ADVANCED SLOW MOTION

ABOUT THIS CHALLENGE In this challenge, students will replicate the process OK Go used to create parts of their music video “The One Moment.” Learners will practice and prepare by applying math to the concept of slow motion. Students will then choose a song to plan equally timed events in slow motion, calculate out how quickly that event should occur in real time to be accurate in slow motion, then record their own slow-motion video! CONTENT AREA Grade Levels: 9-12 Content Area: Mathematics: Number and Quantity, Functions, Statistics and Probability Context for Learning: Before starting this lesson, students should be familiar with rates, rates of change, formulating equations, and using variables.

TOPICS ACADEMIC LANGUAGE Unit Conversions Units Frame Rate Rates Average Rate of Rates Beat Change Graphs Tempo Frame Rates Slope Rate of Change Functions

EDUCATOR GUIDE | PAGE 1 www.OKGoSandbox.org STANDARDS Common Core State Standards CCSS.MATH.CONTENT.HSF.IF.B.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. CCSS.MATH.CONTENT.HSS.ID.C.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. CCSS.MATH.CONTENT.HSN.Q.A.1 Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. CCSS.MATH.CONTENT.HSA.CED.A.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. CCSS.MATH.CONTENT.HSN.Q.A.2 Define appropriate quantities for the purpose of descriptive modeling. CCSS.MATH.CONTENT.HSF.IF.B.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Note: This lesson plan may align with other sets of standards not included here.

EDUCATOR GUIDE | PAGE 2 www.OKGoSandbox.org LEARNING OBJECTIVES

Students will be able to:

Describe what a frame rate is within the context of the activity.

Use conversions to help understand the context of the problems.

Calculate the rate at which an event occurs in real time and in slow motion.

Solve problems that use constant rates and rates of change.

Use prior knowledge to model a linear equation based off of a set of data points.

Graph data from a table and compare the slope to rate of change.

MATERIALS

Paper Device with a slow-motion camera

Pencil Metronome or metronome app

Calculator Event object (balloon, gum, paper, basketball… be creative!) Internet access

EDUCATOR GUIDE | PAGE 3 www.OKGoSandbox.org INSTRUCTIONAL DELIVERY

OPENING ACTIVITIES/MOTIVATION

Show the “The One Moment” music video (4 minutes and 12 seconds). Ask students how they think this video was made so precisely to match the music. Then, lead a discussion where students identify parts in the music video where STEM and art concepts are being used collaboratively.

Next, show students the “The One Moment of Math” video (4 minutes and 34 seconds), which explains the specific math calculations required to create OK Go’s music video “The One Moment.”

Some Vocabulary for this Lesson: The number of still photos taken per second in a video is called frame rate. For example, the slow-motion frame rate is 30 frames per second, meaning there are 30 still photos taken in one second that can are combined to make a video. Beat is the foundation of the rhythm (ex: what you would tap your foot to at a steady pace). For the purpose of making the slow-motion activity possible to create in real time, OK Go and your students will make the beat half of the tempo. Tempo is the speed of the music. The tempo always directly correlates with the beat. In this activity, the tempo is twice the speed of the beat. Slow motion is the action of showing film or playing back video more slowly than it was made or recorded, so that the action appears slower than in real life. One thing to remember is that slow motion is relative to the speed a video was recorded at. For example, if a slow motion video was recorded at 550 fps and played back at 30 fps, the video will be 18.3 times longer than the time it was recorded.

The change in one variable in relation to another variable, such as beats per minute or frames per event is called rate of change. This is often represented by the slope on a line. Rates are different units that can be used to measure a relational change in an event (ex: seconds per minute, fingers per hand, inches per foot, frames per event).

EDUCATOR GUIDE | PAGE 4 www.OKGoSandbox.org PART ONE: LEARNING THE BASICS

Explore the mathematical processes behind OK Go’s music video. Guide the students through the associated worksheet. Read through the worksheet and the answers to prepare to help students. It is recommended to have a copy of the worksheet in hand while teaching this lesson. It could be helpful to discuss vocabulary with students, as well as variables that we will be looking at (such as beats per minute or frames per second). Practice rate calculations with students by having them complete Part 1 of the student worksheet. Students will be solving for a specific variable within the rate problems. Mimic the example problem setup from the “One Moment of Math” video to help with this. Have the students graph the data provided in the table. Then have them make observations about the graph, particularly the slope of the graph. Have the students create a linear equation based off of a set of data points provided. Assist when needed to help them solve for specific solutions using this equation. (Teachers: prompt students to create a function rather than using basic addition.) Explain what rates of change are and how they can relate to the events in the slow-motion video. Briefly describe that there are two different kinds of rates of change, constant and varying, but that this worksheet will only cover constant rates of change.

