Math.8.SP.A.4

Common core State Standards

  • Math:  Math
  • 8:  Grade 8
  • SP:  Statistics & Probability
  • A:  Investigate patterns of association in bivariate data
  • 4: 
    Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables.


    For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?

Download Common Core State Standards (PDF 1.2 MB)

To the Moon!
Lesson Objective: Engage in an engineering design challenge of hitting a target with a paper rocket
Grade 8 / Engineering / NGSS
Math.8.SP.A.4

Thought starters

  1. How do students use science and engineering practices in this lesson?
  2. How could you make disciplinary core ideas more explicit throughout the lesson?
  3. How do students use data analysis to inform their decisions?
97 Comments
Wow! Look at those kids problem solve their way to designing their rocket to land on the "moon". Thanks for opening up your class.
Recommended (2)
Hi Michael! No problem. I have learned so much from the educators that have shared their ideas/content on this site. I am just trying to do my part to contribute to the community. And yes- I am quite proud of my students. Bright kids for sure....
Recommended (0)
I wish teaching channel has a way of communicating between teachers more privately. So, for the math teachers out there like myself, that data you collected is important. If I were collaborating with you I would ask you or your students to study the data and do some kind of a regression analysis on the height of the projectile vs. time, or height versus distance from launch pad, etc...I wonder if it's okay if I borrow your data. Sorry, I just have to ask.
Recommended (0)
Michael- No problem. Please send an email to tjenkins@greenonschools.org and I will try to dig up the data sheet. I believe that it is on my school computer.
Recommended (1)
Great video & lesson. I'm now making an effort to figure out scheduling to have my math and science teachers collaborate to try to make this happen. Thanks Tom.
Recommended (2)

