In the year 2000, New York City theatergoers were treated to an especially mathematical season. That year marked the premiere of both Fermat’s Last Tango, a musical based on a centuries-long quest to prove Fermat’s Last Theorem, and Proof, a play about a breakthrough mathematical proof that a father leaves behind to his daughter.
The people writing and directing those shows had to deal with math in an unusually direct way. But even when the show contains no theorems or proofs, there is still a lot of math to be found. People involved in different aspects of any production, such as stage designers, lighting designers, and theater architects, all wrestle with some complicated math problems. On a Broadway stage, where shows can sell thousands of tickets and cost millions of dollars, the stakes can get very high.
In the video “Math Meets Broadway: Teaching Math Through Theater,” we go behind the scenes of the Broadway musical Water for Elephants and see how math was used to make the story come to life every week. The video focuses on a few applications of math to theater, such as modeling sight lines or calculating how much light will come from a source. Teachers can use the video as a fun way to start a class, especially if teaching a lesson that connects math and theater. We’ve provided a few ideas below.
5 activities to teach math through theater
Activity 1: Produce a show (Grades 1 and up)
Students can take on the role of producer, conducting a survey to see what people want to see and interpreting the data to decide what to produce. Key math skills practiced:
- Represent a simple data set with two categories (Grades 1–2)
- Find a percent of a quantity as a rate per 100, and solve problems involving the percent (Grades 6–8)
- Calculate and interpret a confidence interval (Grades 8 and up)
For people who run theaters, one of the hardest details is figuring out what show to produce in the first place. A common question for many theaters is should we produce a play or a musical? A play (usually) doesn’t require the actors to sing, whereas a musical has the actors telling part or all of the story through songs with musicians playing along.
Ask students if they have seen any live plays or musicals and find out what they prefer and why. Consider showing short online clips from shows they may be familiar with, such as ones the school has produced; shows currently popular; or theatrical adaptations of TV shows, movies, or other franchises they know about.
For students in Grades 1–8, you can conduct a survey. What would you rather see at your local theater each month? A play or a musical? Then, facilitate a discussion around survey results. Here are possible questions you could ask:
- Which choice was more popular?
- What percent of the class voted on musicals?
- If your class represented a town of 1000 people, then about how many people in the town would vote on musicals? Why?
- If the theater puts on one show every month for your town, how many of them should be plays and how many should be musicals? Why?
For older students, the Into Algebra 2 activity below should only take a few minutes to complete and has students calculating 95% and 99% confidence intervals about a community arts center survey on plays vs. musicals.
Activity 2: Prop director (Grades K–12)
In this activity, students build and analyze a three-dimensional model. Key math skills practiced:
- Identify and compose three-dimensional shapes (Grades K–1)
- Represent three-dimensional figures using two-dimensional nets and find the surface area of these figures (Grade 6)
- Solve real-world problems involving the volume and surface area of three-dimensional objects (Grade 7)
In theater and film, props (short for “property”) refer to objects used in a production and can be as small as an earring or as large as a car. Many shows have a prop director (or prop master or property master) who oversees supplying and storing props.
One prop in Water for Elephants is a barbell with weights on it that an actor lifts to show how strong the character is. Unlike a real barbell, the prop must be light enough that it can be easily moved and used without hurting anyone. Consider these lesson plans that have students thinking critically about making a prop barbell.
- Grades K–2: Have students discuss what 3-D shapes are needed to create a barbell with weights. Provide materials like foam balls, cardboard rolls, and markers so that students can make one that looks like it would be heavy but really isn’t. Then have students practice their acting skills. How would they lift it?
- Grades 3–6: Either on paper or using a computer, have students design a barbell with weights. It should look realistic but not weigh more than a few pounds. What materials would they use to make it? For a longer activity, students could include precise dimensions and determine how much of each material is needed.