EDUCATOR GUIDE | PAGE 5 www.OKGoSandbox.org PART TWO: PRACTICE

Apply math concepts to plan a sequence of events to match a song of choice. Prompt the students to choose one song and at least one object they want to use for an event for their video (the object can be provided by the teacher or by the students themselves as part of a two-day activity). Have students go onto the internet and search for the song tempo (the tempo divided in half will be called the beat for ease of recording in real time). If students are having a hard time choosing a song, some OK Go songs and tempos are: Upside Down and Inside Out (tempo-93), This Too Shall Pass (tempo-160), the Writing’s On The Wall (tempo-103). Assist students when needed to clearly define the important variables on their worksheet for creating their own videos: 1 event per beat, frames per second (real time), frames per second (slow motion), tempo, beats per minute (½ of the tempo). Verify the frame rates for filming on the available recording devices. Support the students in finding the time in seconds between each event (T) of the slow-motion video, as well as the corresponding number of frames (Q). Have the students find the time in seconds that would pass between each event of the real-time recording (J), and have them compare this to their slow-motion findings. Aid the students if needed in calculating the beats per minute of the real-time recording for their song (H). Optional: Facilitate a peer review. Have students list all of their variables in the top left corner of a blank piece of paper and trade with a partner. Ask students to repeat this process with another student’s variables. Once they are finished, have both the creator and duplicator of the project compare answers to see if they are the same.

EDUCATOR GUIDE | PAGE 6 www.OKGoSandbox.org PART THREE: CHALLENGE

Students create their own slow-motion videos! Use slow-motion cameras (found on most smart phones) and math equations to create a short video! Have the class separate into groups of 4 or more. Each student within the group of 4 is creating their own slow-motion video. They will have the opportunity to be the “group leader” for their video, using the other 3 members to help create events within their real-time recording. This way, each recording has events happening on at least 4 beats. Start by having each student calculate the beats per minute for the real-time recording of their song. Explain to students the process they will go through to create their slow-motion videos. They will set a metronome (can use a metronome app) to the real-time beat of the first student’s song. While the metronome is playing, the first student will press record on their slow-motion camera device. They will create the first event. When the first student indicates (by counting, signaling, etc.), the following 3 students will create an event on the next 3 consecutive beats. When the first student presses stop on their camera, they should have a slow-motion video with 4 correctly timed events in it. Repeat this process with all students in the group until 4 or more short videos have been created. Ask a few students to share with the class! Have them pull up the audio for their song on the internet and play it. At the same time, have them play their slow-motion recording for the class. If calculations were done correctly, the slow-motion recording should be at an even tempo with the song tempo.

EDUCATOR GUIDE | PAGE 7 www.OKGoSandbox.org ASSESSMENT

Evaluation of Learning Objectives: To demonstrate their understanding of the topics included in this lesson, have the students turn in their completed student worksheet and check the answers (answer sheet provided on page 9). Closure: Bring the class back together to discuss the answers to the worksheet, as well as reflecting on their learning through large or small group discussion. Share: Reach out to OK Go Sandbox through email or social media at @okgosandbox and share your videos of this challenge with us! Have any feedback? We want to hear it! Discussion Questions: What was challenging about creating slow-motion videos? What are examples of rates of change that we use today? What was helpful or challenging about working with the song you chose? Which of your classmates’ videos worked well with this activity? Why?

EDUCATOR GUIDE | PAGE 8 www.OKGoSandbox.org STUDENT GUIDE ANSWER SHEET

Part One Part Two (1a) 8,250 frames Calculations and observations will vary (1b) 450 frames based on students song choice and events. (2a) 360 frames (2b) 3,600 frames

(3) x=.81 seconds

(4) x= 60 seconds

(5) Observations made by students

(6) 22nd crash = 128.694 seconds 50th crash = 155.770 seconds

(7) .967 seconds

(8) .967 seconds, constant.

EDUCATOR GUIDE | PAGE 9 www.OKGoSandbox.org SLOW MOTION WORKSHEET: PART ONE

(1) The series of ball crashes that Damian explains in the video takes a total of almost 15 seconds with the beats of the real-time music. To make filming easier, we need to find the amount of still frames that occur over 15 seconds, for both the high-speed 550 fps filming camera and the 30 fps slow-motion rate. How would you do this? 550 fps = Frames 30 fps = Frames

(2) If you filmed the same series of ball crashes across 15 seconds, your phone camera frame rates would be the same ones Damian jumped to in the “The One Moment Q&A” video: 24 fps as the slow-motion rate and 240 fps as the filming rate. How many frames are captured for every 15 seconds of video filmed at those frame rates? 24 fps = Frames 240 fps = Frames

STUDENT GUIDE | PAGE 10 www.OKGoSandbox.org Slow motion seems to elongate time. In a normal video, we are just watching more frames in the same amount of time. When the frame rates are changed, time seems to slow down. “The One Moment” music video took about 4 seconds to film, but the slow-motion video is 4 minutes long. For example, if we have a 1 second video at 120 fps and slow it down to 30 fps, the resulting video would take 4 seconds. Example: X seconds = 120 frames → x= 4 seconds 1 second = 30 fps

(3) If all of the ball crashes occur in 15 seconds in the slow-motion rate of 30 fps, how long would the video of ball crashes be at the recording rate of 550 fps? Calculate:

(4) What if we filmed another phone video of you jumping for 6 seconds? If we filmed at a recording rate of 240 fps and slowed down the film by changing it to a slow-motion rate of 24 fps, how many seconds would you be jumping in slow motion? Calculate:

WOW, that’s a lot of jumping!

