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Practice sheet · Theatre & Shakespeare Path · Lens 1: Math

Scale & timing

Practice for The Math of Theatre & Shakespeare: box office, budgets, scale models, stage maps, lighting, sound, iambic pentameter, timing and data (pp.8–16), plus A1–A2 (pp.17–18).
Warm-upCoreLevel Up
Name Date Time I spent
Remember

Scale 1 : 25: real = model × 25. Distance between stage points: Pythagoras. A line of iambic pentameter has 10 syllables and 5 stresses. Sound travels about 343 m/s.

Revenue = price × tickets. Break even when revenue = costs. In open air, doubling the distance makes sound about 6 dB quieter. A circle graph slice = percent × 360°.

Warm-up

One step

Seats, scale and syllables.
1

House

A 350-seat theatre sells 266 tickets. What percent is full? How many seats are empty?

2

Model box

A set model is built at 1 : 25. A wall is 18 cm on the model: how tall is the real wall? A real 3 m platform: how long on the model?

3

Pentameter

A speech is 22 lines of regular iambic pentameter. How many syllables? How many stressed beats?

4

Back row

The back row is 41 m from the stage. How long does sound take to get there?

Core

Two or three steps

Sketch the stage or the timeline.
5

Budget

A $12,000 show budget is split 40% set, 20% costumes, 25% lights and sound, 10% rights and 5% extras. Find each amount and the set’s angle on a circle graph.

6

Stage map

On a stage grid in metres, an actor crosses from (2, 1) to (14, 6). How far do they walk in a straight line?

Theatre Practice · Theatre & Shakespeare Path · Unizon1/2
Theatre & Shakespeare Path · Unizon · PracticePercent, scale & timing
7

Lighting

A light hangs 5 m above and 5 m in front of an actor’s head. How long is the throw? A 30° beam spreads to what width at that distance?

8

Sound fades

An actor is 78 dB at 2 m. About how loud at 4, 8 and 16 m (open air)?

9

Show night

Curtain is 7:00 p.m. Act 1 runs 70 min, interval 15, Act 2 50. When does it end? Cast arrive 30 min for warm-up, 20 for costumes and 20 for makeup before curtain: when?

10

Chance & data

800 people enter a lottery for 160 cheap tickets. What is the chance of being picked? Of not being picked two years in a row? Reviews: 62, 70, 75, 75, 93. Find the mean, median and range.

Level Up

Equations

A1–A2 (pp.17–18).
11

Break even

A show costs $1,500 to put on, plus $2 a ticket. Tickets sell at $14. Solve 14n = 1,500 + 2n. How many to cover an extra $1,800 for lights?

12

Two prices

Adult tickets are $20 and student tickets $12. 150 tickets brought in $2,440. How many of each?

13

Best price

At price p, 200 − 5p people come (made-up). Revenue R = p(200 − 5p). Which price earns the most, and how many come?

14

Two answers

Which ticket prices make R = $1,875?

Make your own problem

Your turn to be the stage manager

  1. Pick a play, musical or school show.
  2. Write a question about its seats, budget, set scale, lighting or timing.
  3. Solve it, then plan show night backwards from curtain.

My problem, and my worked answer:

Theatre Practice · Theatre & Shakespeare Path · Unizon2/2
Theatre & Shakespeare Path · Unizon · PracticePercent, scale & timing

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

The key never prints with Print my work or Print blank. Open it to get its own Print the answer key button.

Answer key

Worked solutions. Costs, prices and the audience model are made-up examples.

Warm-up
1
76% · 84 empty 266 ÷ 350 = 0.76; 350 − 266 = 84.
2
4.5 m · 12 cm 18 × 25 = 450 cm. 300 ÷ 25 = 12 cm.
3
220 syllables · 110 stresses 22 × 10 = 220; 22 × 5 = 110 (da-DUM five times a line).
4
≈ 0.12 s 41 ÷ 343 ≈ 0.12 s.
Core
5
$4,800 · $2,400 · $3,000 · $1,200 · $600 · 144° Percent × 12,000. They add to $12,000. 0.40 × 360 = 144°.
6
13 m Across 12, back 5: √(12² + 5²) = 13.
7
≈ 7.07 m · ≈ 3.79 m √(5² + 5²) ≈ 7.07. Width = 2 × 7.07 × tan 15° ≈ 3.79.
8
72 · 66 · 60 dB Each doubling loses about 6 dB (10 × log₁₀ ¼ ≈ −6). Indoors, walls and seats change this.
9
9:15 p.m. · 5:50 p.m. 70 + 15 + 50 = 135 min after 7:00. 30 + 20 + 20 = 70 min before 7:00.
10
20% · 64% · mean 75, median 75, range 31 160 ÷ 800 = 0.2. 0.8 × 0.8 = 0.64. 375 ÷ 5 = 75; middle value 75; 93 − 62 = 31.
Level Up
11
125 tickets · 275 tickets 12n = 1,500 → 125. 12n = 3,300 → 275.
12
80 adult · 70 student If all 150 were students: $1,800. The extra $640 ÷ $8 = 80 adults.
13
$20 · 100 people · $2,000 R is a parabola with zeros at 0 and 40; the top is halfway, at p = 20. 200 − 100 = 100 people.
14
$15 or $25 5p² − 200p + 1,875 = 0 → p² − 40p + 375 = 0 → (p − 15)(p − 25) = 0.
Make your own: sketch the stage, plan show night backwards from curtain, and check that budget slices add to 100%.
Theatre Practice · Theatre & Shakespeare Path · UnizonAnswer key