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.