STUDENT GUIDE | PAGE 11 www.OKGoSandbox.org In the “The One Moment of Math” challenge video, you saw the times between the balls filled with paint falling and crashing. These were constant rates. In the song, the beats, or crashes, are .967 seconds apart. To account for the slow motion, the real-time drops had to fall approximately .053 seconds apart. Each ball crash relates directly to its time in the final version of the video. Here’s a table to help display that.

Ball: 1 2 3 4 5 6 7 8 9 10

Time: 108.387 109.354 110.321 111.288 112.255 113.222 114.189 115.156 116.123 117.090

(5) Graph the data in the table above on graphing paper, or on the graph provided below. Make sure you label your graph! What are two observations you can make after graphing time and ball drop? What do you notice about the slope of your graph?

Observations: 1)

2)

Slope:

STUDENT GUIDE | PAGE 12 www.OKGoSandbox.org (6) The band wants to extend their song a bit and repeat a lyric, so they add 12 more ball crashes for a total of 22. At what time in the song would the last ball fall? If they were to drop 50 balls, what time would the last ball drop? Calculate: t=time, b=ball

22nd crash = seconds 50th crash = seconds

Other than frame rates and functions, another way we can think about these important gaps of time is by looking at the average rate of change between them. This helps us to describe what happens between events, so for any ball release in the video, we know information about the timing. Functions can be written as f(x), because the notation f(x) means a function of the variable x. We can look at any two points and compare them using the rate of change equation:

f(b) - f(a) Rate of Change = b - a

In this case, our rate of change equation would look more like this:

t2 - t1 Rate of Change = b2 - b1

STUDENT GUIDE | PAGE 13 www.OKGoSandbox.org Pick any two pairs of ball releases (b1,t1) and (b2,t2) and compare your rate of change results.

What are your t1 and t2 values? t1 = t2 =

What are your b1 and b2 values? b1 = b2 =

(7) What is your calculated rate of change? Answer:

(8) In order to make sure the rate of change is constant between all variables, repeat the above process with a different pair of points. Do you get the same value? Should you get the same value? What does this say about these rates? What is your calculated rate of change? How does this relate to the slope of your graph? Answer:

STUDENT GUIDE | PAGE 14 www.OKGoSandbox.org SLOW MOTION WORKSHEET: PART TWO

OK Go is shooting a new slow-motion music video tonight and needs YOUR help planning it! Work in small groups to plan your videos. (Reminder: make sure you label your numbers with units!) Initial Brainstorming: What song are they making a slow-motion video to? (Make sure to get the song approved by your teacher before continuing.) Song:

What is the tempo of that song? Tempo:

OK Go wants to time events to match the beat of the song. To make recording in real time possible, the beat of the song will be the tempo divided in half. What is the beat of the song, and what kinds of events will occur on each beat? Beat:

STUDENT GUIDE | PAGE 15 www.OKGoSandbox.org What will these events look like? List some ideas and examples that you could film. Brainstorm: 1. Example: classmate jumping 2. 3. 4. 5. 6. 7. 8. 9. 10.

Math Behind the Music Video The slow-motion camera OK Go used to record their video has a frame rate of 550 fps when recording in real time, and 30 fps when played in slow motion. The time between each event in the slow-motion music video “The One Moment” was .967 seconds per event. Your recording frame rate is 120 frames per second or 240 frames per second, depending on your recording device. Ask your instructor or search online to verify this number. Your slow-motion rate is 30 frames per second. How many seconds will there be between every event of your slow- motion music video? Calculate:

Seconds

STUDENT GUIDE | PAGE 16 www.OKGoSandbox.org The cameraman needs to know the number of frames between every event in order to make sure the video is correct. How many frames are there for each event that occurs? Calculate:

Frames per event Because the band needs to be able to match the events from the slow motion video to a real-time video, they need to know how many seconds will occur between every event while recording. For the song you chose, how many seconds per event will there be in real time? Calculate:

Seconds per event OK Go is almost ready to film! How many beats per minute will be in the real-time recording of the song you chose? Calculate:

Beats per minute Now, list all your variables on the next page and keep it handy while you film your very own slow-motion music video!

STUDENT GUIDE | PAGE 17 www.OKGoSandbox.org SLOW-MOTION MUSIC VIDEO

Directed by:

Use this page to record the calculations you did on the previous pages as a quick reference for when you record your slow motion music video! Events per beat

Beats per minute (bpm)

Frames per second (fps) slow motion

Frames per second (fps) real time

Seconds between events

Seconds per event

Frames per event

Now you’re ready to film! Set a metronome or use a metronome app to the real-time beat of the first student’s song in your group. While the metronome is playing, have the first student press record on their slow- motion camera device. They will create the first event. When the first student indicates (by counting, signaling, etc.), the following 3 students will create an event on the next 3 consecutive beats. When the first student presses stop on their camera, they should have a slow-motion video with 4 correctly timed events in it. Repeat this process until all your group members have finished their slow motion music videos!

STUDENT GUIDE | PAGE 18 www.OKGoSandbox.org