Math.8.EE.C.8c

Common core State Standards

  • Math:  Math
  • 8:  Grade 8
  • EE:  Expressions & Equations
  • C:  Analyze and solve linear equations and pairs of simultaneous linear equations
  • 8c: 
    Analyze and solve pairs of simultaneous linear equations.


    a. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.


    b. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.


    c. Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.

Download Common Core State Standards (PDF 1.2 MB)

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Math.8.SP.A.1

Common core State Standards

  • Math:  Math
  • 8:  Grade 8
  • SP:  Statistics & Probability
  • A:  Investigate patterns of association in bivariate data
  • 1: 
    Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.

Download Common Core State Standards (PDF 1.2 MB)

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Math.8.SP.A.2

Common core State Standards

  • Math:  Math
  • 8:  Grade 8
  • SP:  Statistics & Probability
  • A:  Investigate patterns of association in bivariate data
  • 2: 
    Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.

Download Common Core State Standards (PDF 1.2 MB)

Experimenting with STEM: The Barbie Bungee Jump
Lesson Objective: Apply knowledge of the line of best fit when designing bungee jumps
Grades 6-8 / Math / Engineering
Math.8.EE.C.8c | Math.8.SP.A.1 | Math.8.SP.A.2

Thought starters

  1. How does Mr. Roda differentiate to push each student's learning?
  2. Why does Mr. Roda have each group start with two rubber bands?
  3. How does Mr. Roda facilitate successful group work?
31 Comments
@the Sabrinas: Only the first supporting material, Barbie Bungee Concepts and Examples, is a pdf file, so depending on your browser it may open in a new tab or download. The other three supporting materials are word docs, so when you click on them they should automatically download to wherever you've set your browser to house downloaded files. It happens pretty quickly visually, so I only see the download arrow for literally a second before it disappears. Let me know if you're still having issues and I can email you the files directly. Happy new year, and apologies for the trouble you're having!
Recommended (0)
@Sabrina Kowalski Hi there Sabrina!! For some reason even signed in the links will not work for me.
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@Sabrina galletto-edmonds...if you sign in, all the supporting materials to the right become active and you can click on the link to open and print them
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does anyone still have access to these documents? I would like to recreate this activity in my STEM class. thank you
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Great Project. I'm not sure why someone would care if it is a Barbie or a G.I. Joe. Could use anything. What does Fifty Shades of Grey have to do with anything.
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Transcripts

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    01:26:52;00 STEM LESSON IDEAS
    THE BUNGEE JUMP EXPERIMENT

    BEGIN SEGMENT

    PATRICK RODA:
    3…2…1

    RODA (interview):
    The activity is called, uh, the Barbie Bungee

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    01:26:52;00 STEM LESSON IDEAS
    THE BUNGEE JUMP EXPERIMENT

    BEGIN SEGMENT

    PATRICK RODA:
    3…2…1

    RODA (interview):
    The activity is called, uh, the Barbie Bungee Jump. It’s the culminating activity after the students have learned how to find the Line of Best Fit.

    RODA (interview):
    The Line of Best Fit allows them to make predictions based on the data they gathered. So in this activity, they’re actually gathering data to make sure the Barbie gets as close to the step as possible.

    RODA:
    3…2…1

    CLASS:
    Ooooh!

    RODA (Interview):
    It definitely does has a science feel to it. The kids are acting on their formulas and are testing out the theory.

    STUDENT:
    Thirty.

    STUDENT 2:
    Thirty? Okay.

    RODA (interview):
    They’re performing experiments.

    RODA:
    So we’ve seen Line of Best Fit in the books. We’ve taken notes. Ah, we’ve done examples but we’re gonna see how it really works in real life.

    RODA (interview):
    The students in this lesson are a group of eight graders that are taking Algebra I that will receive high school credits upon passing their end-of-course Algebra I exam.

    RODA:
    So here’s the experiment. We’re gonna take my daughters, not mine, my daughters Barbies and we are gonna actually make them bungee jump. Okay? And what we’re gonna do is we are gonna make a prediction based on data that you’re gonna collect in this room, how many rubber bands we would need to take this Barbie on the stairwell, put it on the top railing, drop it down, to make it just miss the bottom step on the first floor. We don’t want it to hit. Like I said, it’s my daughters. You break it, you buy it. Just kidding. So how we gonna do that? To make a prediction what did we say? We need to… Maria?

    MARIA:
    Gather up information.

    RODA:
    Very good.

    RODA (interview):
    The material they need are a Barbie doll, rubber bands, a tape measure, a ruler. To make the actual bungee you’re starting with two rubber bands of equal size. I explain it as a Venn Diagram, which they’re used to so they’re seeing the two circles of the rubber band and then you just kinda loop one into the other and pull. It’s attached.

    RODA (interview):
    When I give them their worksheet, I already insert “2” into the table of values so they know that’s where they’re starting and it’s given to them. See how far the Barbie drops, record it. If you want to do two or three times to get an average, that’s fine. Again, the more you do the more accurate you’ll be. Any questions? Go to it.

