GENERAL SLOW MOTION
ABOUT THIS CHALLENGE In this challenge, students will explore the math OK Go used to create parts of the video “The One Moment.” They will learn about frame rates and how they connect to math concepts. Students will have the opportunity to review rates of change, multi- digit division, and fraction multiplication through practice equations. Then, they will be able to apply their knowledge of these concepts to create a slow-motion music video! CONTENT AREA Grade Levels: 5-6 Content Area: Mathematics: Pre-Algebra, Algebra Context for Learning: Before starting this challenge, students must be somewhat familiar with multiplication, fractions, multiplication of fractions, long division, graphing, and using equations to make calculations.
TOPICS ACADEMIC LANGUAGE Units Unit Conversion Frame Rate Units Rates Long division Beat Slow Motion Multiplication of Graphing Rates Fractions Equations
EDUCATOR GUIDE | PAGE 1 www.OKGoSandbox.org STANDARDS Common Core State Standards: CCSS.MATH.CONTENT.5.NBT.B.5: Fluently multiply multi-digit whole numbers using the standard algorithm. CCSS.MATH.CONTENT.5.NBT.B.6: Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. CCSS.MATH.CONTENT.5.MD.A.1: Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. CCSS.MATH.CONTENT.6.RP.A.3.D: Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. 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:
Solve multiplication and division equations that use fractions and rates.
Use knowledge of variables to set up rate equations to solve for one variable.
Apply their prior knowledge to solve two-digit division equations.
Employ graphing knowledge to practice real-life applications.
Effectively complete unit conversion word problems.
MATERIALS
Paper Metronome or metronome app
Pencil Reactive object (balloon, gum, paper, basketball… be creative!) Device with a slow-motion camera
EDUCATOR GUIDE | PAGE 3 www.OKGoSandbox.org INSTRUCTIONAL DELIVERY
OPENING ACTIVITIES/MOTIVATION
Go to OKGoSandbox.org and play the “The One Moment” music video (4 min 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.
Once students have shared a few ideas, show the “Making The One Moment” video (5 min 25 seconds). In this Q&A, OK Go explains the creative and scientific processes they went through to create their music video. Discuss rates with students, informing them how two different measurements can relate, one of the measurements most often being time. This would be a good time to introduce slow motion in the context of frame rates.
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). 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: INQUIRY
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. Explain and/or practice calculations using rates with the students. Emphasize that rates are a particular kind of fraction so problems can be set up using fractions to calculate solutions. Students will be solving for a specific variable within the rate problems. Briefly explain how variables can act as placeholders for values. Mimic the example problem setup from the “The One Moment of Math” video to help with this explanation. Support the students in setting up and solving rate problems, as well as multiplication and division using rates, in order to find an answer with a single unit. Assist the students when necessary to find rates that represent seconds between events by setting up and solving long division equations. Prompt students to set up equations that would help them find the number of frames for specific reaction events. Aid the students in practicing graphing a real-life scenario. Guide them to analyze what the graph means and represents for the scenario. Discuss real-life scenarios of which factors could change a rate using the feather- balloon example. Explain how weight impacts how quickly something falls, and how this impacts the times for events.
EDUCATOR GUIDE | PAGE 5 www.OKGoSandbox.org PART TWO: CHALLENGE
Use a slow-motion camera to create a short video as a class! Warm up your class with the exercise “Pass the Pulse.” To do this, have students stand in a circle around the classroom and hold hands. Whenever everyone is ready, ask them to close their eyes and wait to feel the person to their left squeeze their hand. When they do, ask the student to squeeze the hand of the person to their right. The squeeze, or “pulse,” should make it all the way around the circle. This will warm students up to the idea of waiting for their neighbor to cause an event before they cause their own event.
Next, use OK Go’s music video “The One Moment” to make a slow-motion video of your own. Because the tempo of the song is 62 beats per minute in slow motion, the real-time video will be 250 beats per minute, found through frames per second and slow-motion calculations.
Choose a reactive object. Each student will have the opportunity to make their own object react, so choose something that you can get in bulk (balloons, glowstick, paper tear, ball bounce, clapping, etc.).
Set a metronome to the beat of the song (250 beats per minute). If this seems too fast, the metronome can be played at 125 to have half as many events occur. While the metronome is playing, have the teacher press record on their slow-motion camera device. The teacher will count off to begin the events. When the teacher indicates so, the first student will make their object react. Students will each cause an event one or more beats after the student next to them.
Once each student has made their object react, stop the video, re-watch it as a class, and reflect! Repeat the process if you would like to.
