Run!8 Students will practice creating and analyzing distance-time graphs by engaging in timed runs and using their collected data to plot distance-time graphs. They will recognize the slope of a line on a distance-time graph represents the object’s speed. Suggested Grade Range: 6-12 Approximate Time: 1 hour State of California Content Standards: Science Standards Grade 8: Physical Science Motion 1. The velocity of an object is the rate of change of its position. As a basis for understanding this concept: c. Students know how to solve problems involving distance, time, and average speed. f. Students know how to interpret graphs of position versus time and graphs of speed versus time for motion in a single direction. Science Standards Grades 9-12: Physics 1. Newton’s laws predict the motion of most objects. As a basis for understanding this concept: a. Students know how to solve problems that involve constant speed and average speed. Mathematics Standards Grade 6: Algebra and Functions 2.0 Students analyze and use tables, graphs, and rules to solve problems involving rates and proportions: 2.3 Solve problems involving rates, average speed, distance, and time. Relevant National Content Standards: Mathematics Common Core State Standard: 8.EE Understand the connections between proportional relationships, lines, and linear equations: 5. Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. Mathematics Common Core State Standard: 8.F.B 5. Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.
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An early version of this lesson was adapted and field-tested by Beverly Wiegand, a participant in the California State University, Long Beach Foundational Level Mathematics/General Science Credential Program
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Mathematics Common Core State Standard: 7.RP.A 2d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate. Next Generation Science Standards: MS-PS2-2. Plan an investigation to provide evidence that the change in an object’s motion depends on the sum of the forces on the object and the mass of the object. [Clarification Statement: Emphasis is on balanced (Newton’s First Law) and unbalanced forces in a system, qualitative comparisons of forces, mass and changes in motion (Newton’s Second Law), frame of reference, and specification of units.] [Assessment Boundary: Assessment is limited to forces and changes in motion in one-dimension in an inertial reference frame and to change in one variable at a time. Assessment does not include the use of trigonometry.] Lesson Content Objectives: Accurately use a stopwatch to collect data for timed runs. Use a table to organize the collected data. Create and compare distance-time graphs for different travel modes (running, walking skipping, etc.). Make inferences from the distance-time graphs to determine their quickest and slowest travel modes. Materials Needed: One copy per student of the “Run! Warm Up” activity sheet (included) One copy per student of the “Run! Data Record Sheet” (included) One piece of graph paper per student One ruler per student One stopwatch for each pair of students Masking tape to mark the beginning and end points of the run distance Space to run
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Summary of Lesson Sequence Allow students to use the data provided on the “Run! Warm Up” activity sheet (included) to find the slope of the line of best fit to introduce the lesson. Students will work in pairs to time each other as they run, walk, and choose a third mode to travel a designated distance. Students will organize their data in a table provided on the “Run! Data Record Sheet.” Students will use their own data to create distance-time graphs for each of their three trials on one coordinate plane to compare their speeds during each trial. The teacher will check for understanding by asking the provided key questions. To close the lesson, the teacher will lead a discussion about how the graphical representation of the students’ trials was useful for understanding how they travel at different speeds using different modes of travel. Assumed Prior Knowledge Prior to this lesson students should be able to organize data into a table and graph data on a coordinate plane. Students should be familiar with the slope of a line and be able to calculate it. Students should also be able to calculate the average speed of an object using measured distance and time. Classroom Set Up Students should work in pairs to time each other and have space to run in a straight line for about 15 meters. Students may measure a path to travel using meter sticks and mark the beginning and end points using masking tape, or specific landmarks may be used to designate the path such as the beginning and end of a grassy field. Students will need to know the exact distance that they travel and students may measure this distance or it may be measured ahead of time for them. Lesson Description Introduction Provide each student with the “Run! Warm Up” activity sheet (included) and allow them to plot the data, find a line of best fit, and calculate the slope of the line. Students should be able to relate the provided data to the speed of an object and understand that a steeper line indicates a faster speed while a more shallow line represents a slower speed. Explain to students: Today you will be traveling a designated distance by running, walking and choosing a third way to travel such as skipping, hopping, dancing, walking backwards, etc. Your partner will time you for each trial. You will keep track of your times in a table so that you can create a distance-time graph to represent your three trials on one coordinate plane. You will then be able to use your graphs to understand how your speed differed during each trial. Maybe you can predict how your speed will compare for each of the trials already, can you predict how the graphs of each of your trials will compare? STEM Activities for Middle and High School Students Run!
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Model and Guided Practice Assemble students, along with their materials, in an area where each pair has space to run about 15 meters or some other designated distance. Model for the entire class how each pair will be timing each other as they complete three trials. Each student should run the entire distance, walk the entire distance, and choose a third way to travel (skip, hop, dance, speed walk, etc.) while their partner times each trial for them. Students should record their own trial times on their data sheet. As students are completing their trials, ask the following questions: For which trial were you fastest? Slowest? How could you find your speed for each trial from the data you collected? When each pair has had the opportunity to complete their trials and collect their data, bring the class back into the classroom to create distance-time graphs and analyze them. Check for Understanding Check for students’ understanding while they are creating a distance-time graph for their trials by asking the following key questions: For which trial were you fastest? For which trial were you slowest? Describe the slope of each trial and how it relates to your speed. Move around the room checking with individual students by asking the key questions while helping students create distance-time graphs using the data from their trials. Independent Practice Allow students to work independently to write a description of their distance-time graphs by comparing their mode of travel, times, and the graphs of their trials. Students should relate their speed during each trial to the slope of each trial and make comparisons among the three trials. Closure To close the lesson, students may share their descriptions and compare graphs. Asking the following questions may generate a discussion: How was it useful to have a graphical representation of your trials in order to analyze your different speeds? STEM Activities for Middle and High School Students Run!
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Describe how the distance-time graph representing a fast runner would compare to a slower runner. Suggestions for Differentiation and Extension PHET Simulation: Visit the website http://phet.colorado.edu/en/simulation/moving-man which provides a downloadable simulation activity showing a distance-time graph for a person standing still, moving away from, and moving towards an observer. Students may use graphing calculators to graph their trials on the same screen to compare them.
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Run! Warm Up Several students in Mr. Hall’s class collected the following data representing the height of a growing seedling over several days. Plot the data on a coordinate plane and find the line of best fit to create a distance-time graph. From the distance-time graph, calculate the slope of the line of best fit. Day 1 2 3 4 5 8 9 10 11 12
Height (cm) 2 2.5 3.5 3.5 4.5 7 8 8.5 8.5 9
How can you use the graph above to find the average growth rate of the seedling?
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Run! Data Record and Analysis Sheet Record the data for your three trials in the table then create a distance-time graph for each trial. You should graph one line for each trial using the origin (0,0) as one point and your timedistance data (seconds, meters) as your second point. The result will be one coordinate plane with three lines beginning at the origin. Be sure to label the axes and graphs with titles. Travel Mode
Time (seconds)
Distance (meters)
Slope (m/s)
Walk Run Other:
Summarize Your Findings 1.Use your distance-time graphs to compare the slopes for each of your trials and describe your observation.
2. Describe what the slope represents in this activity.
3. If you looked at all the distance-time graphs that your classmates created, what would you look for to find out who is a very fast runner?
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