    RODA (interview):
    They take the tape measure hanging down to the floor. They’ll put the Barbie at the edge of the desk, holding the band and release the Barbie. The other three students are seeing where the Barbie hits the tape measure.

    STUDENT:
    120.

    RODA (interview):
    If there’s three students looking at the tape measure, they all might have a different view of it and they might get different answers so they might drop the Barbie two or three times. If they still have varying answers, they can make an estimate of those.

    STUDENT:
    30

    STUDENT 2:
    30

    STUDENT 3:
    One more time?

    STUDENT 2:
    Yeah.

    STUDENT 3:
    Yeah.

    RODA (interview):
    Then what they do is they add rubber bands to the bungee, increasing the distance.

    STUDENT:
    1…2…3… go.

    RODA (interview):
    And they can add either one or two rubber bands. We are limited because we can only go so high in the classroom. This is my third year doing it. I think seven trials is a really good number. Time permitting, if we could do more, maybe ten would be optimal. We just don’t have the time and the height to do that many.

    RODA:
    How many… Should you add two more at this point or maybe just one more?

    STUDENT:
    Two… one more.

    RODA:
    One more, right? Because if you add two more it might reach the bottom.

    STUDENT:
    Ready? Set. Go.

    STUDENT 2:
    I saw 8.

    STUDENT:
    Let’s say 88.

    STUDENT 2:
    You can start putting the numbers here and start plotting them and we’ll get the last one.

    STUDENT 3:
    Okay.

    RODA (interview):
    As they are gathering the data, they are adding it to their input/output table of values. That table of values will then translate to a scatter plot where they’re labeling their x-axis, their y-axis. The x represents the number of rubber bands. The y represents the distance the Barbie is falling. So they’re plotting points. The scatter plot needs to be represented by an average, which is then the Line of Best Fit.

    STUDENT:
    We’ve been learning methods of how to find Line of Best Fit which is the eyeball, the average, um, the two-point form, the q points and the point slope form.

    RODA (interview):
    We give the students the opportunity to choose the method they wants to chose the Line of Best Fit.

    RODA:
    You want to do the average method? You good with 7 2/3rd x or do you want to try to be more specific and do point slope?

    STUDENT:
    Point slope.

    RODA:
    Then go for it.

    RODA (interview):
    If they chose the eyeball approach, their work is pretty much finished. They’re putting in a line kinda through the middle of the points. If they’re choosing a more sophisticated method, then that’s where the real algebra comes in, especially with the Q points.

    RODA:
    Okay so what were the Q points you came up with?

    STUDENT:
    Four comma thirty and nine comma sixty-two.

    RODA:
    Good. So what’d you do with those Q points?

    STUDENT 2:
    We plugged them in to the two-point form.

    RODA:
    Very good. So what was the slope you came up with?

    STUDENT:
    Six point four.

    RODA:
    Good and what does that represent?

    STUDENT 2:
    The trend line.

    RODA:
    The trend line. OK. Now it’s increasing. If we talk about it in terms of rubber bands and distance, what would six point four…

    STUDENT:
    The average inches it fell per…

    RODA:
    …per rubber band. Excellent. That’s very good.

    RODA (interview):
    That’s absolutely possible to do this activity with a lower ability level. They could do the eyeball approach and the average approach and even the slope where they’re using the two-point form. It could work just as well in a regular eighth grade math class. But we would limit the difficulty in the methods.

    RODA:
    What was your final equation?

    STUDENT:
    Y equals 6.4x + 4.4.

    RODA:
    Good and now how do you use that to make your final prediction. Amir, do you want to get involved here?

    AMIR:
    Um, we’re gonna plug in 185 as y.

    RODA (interview):
    Their final result of their method is an equation of a line. The line representing the Line of Best Fit of their data. So it’s in the form y=mx+b, where they’re finding their slope, they’re finding their y intercept. The final equation will then allow them to make their prediction by plugging in the height from the railing to the bottom step, which I give them. I tell them its 185 inches and they need to know to take that number and plug it in either for the x or the y. And hopefully they’re paying attention and they’re gonna plug it into the y which represents distance fallen.

    RODA:
    What is 185 represent?

    AMIR:
    Um, how many like centimeter, inches, inches, we want to go.

    RODA:
    Good. Good. And that’s the distance that the Barbies gonna fall, right? We know the distance falling now we’re working backwards to get the rubber band. See we started out with the rubber bands, checking the distance, now we’re flipping it. So when we plug in for y, we’re gonna get our x which is how many rubber bands.

    RODA (interview):
    As they were doing the activity, they were increasing the rubber bands, finding the distance. Now they know the distance, they have to find the rubber bands. That’s how they’re ultimately getting a prediction.

    RODA:
    So what was your final outcome?

    STUDENT:
    Twenty-eight.

    RODA:
    Twenty-eight, I see… point two. So you don’t got an exact number. You got a decimal. So let’s think about this. Is it over estimate or under?

