Term paper on Fractions

This essay is dedicated to teaching equivalent fractions to pupils of 4 grade. Understanding equivalent fractions is necessary for future actions with fractions and for numerical operations in general. This part of math curriculum appears sometime rather abstract for some pupils, so it should be illustrated as vividly as possible. This essay discusses prerequisite knowledge and definitions, necessary for mastering the topic, key ideas for explanation and probable tasks for pupils.

Prerequisite knowledge

The pupils should know what a fraction is, they should distinguish numerator and denominator of the fraction. Also, they should have some basic skills of working with fractions with unlike denominators: first of all, they should know the idea of fractions with unlike denominators (fractions that have different numbers in the denominator); secondly, they must be able to compare fractions with same numerators and unlike denominators, and finally, they need to know the idea of greatest common factor and identify the greatest common factor of denominators (for two fractions with unlike denominators).

Illustration of equivalent fractions

The concept of the same number being written in multiple forms is difficult for many children. The teacher should set examples and use manipulatives to illustrate the idea. A good example of explanation may be the analogy between different forms of writing the fraction and different names that people call one person (for example, Rebecca and Becky is the same name for one person, as well as 2/4  and ½ are the different notions for the same number).

It is useful to have paper sheets and color pencils for illustrating the idea of equivalent fractions. The previous example can also be explain as shown below. First the children cut a sheets into halves. They need to understand that each half constitutes ½ of the whole. Then they color one half of the sheet, and leave other half blank. The colored and blank halves should be also cut into equal pieces. The teacher explains that each of the pieces is ¼. Children are suggested to estimate the colored area and come to the conclusion: ½ = 2/4. Similar examples with cutting may ease understanding of the topic significantly. The teacher may ask the class to perform some more cuts and write down the equivalent fractions to ensure understanding.

Algorithm of finding equivalent fractions

The teacher should explain the procedure of finding equivalent fractions. Pupils need to know what the simplest form of a fraction is (when the greatest common factor of numerator and denominator is 1). To find an equivalent fraction, the pupils should multiply the numerator and denominator by the same factor.

Test problems

  1. Pupils need to write several forms of 1 (i.e. 1 = 2/2, 1 = 5/5, etc.). Understanding that 1 can be written in different forms can be complicated for some pupils.
  2. Next step is to cut a paper into given number of pieces, write down the fraction denoting one piece, and find an equivalent fraction by dividing the pieces into halves
  3. Teacher sets examples like 1/5 = ?/20 and asks the students to find the missing number
  4. Other kind of examples are the following: 2/? = 3/6; pupils also need to find the missing number
  5. After pupils have mastered the previous tasks, the teacher may build three equivalent fractions (for example, like this: ?/4 = 5/? = 12/24)
  6. A more complicated task related to the topic may be comparing two fractions with unlike denominators (the denominators in this case are supposed to be divisible one by another to ease the task).


Understanding equivalent fractions, as well as reduction of fractions is important for pupils because they will need to deal with fractions all the time, and basic operations cannot be done without understanding fraction equivalence. Successful visualization of this topic and a necessary amount of examples will help to ensure that pupils have understood the topic and can apply the knowledge freely.

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