How full or empty is my glass?

My students are always fascinated with fractions. The moment I say “Today we are learning about fractions “, I can see a lot of joy and excitement in their face. It could be because they get a break from   the time taking mathematical operations with those large numbers, but in all probability I am pretty sure that it is because of the fun filled activities that they get to do here at NumberNagar, unlike the mundane ways of learning Maths at school.

Fraction as a concept invariably has a lot of real life examples to connect to. A typical “fractions” lesson plan involves activities such as paper cutting, paper folding, and ways to share food items especially the pizzas, and candies among friends. Students at NumberNagar have been pampered with variety in terms of activities to learn any concept in many interesting ways. To keep up to these expectations we as facilitators constantly work towards making the sessions productive and exciting for the kids.

At NumberNagar every component serves to teach multiple concepts. It is designed in such a way that one can teach the same concept by using different elements of the lab. This gives the facilitator the freedom to choose different components and play around with them during the session. So today I chose Pascal’s cups. These are a set of cups, few with holes in it. These cups can be arranged in a pattern and then when we pour water into the top cup, the amount of water collected in the cups at the bottom follows a pattern similar to Pascal’s triangle.

For those of you who are new to Pascal’s triangle, simply put, it is one of the most interesting number patterns one can come across.  It is named after Blaise Pascal, a famous French mathematician and philosopher.  Pascal’s triangle is basically a triangular array of binomial coefficients.  To build a Pascal’s triangle, we start with a ‘1’ at the top row and later continue the pattern such that each number is the sum of the two other numbers directly above it.

pascal triangle

Now if you are wondering as to how can we learn fractions using this? Here you go.

The kids were asked to arrange the cups and then try to share 1 cup of water between 2 cups, here they explored “1/2” (fraction) in its physical form which they themselves arrived at. Later they used different arrangements and tried to pour in water, sharing it among multiple cups.


Students were completely engaged in the activity and it was interesting to see them explore and discover for themselves the various other fractions (1/3 rd, ¼ th, ¾ th so on and so forth). They were engrossed in discussions about the amount of water in each cup.


“Oh this could be less than half. Is it 1/3 or 1/4?”

“Why is the cup in the middle getting more water?”

“Can we equally share among 4 cups?

Through this activity not only did our students learn fractions but also got introduced to Pascal’s triangle. I must say the session was fun for both the students and the facilitator, by letting the students explore themselves and guiding them by asking the right questions I was able to make their learning enjoyable.  Overall a very satisfying day at NumberNagar I must admit.

– Jyothi Giri, Facilitator, BRAINSTARS

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