    STUDENT:
    Under.

    RODA:
    Why under?

    STUDENT:
    Because if you go over, you’ll hit the bottom step.

    RODA:
    Very good so you’re taking in all these factors to make your prediction the best it can be. How many rubber bands?

    STUDENT 2:
    Um, we’re gonna do thirty-five. That’s our prediction.

    RODA:
    And what method did you guys use to come up with thirty-five rubber bands?

    STUDENT 2:
    Q points.

    RODA:
    Q points. Good.

    STUDENT 3:
    We predicted that we would need 28 rubber bands for the fall.

    RODA:
    Excellent. Do you guys feel confident with this? What is the Barbie hits the stair or the Barbie comes two feet away from the stair?

    STUDENT 4:
    We check over our work and what we did wrong?

    RODA:
    Right right. So we’re trying it. We’re applying it. We’re trying it and we’re rethinking things. You guys did this process a little bit by starting with the average and then moving to the two-point form. So you’re thinking. That’s the best thing you can do. Always think.

    RODA (interview):
    And then yeah, that’s the exciting part. That’s when we get to go and actually see if their work works.

    RODA:
    One person holds the band. We’re gonna do three drops.

    RODA (interview):
    I’ll tell two members of the group to stay with the Barbie and stay on the second floor. The other three students will come down to the first floor. One will hold the meter stick and the other two are the eyes.

    RODA:
    3…2…1

    STUDENT:
    That’s at fourteen.

    STUDENT 2:
    2…1…

    STUDENT 3:
    33.

    RODA:
    Good. Write it down.

    RODA (interview):
    To see their math come alive and just, wow, our hard work paid off.

    RODA:
    You nervous? Okay. 3…2…1. Well that looked good. What’d you see there? Twenty?

    STUDENT 4:
    Yeah.

    RODA:
    Twenty. Good. Write it down.

    RODA (interview):
    You know even if they’re not touching the step and they’re ten inches away, twenty inches away, they’re work has a meaning now.

    RODA:
    Okay, so what happened?

    STUDENT:
    It hit the ground.

    RODA:
    It hit the ground but last time it was a little bit less so what do you think?

    STUDENT:
    Take about one or two rubber bands off?

    RODA:
    Okay and that’s something we can discuss in class, okay? Maybe your calculations we gotta check. Alright. Good job. Next group.

    RODA (interview):
    So I’m gonna act on that when we come back to the class. I want to ask that, “What do you think?” “What could you have done better?” A great outcome of this project is when you see the students deciding on a method and you know they’re trying to
    take the easy way out and they’ll go with, you know, the average approach and, you know, you’ll let them have their way and they do it.

    RODA (interview):
    And then as they’re dropping the Barbie and they’re not coming as close as the other group, a lot of the groups will realize, maybe they should have used the Q point method which, again, is the more precise method.

    RODA:
    How far away from the step?

    STUDENT:
    Fourteen inches.

    RODA:
    Fourteen inches. So now that you thought about it, what methods did you take to change that prediction? What did you do?

    STUDENT:
    I used the Q points.

    RODA:
    Okay, so you started off with…

    STUDENT:
    Point slope.

    RODA:
    And you went to Q points. What was your prediction after the Q point?

    STUDENT:
    Uh, twenty-eight rubber bands.

    RODA:
    Twenty-eight. So you went from twenty-five to twenty-eight. Are you gonna go with twenty-eight?

    STUDENT:
    Yeah.

    STUDENT 2:
    We’re starting with two new points from when we were in the classroom and now we’re gonna use the two point form. And when we find our new slope, we’re gonna put that into our new equation y=mx+b. And then once we find our answer that’s how we know how many rubber bands we need. And it has to be less than 35 or we’re gonna keep hitting the stairs.

    STUDENT:
    Twenty-eight point two.

    RODA:
    Twenty-eight. And how close were you? Fourteen. So if you added… So instead of 28 you’d do 29. You think that would give you the, the needed distance?

    RODA (interview):
    If you’re constantly just saying, “Okay, solve this
    problem. Solve this problem.” You know what?
    Eventually they may get it but when you’re doing this and they have a beginning, a middle and an end and they’re seeing it in practice, that really stays with them.

    RODA (interview):
    They talk about a project like this for a long time and they will remember it and when they see a Barbie it will transport them back to this situation and ultimately remembering Line of Best Fit. And that’s what it’s all about. How can we get the students to remember and apply what they’ve learned?

    RODA:
    3…2…1… Wow. That was really good. Fourteen? Good.

    *** TRANSCRIPT END ***

    *** TAPE END ***

School Details

Number 28 Elementary School
167 Hancock Ave
Jersey City NJ 07307
Population: 1024

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greatschools

Teachers

Patrick Roda

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All Grades / All Subjects / Collaboration

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All Grades / All Subjects / Engagement

Lesson Idea

Grades 9-12 / ELA / Tch DIY