4 + 4 + 4 + 4
Where is halfway?
Clap or point around Teentaal. Keep the beat steady while fitting more equal taps into each beat. Predict three and four on paper.
Grouping · fractions · rateExplore the cycle →KATHAK × MATHEMATICS · CLASSES 6–8
Rhythm,
Shape & सम.
Feel a fraction. Build a pattern.
Find your way back to the beginning.
A practical classroom project where a 16-beat cycle becomes a place to explore mathematics — with hands, voices, paper and curiosity. सम (sam, pronounced “sum”) is the first beat and a point of return.
Article by Sohini Bandopadhyay
Classroom project developed for Zalki.
Read Sohini’s introduction on NCF Help ↗
Sixteen beats. Endless possibilities.
3 × 40 minute lessons1 shared screen, or paper0 dance experience neededEvery learner can tap, point or observe
FOLLOW YOUR CURIOSITY
Try a beat.
Follow a pattern.
Start with a beat, a turn or a pattern. Tap, draw and play with the ideas below. In class, bring your discoveries together in a shared rhythm score: a grouped cycle, a three-part ending and a diagram of a reflection or rotation.
•••·•••·•••
Can you land on one?
Repeat a short tapping phrase three times. Place its rests, predict the ending, then work backwards to सम.
Sequences · reasoning · arithmeticBuild a three-part ending →↗ ✣ ↖
What changes after a turn?
Turn a paper arrow and arrange tokens. Compare total turn with final direction; test a line of reflection.
Angles · orientation · symmetryExplore shapes and turns →PREDICT → TRY → EXPLAIN
The rhythm studio.
Play with tempo, rhythmic endings and mirror patterns. Start anywhere and follow what catches your ear or eye. Preparing for class? The teacher pack has a complete lesson sequence and worked answers.
TEENTAAL · FOUR GROUPS OF FOUR
X सम / clap: 12, 3 clap: 5, 130 wave: 9
Khali marks the waved division. The beat continues; it is not a rest.
A steady beat.
More ways to divide it.
The clicks are generated timing cues. They are not a tabla recording or a Kathak composition. Sound begins only after Play.
Ask the classAt the same tempo, does double subdivision halve the length of the cycle?
Try it away from the screen
Lay out 16 tokens in four groups. Point on every beat; mark 1, 5 and 13 with a clap, and 9 with a wave. After eight complete beats, half the cycle has elapsed. Beat 9 starts the second half.
A CLASSROOM MODEL OF A THREE-PART ENDING
Three phrases. One destination.
phrase 1 phrase 2 phrase 3— rest
Each cell is one beat slot with its tap at the beginning. The final tap lands at the onset of its labelled beat. This simplified score explores tihai arithmetic; a Kathak teacher can demonstrate authentic compositions and bols.
Make a prediction.
Then test the landing.
Playback uses the tempo and visual-only setting from The cycle.
Ask the classWhy do three phrases need only two gaps? Explain the difference between counting slots and measuring time.
Our counting rule
Slots = 3L + 2G. Beat intervals from the first tap to the final tap = slots − 1. With L = 3 and G = 1, 11 slots span 10 beat intervals. Start at 7: tap 7–9, rest 10; tap 11–13, rest 14; tap 15, 16, next 1.
ROTATION · BEGIN FACING NORTH
Positive = clockwise. Negative = anticlockwise.
Ask the classAfter four whole turns, what is the total turn? Which direction does the arrow face?
REFLECTION · BUILD A TOKEN FORMATION
Make both sides correspond.
Select squares to place tokens. The line of reflection runs through the middle column. We are testing positions only, not dancers’ facing directions.
Every token at (row, column) needs a matching token at (row, 6 − column). Tokens on the centre line reflect onto themselves.
Paper works just as well
Turn a paper arrow on a desk and move counters on a drawn grid. These activities explore ideas connected with chakkars and formations. No spinning, stamping or standing is required.
Notes stay in this browser. No names needed.
Ready to explore.
WALK INTO CLASS WITH A PLAN
Ready to teach.
Ready to print.
Exact lesson timings, prompts, a learner sheet, worked answers and a simple assessment rubric. Includes a paper-only route for every activity.
01 Three 40-minute lesson plans02 Printable learner challenge sheet03 Worked answers & assessment rubric04 Inclusive adaptations & extension ideas
KEEPING THE ART IN VIEW
A starting point for connection.
Kathak brings rhythm, movement, expression and storytelling together. This project takes a few rhythmic and spatial ideas into a mathematics classroom. It does not teach Kathak technique or represent the whole art form. Invite a trained Kathak practitioner to add authentic footwork, bols and expressive context where possible.
Credits, sources and teaching conventions
Article by Sohini Bandopadhyay: Kathak and Mathematics: Exploring the Mathematical Foundations of Rhythm, Geometry, and Movement. The article was developed into this practical classroom project for Zalki, including the lesson sequence, diagrams, interactive tools and teacher resources. Read Sohini’s introduction on NCF Help ↗.
Conventions: one matra per metronome beat; equal-duration beats; fixed tempo; event slots for tihai calculations; clockwise-positive turns. Final facing direction is different from accumulated turn. The tapping patterns are mathematical exercises, not traditional tatkar.