                    With card board

Above activity is helpful to make meaning of fractions. another activity  is give a person material that is made by card board from his back ,by touching with his hands he can try to tell what part of fraction it is , starting this activity with ½,1/4,1/3 and later on after practicing ¼,1/5/,1/8 etc. ,to differentiate among 1/5,1/6,1/8,1/9 need a good familiarity with these materials.

Another activity is to make whole with the use of more than on unit fraction. As-

½+ ¼+ 1/8+ 1/8 =1

1/2+ ¼+2/8 = 1

Fraction scale is another T.L.M that we made from 10” *2” ivory sheet. We use its both side and its 4 edges as shown in picture-

A4 size paper has unique advantage on other sizes of papers. It has 297 mm *210 mm .It is √2:1.

 It is suggested by many to use paper folding materials but problem remained it only 2, 4, 6,8,10 possible denominator. A4 size is easily available and above problem is simplified here. 210 is divisible with2, 3, 5 and 7. It is possible to make material with denominator 7.

One of use fraction scale is to make fraction wall. It produce meaningful visuals in the minds of children if they watch it daily in their classrooms. For making 1/9 we can use following construction-

Divide A4 sheet (length ) in to 3 equal part, draw the diagonal of first part ,now draw bisector of first part, join another diagonal point to mid-point (top to bottom),now draw perpendicular on intersecting point. This length is 1/9. 

This can be proved with the similar triangle properties, we can take an idea from above picture.

Fraction wall –

Some application of fraction wall-

·         As part of whole increasing, their size on fraction wall decreasing. This help making visuals in the mind of children.

·         Understanding of Equivalent fraction

·         Addition /subtraction of equivalent fraction

·         Addition of same denominator like ½ +1/3 can be seen 3/6 +2/6 easily.

·         The difference between sizes of ½ to 1/3, 1/3 to ¼ .1/4 to 1/5 ………is decreasing.

When we were making these material we did so many mistakes and had so many confusion in spite of all instruction was already written on white boards or told us so we should take care with our expectations with children.

Please feel free to correct my understanding. Your feedback and suggestion enrich my understanding