EDUCATOR GUIDE | PAGE 6 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 8). Closure: Bring the class back together for a class discussion about 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 the slow-motion video? How did “Pass the Pulse” help us make a slow-motion video? What else can we calculate using fractions? What else can we divide using a large number?
EDUCATOR GUIDE | PAGE 7 www.OKGoSandbox.org STUDENT GUIDE ANSWER SHEET
Part One Part Two (1) Frames per second (8a) 3.75 seconds/event (8b) 2.727 seconds/event (2a) 24 frames (8c) 5 seconds/event 1 second (8d) .968 seconds/event
(2b) 240 frames (9a) 25 frames/event 1 second (9b) 7.336 frames/event (9c) 12 frames/event (3a) 30 frames (9d) 29.01 frames/event 1 second (10) Linear line graph. Balls on x-axis, time (3a) 550 frames on y-axis. 1 second (11) The graph is linear. (4) Using unit conversion 550 fps = 8250 still frames (12) Yes, the time between the ball releas- 30 fps = 450 still frames es is equal.
(5) 24 fps = 360 still frames (13) Answers vary. 240 fps = 3600 still frames
(6) .81 seconds
(7) 60 seconds
EDUCATOR GUIDE | PAGE 8 www.OKGoSandbox.org SLOW MOTION WORKSHEET: PART ONE OK Go is looking for a mathematician to join the team in filming another slow-motion music video. Are you up for the challenge? (1) In making the “The One Moment” music video, Damian shows us a jumping video he filmed in 24 fps, then 240 fps. FPS is language of the film industry. What do you think FPS stands for? Answer: FPS =
(2) How would the rates 24 fps and 240 fps be written mathematically? Explain the mathematics you are using. Don’t forget to label your answer! Answer: 24 fps =
240 fps =
STUDENT GUIDE | PAGE 9 www.OKGoSandbox.org (3) The published “The One Moment” music video was played back at a slow-motion rate of 30 fps after it was filmed by a high speed camera at a recording rate of 550 fps. How would you write these rates mathematically as a labeled fraction with units? Answer: Frames → frames
Second(s) second(s)
(4) The series of ball events that Damian explains takes a total of almost 15 seconds with the beats of the real-time music. Find how many still frames occur over 15 seconds, for both the high speed 550 fps filming camera and the slowed down 30 fps slow-motion rate. How would you do this? (Hint: use unit conversions!) Calculate:
(5) If you filmed the same series of ball events across 15 seconds, your phone camera frame rate would be the same ones Damian jumped to in the “Making The One Moment” video: 24 fps as the slow-motion playback rate and 240 fps as the filming rate. How many still frames are captured for every 15 seconds of video filmed at those frame rates? Calculate:
STUDENT GUIDE | PAGE 10 www.OKGoSandbox.org Slow motion acts to elongate time. 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: 30 frames = 120 frames → x= 4 seconds 1 second = X seconds
(6) 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:
(7) 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 SLOW MOTION WORKSHEET: PART TWO
(8) There were a few different events and bursts during the “The One Moment” video, and we can find the rates for each occurrence. How many seconds occur between each event? What units would you use to describe these answers? Calculate: 8 events 30 seconds =
22 events 60 seconds =
3 events 15 seconds =
62 events 60 seconds =
STUDENT GUIDE | PAGE 12 www.OKGoSandbox.org (9) Once we know the number of seconds per event, we can also find the number of frames for each event. What mathematical operation would you use? What units would you use to describe these results? Calculate: .05 seconds 5 frames → x = 1 event 1 second
1.048 seconds 7 frames → x = 1 event 1 second
1.26 seconds 10 frames → x = 1 event 1 second
.967 seconds 30 frames → x = 1 event 1 second
(10) Damian explained that each falling ball of paint was released after a fixed time period so that they hit on each beat of the song, and the beats are evenly spaced. Here’s a table that models at how many seconds each ball was released. This data is edited and based off of filming at 550 fps.
Ball: 1 2 3 4 5 6 7 8 9 10
Time: 0 .97 1.94 2.91 3.88 4.85 5.82 6.79 7.76 8.73
Let’s plot this process. Use a piece of graph paper or plot your points on the next page.
STUDENT GUIDE | PAGE 13 www.OKGoSandbox.org (11) What do you notice about the line?
(12) Does this match what we know about the time between ball releases?
(13) In the music video, the balls were filled with paint so colors would burst out of them when they broke. What do you think would happen if instead we fill balloons with colored feathers and drop them?
STUDENT GUIDE | PAGE 14 www.OKGoSandbox.org