Parts and Whole – Dealing with a Different Approach

Introduction to Concrete Representation of Abstract (CRA) Approach:

It was a  wonderful experience using the CRA approach in Math class and I am thankful to the Azim Premji Foundation, Puducherry, for conducting the Math workshop on CRA.

CRA stands for Concrete, Representation (Picture, verbal) of Abstract. All teachers follow this approach in their classrooms, but they do it in a fragmented way. CRA logically combines many methods/techniques, and it is used to teach mathematical concepts. This approach allows students to have a better understanding of mathematical concepts, which can be retained in their minds for a long time.

In short, children make use of concrete objects in order to understand a concept, represent it in pictorial form, and then represent it verbally by creating a story. Following this, they write it in the form of a mathematical representation (the abstract form).

I tried to employ the CRA approach for students of Class 5 while teaching ‘parts and whole’.

Concrete:

A few children, who had volunteered, were given a strip of paper. They were asked to fold that paper in different ways. Their folded strips were used to introduce the concept of “parts and whole”.

Representation –Pictorial Representation

Children were made to sit in groups of two, and a paper strip was given to them. They folded the paper strip in equal parts to make their own model. They made parts and colored a few of those to form a fraction. Following this, they drew a picture in the notebook that represented the same fraction.

Verbal Representation:

Each group had a discussion and came up with a story for their ’parts and whole’. They presented the story, along with the picture, to their peers.

Abstract:

Each group wrote a mathematical representation for the picture they had drawn in the form part/whole, as can be seen in the example provided below.

Story:

A pair folded the paper strip into 16 equal parts, of which they coloured6 parts. They drew 16 small ships and coloured 6 ships. The story they had come up with is as follows: I had 16 ships, and I gave 3 ships to my sister and took 3 ships for myself to sail on the sea. What fraction of ships were taken by us? The answer is 6/16,and the children represented6/16 in abstract form.

Employing the same approach, proper, improper, and equivalent fractions were also discussed.

Half Concept:

Another activity was conducted to let the children understand whether all halves are equal. Different shapes (Square, circle, rectangle) were given to them. Different sizes were also used. The children were asked to show the half of the shape they had been given. Everyone was asked to show their result, and all the children agreed whether what they had managed to produce the half. When all the halves were shown at the same time, the children were asked whether they were the same/equal. The children replied “no”. Few different answers came, and, finally, one boy answered that it depended on the whole. He was appreciated.

Assessment:

Rubik’s cube/Tablet strips:

Rubik’s cube was used as a tool to assess the concept of parts and whole. The children were divided in groups, and each group was provided with a Rubik’s cube. They shuffled the Rubik’s Cube and chose a side. Then, they drew a picture, representing each colour in the form of a fraction. They related their fractions to real life and narrated a story based on it. Tablet strips were used in the same way, where used and unused tablets were represented in the form of fraction.

Game-Based Learning (GBL):

A workshop on GBL gave me the idea to integrate CRA with GBL. A game for the same concept was designed and played in the classroom.

Treasure Hunt:

Children were divided into 5 groups, each having three members. They decided their group number by picking lots. Clue cards with a group number were spread on the floor. Each group took their cards. The clue cards provided a hint for the children to find the treasure. Each group read the card and searched for their treasure, which was hidden in or around the classroom. The treasure consisted of a few pistachio shells. After finding the treasure, the team came back to the classroom and took a chart and some required materials to make their picture using those shells.

A story for the “parts and whole” was also developed by the children, and they presented it in front of the class.

Points were allotted on the following basis:

The group who finishes

I- 5 points

II- 4 points

III- 3 points

IV- 2 points

V- 1 points

The group that scored the highest was declared the winner.

The children thoroughly enjoyed themselves while playing this game and learnt the concept in different ways. They were able to express fractions with the help of a picture. They were also ready to narrate a story with a picture. I felt very satisfied and happy to follow CRA and GBL approach to teach this concept.

Reflection:

Some groups required more clarification about the game. These groups were too excited and did not pay heed to the instructions that were given. So, they clarified doubts from time to time.

There are many approaches to applying CRA in the classroom – while some of them may work with students some may not be very fruitful. However, if the students’ ability to think and learn is ignited, then, I think, the approach is a success.

Kayalvizhi S, GHS Kalmandapam