The plus and minus of fractions

Suma Vivekanandan

I have noticed that many children find it difficult to add and subtract fractions; they are confused as to why we add only the numerators and not the denominators. Often they add both the numerator and the denominator. Fractions are not all that difficult, but children find them confusing because they are not taught in ways they can understand. If students simply try to memorize the rules of fractions without knowing why they exist, things will only get messy for them.

Here is an activity that will help children comprehend the rule of addition and subtraction in fractions.
• Make groups of five children each.
• Have a discussion.
o What is addition?
o What are the words (vocabulary) related to addition?
o When we add what happens? (value increases or decreases?)
o What do you think happens when you add fractions?
• Ask each group to select a leader.

• Let the teacher bring square or rectangular pieces of paper (even newspaper will do), one for each group. Also bring some fruits. Apples or bananas will work well.
• For the first task ask the group leaders to take a paper or fruit in one hand and do the following…
o Cut it into eight equal parts and give one part each to a team member.
o What fraction is given?
o What fraction is left with you?

Here the question is to the group leader. One piece of paper cut it into 8 equal parts. One piece is given to each member. There are 5 members.
o What fraction is given? 5/8
o What is left with you? 3/8

The concept is 1/8+1/8+1/8+1/8+1/8=5/8. Here the children will realize that there is no change in the denominator and only the numerator has to be added.

• Now give the second task
o Cut the second object into 10 equal parts. Give 2 parts to each member of the group.
o What fraction is given?
o What fraction is left with you?
o The group leader will take back one piece from each team member.

Now what fraction does the leader have?
Allow the group members to discuss and find the answers.
Ask them if the activities helped them identify any rule.
They themselves will come out with the rule.
We have to only add or subtract the numerators. The denominators always remain the same.
This activity I have done with my grade 4 students. It was a great success.

The author is a mathematics teacher and primary school math coordinator in Atul Vidyalaya, Atul, Gujarat. She can be reached at suma_vivekanandan@atulvidyalaya.ac.in.