First, you’ll watch a video about Jeremy Chernick, a designer at J&M Effects. You'll learn how he ended up creating effects as a career and how he uses math in his work. At the end of the video Jeremy sets up a special effects-related challenge about the algebra behind lighting high-speed effects like explosions. You may work with a partner to solve the challenge.

Before you begin, record your name(s) in the space below.

After you’ve finished this activity, you will know how to:

• Describe scenarios that require special effects technicians to use mathematics and algebraic reasoning in lighting and high-speed photography;
• Identify a strategy and create a model for problem solving;
• Compare direct and inverse variation; and
• Solve real-life and mathematical problems involving the area of a circle.

Vocabulary

Read these words and their definitions. When you see them, you may click on them to read the definition again.

• Direct variation
• Inverse variation
• Constant of variation for an inverse variation
• Aperture
• Diameter of aperture (a)
• Area of aperture (A)
• Focal length (f)
• Image plane
• F-stop (s)

We have all watched movies, music videos, and television at one time or another. You know that behind the scenes there can be hundreds of people involved in producing what you watch. Now think about the special effects in a summer blockbuster or a flashy music video. Did you know that mathematics is used in creating the special effects you see?

Discuss these questions with your partner, then record your answers in the box below. Don’t forget to save your work!

• What kinds of music videos do you like to watch? What is it about the video that you like (e.g., the artist/band, set design, costumes, location, the way it’s shot, etc.)?
• How do you think mathematics might be used in the creation of a music video?

This video features Jeremy Chernick, a special effects designer who describes how he uses mathematics to help create a high-speed explosion. Click “View” on the left to watch the video. You may want to watch the video multiple times before answering the question below.

• As you watch the video, write down a few of the ways Jeremy Chernick uses math in his work.

In the video you just watched, you met Jeremy Chernick. You learned about how he got involved in special effects, how he struggled with math growing up, and the ways he uses math in his job today. Jeremy goes so far as to say that he uses math in every effect he creates!

Describe the challenge Jeremy posed to the teams in the video. What are they asked to do?

Now it’s your turn to solve the challenge. First, click “View” on the left to open the Math in Special Effects: Take the Challenge handout. Print out the handout.

Next, click “View” on the left to explore the Take the Challenge interactive. Work with your partner to develop a strategy and complete the handout as you work through the activity.

It’s time to see how the teams in the video solved the challenge. Click “View” on the left to watch the video. Be sure to carefully observe the strategies the teams used. You may watch the video more than once if necessary. Then, answer the questions below.

• How do the teams' strategies compare to the one you used? Be sure to use evidence from your work and the video to explain your answer.
• What difficulties did you face (if any) when completing the challenge and how did you overcome those obstacles?

Now that you have developed a strategy and completed the first activity, it’s time to try another challenge. As you’ve already learned, when filming special effects, a high-speed photographer needs to control the duration and impact of light by adjusting a number of settings including frame rate, shutter angle, and f-stop. Knowing the relationship between these variables can help you figure out how to get the best shot.

In this next activity, you’ll learn how a camera setting, called f-stop, affects the amount of light coming through the lens. Click “View” on the left to open the Math in Special Effects: Try Other Challenges handout. Print the handout.

Next, click “View” on the left to explore the interactive. Work with your partner to develop a strategy and complete the handout as you work through the activity.

Reflection: Now take the time to reflect on this activity and record your thoughts. Click “View” on the left to download the Reflection handout. Print out the handout.

Instructions

Discuss the questions on the handout with your partner. Then, answer the questions on your own. Be ready to present your conclusions for a classroom discussion.

When you're finished, print out your notes from this lesson and hand them in to your teacher along with both handouts and your reflection.