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Practice sheet · Dance Path · Lens 1: Math

Tempo & counts

Practice for The Math of Dance: counting music, tempo, syncopation, rhythm cycles, symmetry, stage geometry, turns and choreography (pp.8–16), plus Algebra A1–A2 (pp.17–18).
Warm-upCoreLevel Up
Name Date Time I spent
Remember

Seconds per beat = 60 ÷ BPM. Beats = minutes × BPM. An eight-count is 8 beats. One full turn = 360°.

Reflect across the centre line: (x, y) → (−x, y). Rotate 90° anticlockwise: (x, y) → (−y, x). Diagonal of a stage: Pythagoras.

Warm-up

One step

Beats, counts and turns.
1

Beat length

A song is 150 BPM. How long is one beat?

2

Eight-counts

A 3-minute song is 128 BPM. How many beats? How many eight-counts?

3

Mirror and spin

A dancer stands at (4, −1). Where is the mirror spot across the centre line? Where after a 90° anticlockwise rotation about centre?

4

Turns

A dancer does 2½ turns. How many degrees is that?

Core

Two or three steps

Count it out loud if it helps.
5

Phrase time

A routine is 10 eight-counts at 100 BPM. How many beats, and how many seconds?

6

Clave

The rumba clave hits on counts 1, 4, 8, 11 and 13 of 16. Find the gaps (back round to 1). What percent of hits miss the main beats 1, 5, 9 and 13?

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Dance Path · Unizon · PracticeTempo, counts & stage geometry
7

Tihai

A tihai repeats a 3-beat phrase three times with 2-beat gaps. How many beats? Started on beat 1, where does it end? Where must it start to land on beat 17 (sam)?

8

Diagonal cross

A stage is 12 m wide and 9 m deep. How long is the corner-to-corner diagonal? How many 0.75 m steps is that?

9

Fouettés

A dancer does 32 turns in 20 seconds. How many turns a second? How many degrees a second?

10

Orders

Five dancers enter one at a time. How many orders are there? A phrase has 3 counts, and each count can be any of 5 moves. How many different phrases are there?

Level Up

Equations

A1–A2 (pp.17–18).
11

Find the tempo

Time = 60 × beats ÷ BPM. A 96-beat section lasts 45 s. Solve 45 = 60 × 96 ÷ BPM.

12

Find the counts

At 96 BPM, a section lasts 90 s. Solve 90 = 60c ÷ 96. How many eight-counts is that?

13

Missing side

A diagonal cross is 17 m; the stage is 15 m wide. Solve 15² + b² = 17² for the depth.

14

Circle formation

12 dancers each need 3 m² inside a circle. Solve πr² = 36 for the radius.

Make your own problem

Your turn to be the choreographer

  1. Pick a song and find its BPM.
  2. Write a question about its beats, counts, turns or a floor pattern.
  3. Solve it, then try the phrase: does it fit the music?

My problem, and my worked answer:

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Dance Path · Unizon · PracticeTempo, counts & stage geometry

Try every problem first, then check here. Wrong answers are useful: find the step where your work and the key split apart.

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Answer key

Worked solutions. Tempos and stage sizes are example numbers.

Warm-up
1
0.4 s 60 ÷ 150 = 0.4.
2
384 beats · 48 eight-counts 3 × 128 = 384; 384 ÷ 8 = 48.
3
(−4, −1) · (1, 4) Mirror: change the sign of x. Rotate: (x, y) → (−y, x) = (1, 4).
4
900° 2.5 × 360 = 900.
Core
5
80 beats · 48 s 10 × 8 = 80; 80 × 60 ÷ 100 = 48.
6
gaps 3, 4, 3, 2, 4 · 60% They add to 16. Only 1 and 13 are main beats: 3 of 5 = 60% off the beat, which is syncopation.
7
13 beats · ends on 13 · start on 5 3 + 2 + 3 + 2 + 3 = 13. A 13-beat tihai ends 12 beats after it starts: 17 − 12 = 5.
8
15 m · 20 steps √(12² + 9²) = √225 = 15. 15 ÷ 0.75 = 20.
9
1.6 turns/s · 576°/s 32 ÷ 20 = 1.6; 1.6 × 360 = 576.
10
120 · 125 5! = 5 × 4 × 3 × 2 × 1 = 120. 5 choices for each of 3 counts: 5 × 5 × 5 = 5³ = 125.
Level Up
11
128 BPM BPM = 60 × 96 ÷ 45 = 128.
12
144 counts · 18 eight-counts c = 90 × 96 ÷ 60 = 144; 144 ÷ 8 = 18.
13
8 m b² = 289 − 225 = 64 → b = 8.
14
r ≈ 3.39 m r² = 36 ÷ π ≈ 11.46 → r ≈ 3.39.
Make your own: turn everything into beats first, then into seconds, and sketch the stage before you use Pythagoras.
Dance Practice · Dance Path · UnizonAnswer key