The Arizona STEM Acceleration Project

All Graphs Tell a Story

All Graphs Tell a Story

A 8th grade STEM lesson

Author:

Tianna Griffin

Date

12/22/22

Notes for teachers

Prepare your graphs and tables before class.

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Students may need instructions on how to use the stopwatch.

List of Materials

• Large display area(easel pad or display board)
• Class Set of stopwatches
• Large easel Graph Paper
• Markers
• Set of name cards of class members in a paper bag or container
• Exit Ticket
• Pre-labeled coordinate plane

Math Standards

8.F.A.2 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.

8.F.B.4 Given a description of a situation, generate a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or a graph. Track how the values of the two quantities change together. Interpret the rate of change and initial value of a linear function in terms of the situation it models, its graph, or its table of values.

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Standard 5. Computational Thinker - Students develop and employ strategies for understanding and solving problems in ways that leverage the power of technological methods to develop and test solutions.

6-8.5.b. Students find and organize data and use technology to analyze and represent it to solve problems and make decisions.

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Technology Standards

Objectives:

SW use a table to organize information.

SW create a graph to display data, using correct labels.

SW recognize the relationship among the table, the graph, and the slope of a line as the constant rate of change.

Agenda (90 min)

Introduction

Friends Activity

Walking Task

Graph Data

Graph data using online graphing calculator

Exit Ticket

What are the qualities of a good friend?

Can you have more than one friend at

a time?

Making Friends Instructions

1. Prepare a large graph before playing. The horizontal axis represents time in rounds of the game. The vertical axis record the number of Friends and is labeled with the number of students in the class. Also prepare a table. You will graph two or three games on the same graph for comparison, but you will use a new table for each game.
2. Ask students how they make friends. What qualities define a good friend? Can you have more that one friend at a time? What are behaviors and skills that they can practice to be good friends? If your class has built community this conversation can be rich and earnest.
3. Explain that students are going to play a simulation game in which players pretend to make friends. They will play Making Friends until all the members of the class are on the Friends Team.

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4. Choose two or three students to begin the game on the Friends Team and remove their names from the container of the name cards. (Choosing three works well if the total number of players is a multiple of three; otherwise choose two.) Move the chosen players to a designated area of the classroom where the Friends Team will meet. Record the data on the table.

5. On a signal from the teacher, the rest of the students close their eyes. The first Friends Team players each randomly draw one student name card from the container. They silently tag those students gently, implying that they have employed their friendship skills. The tagged students open their eyes and join the taggers in the Friends Team area. When the turn is completed, everybody opens their eyes and helps record the data for that round.

6. The original Friends Team players stay in the Friends Teams area and the newly chosen players prepare for their turn. Students close their eyes, while the new players draw name cards and bring one more person each back to the Friends Team area. Again, count and record the number of friends on the team.

Game 1

Game 1

Game 1

Making Friends Cont.

8. Tell students that they will play another game. The rules will change. This time, instead of simply sitting in the Friends Team area after choosing a new friend once, every friend will now be able to choose a new friend every round. After all, people are not restricted to one friend! People can use their friendship skills over and over.

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—What do the students predict will happen? Ask for the opinions and record the predictions on the board. Predictions are just best guesses for now–they help students think about the results as they unfold.

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Play the game and record the results on a data table similar to the table used for Game 1. Before each round, ask students to predict what will happen to the number of friends in that round and in future rounds. Is a pattern emerging?

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7. When the game is over, use the data to make a line graph as a class, tracking the number of players on the Friends Team. Help students locate the points on the graph and connect them. Ask students to analyze what happened.

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Game 2

Making Friends Cont.

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Questions:

What does the graph tell us about what happened to the number of friends in Game 1 and Game 2?

How are the times different how are they similar?

Did the rate of making new friends change in Game 2 compared to Game 1? Why?

Why does Game 1 produce a straight line and Game 2 produce a curved line?

What would happen in Game 2 if another class joined the game?

Which set of rules creates a fully inclusive Friends Team faster?

9. Graph Game 2 on the same graph as Game 1, but use a different color marker for line.

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Bringing the Lesson Home:

Use the graph and questions to focus the discussion on what happened to the number of friends in the game. Then, relate the lesson to the students own experience.

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Game 2

Game 2

What’s a walkathon?

Do you think if you run fast, you walk fast?

What tools can we use to see how fast we walk?

Hands-on Activity Instructions

• Working in teams of two people, set up an experiment in which one person, the walker, walks one quarter of a given distance (one-quarter of 80 or 100 feet).
• The walker chooses to use a short, regular, or long stride and uses this stride for one-quarter of the predetermined distance.
• A second person, the timekeeper, records the time it takes the walker to walk this distance.
• The walker repeats this procedure for each of the three strides. Then the walker and the timekeeper switch places and repeat the experiment.

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Walking Strides

• Once a team has completed gathering the data, each student uses this information to estimate the time it would take to walk half the distance, three quarters the distance, and, finally, the total distance, using each of the three strides and assuming that each student’s pace is constant for a given stride.
• These estimates are also recorded.
• The next step is to make graphs of this data, plotting the points by hand on a coordinate grid and using a online graphing calculator @ https://www.desmos.com/calculator.

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Discussion

• What features are the same? Different?
• What are the independent and dependent variables?
• What is the rate of change?
• What does the difference between the steepness of two lines tell us?
• What could we say about the distance traveled if a line were vertical? Horizontal?
• What story can you tell about walking using strides of different sizes?

Walking Paces (______________ Total Distance)

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Time in Second for Different Strides

Record your actual times here

Estimate your time on the basis of your actual times for one-quarter of the distance.

Make a graph of this data.

Assessment

Name Walking Rate

Anna 1 meter per second

Felipe 1.5 meter per second

Jasmine 2 meters per second

Time in Seconds

Distance in Meters

Directions:

a.) Complete the table for several times.

b.) One a coordinate plane, make a graph of the time and distance for three people.

c.) Describe how the walking rates affects the graphs.

Differentiation

Modify requirements in Making Friends Activity–place name cards towards the middle end of the round when the pattern has been established. At the beginning of the period state the goal–look at how many go in and out not on who goes in and out.

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Modified exit ticket: Give table with just Anna and Jasmine. Complete 1 or 2 rows only. Graph 2 data points for each. Provide pre-labeled coordinate plane.

Remediation

Extension/Enrichment

How far would Anna, Felipe, and Jasmine walk in 5 minutes? 1 hour? 8 hours?

How long would it take to walk a 10-kilometer race?

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Brianstorm ideas of what we can fundraise for. This is our last year in elementary school, what do we want to do this year?

What pledge plans can help us reach our goals? How can we determine if our families will sponsor us? Who are some other potential sponsors? Is this a price our families can afford?

What would it take to get our community involved in a walkathon? Are there currently any walkathon events happening in our area?

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