- Grades 7 and up: Extend the activity described for Grades 3–6. How much will the materials cost, and how much will it cost in total? How would they design it differently if their budget were $5? What if it were $100? $10,000?
Activity 3: Create a set piece (Grades K–12)
In this activity, students build and analyze a different three-dimensional model. Key math skills practiced:
- Identify and compose three-dimensional shapes (Grades K–1)
- Plot and interpret data (Grade 5)
- Recognize and represent proportional relationships between quantities (Grade 7)
The stage designers for Water for Elephants needed to construct a set piece that looked like a moving train for the audience. The train was made up of different parts that could be moved around on stage and look like different parts of the train as needed. You can task students with building their own miniature train using materials that you have available, such as toothpicks, craft sticks, glue, paper, scissors, markers, and glitter.
- Grades K–2: Have students make a list of everything needed to build their model train. How many toothpicks? How many pieces of paper? Then, task students with creating a second part of the train that can connect to what they already built. What shapes allow their trains to connect?
- Grades 3–5: What train can hold the most weight? Use different toys and objects to see how much each model can support without breaking. Which train can hold the most weight, and why? For a more advanced investigation, have students weigh each train beforehand and plot the train’s weight on one axis and the amount of weight it can support on the other axis. Is there a pattern?
- Grades 6 and up: Task students with making scale model drawings of their trains. Have them draw their trains proportional to what they built, and ensure they include a key so a set designer would know how to build them to scale (for example, 1 inch = 2 feet). What materials would be needed, and exactly how much of each material is needed?
Activity 4: Light the Lights (Grades 5–8)
In this activity, students draw a model using proportional reasoning and with precise measurements. Key math skills practiced:
- Multiply decimals to hundredths using drawings and other strategies (Grade 5)
- Solve problems involving surface area of three-dimensional objects (Grade 7)
- Model with mathematics (all grades)
The activity lists three light sources with different features and multiplication factors. Students are tasked with drawing how the light will appear on the stage to scale.
There are different ways to complete the activity. Students could invent a show and draw a scene as a way to tap into other interests and connect this activity to ELA, art, and drama skills. Alternatively, all students can be given a show and scene to shorten the activity and keep it focused on the core calculation and scale model drawing.
You can think of theater lights as a cone with a vertex at the light source and the base showing what’s being illuminated. In Activity 4, students are tasked with drawing a theater light with accurate proportions.
Activity 5: Build a theater (Grades K–12)
In this activity, students use properties of circles, triangles, and other shapes to investigate different mathematical questions. Key math skills practiced:
- Model with mathematics (all grades)
- Identify and describe relationships among central angles, inscribed angles, and circumference (high school)
Ideally, there is an actual theater or auditorium in your school that students can go to. The video mentions the C-value in theater architecture, a value that older students can calculate and discuss how different measurements affect how well audience members can see the stage. This value is complicated to obtain and requires taking careful real-world measurements. Use online resources, such as these stadium guidelines from FIFA, to determine how to calculate the C-value.
Younger students can analyze a performance space in different ways, perhaps in coordination with a lesson on drama:
- What shapes do you see in the auditorium? Consider both up close and far away. (Grades K–1)
- How many rows of seats are there? How many seats are in each row? How could you estimate the total number of seats? (Grades K–3)
- What information would you need to measure the angle of a sightline, and what are different ways you could interpret it? (Grades 4–5)
Even if you can’t take a field trip to the theater, the Spark Your Learning activity from Into Geometry below is a quick activity for students in Grades 8 and up to practice asking mathematical questions about an outdoor amphitheater containing semicircular rows of seats surrounding a semicircular stage.
Math in the real world: More than just theater
Once you know to look for it, math is found in more than just theater; it can be found everywhere. Math can be found in businesses and homes and in the food you eat, the art you see, the sports you watch and play, and the clothes you wear.
The next time you’re at a theater, pay special attention to the lights and props and look at how the seats are arranged. What math do you notice?
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