Transcripts

  • To the Moon! Applying the Engineering Design Process Transcript

    Tom: My name is Tom Jenkins. I'm an eighth grade science teacher at

    To the Moon! Applying the Engineering Design Process Transcript

    Tom: My name is Tom Jenkins. I'm an eighth grade science teacher at Greenon Junior High School in Springfield, Ohio.
    Male: Page 35 I'm okay with, what did you put for your angle?
    Tom: I hope my students walk out of here with a sense of understanding how math and science are inter-related and how each piece went together to paint this big picture of trying to get a rocket to hit a target.
    Male: Timers, are you ready? 3, 2, 1, go.
    Male: I got it. Oh.
    Tom: If I were to describe this unit, I would say that it's a module over a series of sessions. We put the students in 6 groups of 4. The groups had the expectation that they were going to work collaboratively to use the engineering design process to develop a product that would accomplish the goal, which was hitting the moon.
    (Laughs) So close.
    At the beginning of the week, we had a guest speaker, who was actually a rocket scientist, because I wanted to make that very overt career connection.
    Remember he said that when he worked for the Navy, his primary job was to develop these missile interceptors.
    He and I co-taught some physics background, which included Newton's Laws as well as forces of flight. When the kids see that they're going to use a similar math to what some of our top engineers are doing, then I think that really lends some importance to what they're learning. We then proceeded to go to 2 days of data generation where we launched, basically, stock rockets. All made out of construction paper, masking tape, and the quantity of mass, 0 to 4 grams, inside the nose cone.
    2, 1 ...
    Each one had one variable that was different. That gave us data sets to where the students could break it down and see how the different variables came into play and effected the flight of the rocket.
    Female: 35 PSI, 40 angle.
    Tom: Aim down again, counterclockwise.
    Female: Like this?
    Tom: Yep.
    The launcher came from blueprints which I was given at Honeywell's educators for space camp.
    3, 2, 1 ...
    For under 20 bucks and for probably about 2 hours worth of labor, the results are quite impressive.
    Male: It's like a foot.
    Tom: Please make sure that you have your calculators out.
    The math portion of the lesson was very important to set everything up.
    One of the things I'll be passing out to you right now, is the data sheet that we've gathered over the last few days. You'll notice I typed it up and cleaned it up a bit. Over the whole course of these sessions, [Tyna 00:02:51] North and I co-taught.
    Tyna: As you look at your data sheet, we have the time there in seconds, the distance in feet, then we have a blank for the speed.
    Tom: With her math background, she was able to show them how to synthesize that data into a useful product.
    Tyna: I need somebody to come up and draw the flight of the rocket.
    Bridging into the math lesson, we had 18 rocket launches in the prior 2 days that we collected data for.
    What'd he just draw?
    Female: Parabola.
    Tyna: He just drew a parabola.
    We want to try to find our max height. On our first rocket, what angle did we shoot this from. We shot it from 40. We know the whole distance. We do not know either one of those, which side are we trying to shoot for. We're solving for opposite.
    In the math lesson, I wanted to make sure the students could recall the formulas for distance and the trig functions.
    27.20, she doesn't have 27.20, let's push it again.
    I wanted to make sure that they could solve for an unknown variable.
    Female: 22.5, is that what it is?
    Tom: Try to find things that you think show a pattern or changes that did interesting things to the numbers.
    Tyna: Come up with your own data set when we launch to try to hit the moon. So which data set do I like the best, or I'm going to tweak it.
    Analyzing the data is probably the hugest piece, I think. When they're looking at 18 sets of data and trying to make decisions, how can I make my rocket better and realizing that even though it is just one unit, there's just so many different avenues coming in to make this a whole, in terms of math.
    Female: We're really varying data.
    Female: Two of them have the same distance, but different angles. So since that variables the same it just shows how much the angle effects the maximum height.
    Female: Oh wait that's because of the angle.
    Female: This was because of the distance.
    Tom: You guys, noticing the patterns? The further they go, distance-wise, also tells you what? The higher. Go ahead and get us started with something you noticed.
    Male: We noticed that if you add the mass to it, they tend to go a lot higher than all the other ones. Like the 3rd one down went 110 feet while the 5th one down went 68 feet.
    Tom: So, if we add mass to it, it tended to go further. Which one of Newton's Laws helps us to better understand that idea?
    Male: Mass times acceleration.
    Tom: When we're talking about the content itself, again, these are all things that allow the students to see a practical application of the concepts that we've learned in class.
    What we need you to do at this point, as again we're going to go through our numbers, I want an individual design first. Make sure that you note everything.
    Once they have their individual product, we will sit there and just listen to each person to take their turn to share their idea.
    Make sure, not that you say what, but you say why.
    Male: I think we should do one with a higher angle first, so that we know what ... Can we adjust it.
    Female: 40 degree angle, no mass, because we don't want it going too far.
    Tom: Then they work together to come up with a common group design.
    Male: I think actually the more mass adds to the accuracy, because look at the first two. A lot lower.
    Male: We need to agree on variables so we know what to change.
    Female: Yeah, we're not changing the PSI because we don't have any data to back up a change.
    Tom: The PSI's all 40 but you can go down to 30. That's why we're giving you 3 rockets.
    Male: What about the mass?
    Female: 2 grams, 3 fins on it.
    Female: Triangles.
    Male: 40 degree angle.
    Tom: You guys have a final design, here?
    Female: This is the final one.
    Tom: Since we've signed off on your papers, you're going to make 3 identical rockets. You have about 15, 20 minutes.
    Female: 3rd time's the charm.
    Tom: The trick is, to get them tight enough to where they'll catch the air, but not too tight that they'll stick and blow up.
    I'm curious, since you guys are going with no mass, what angle of launch are you guys going to try?
    Female: Still 40, but we're going to go lower PSI probably because the lines when we were shooting with this design were like 180.
    Tom: Yeah.
    Okay, so we're going to transition at this point. We're going to have everybody share their mass, their fin, and their shape.
    Female: Okay what's your mass?
    Female: 1.5.
    Tom: We wanted to make sure that there was plenty of data to take away. We thought that having sets of data from each team would not only be useful to that team, but the other teams as well.
    Gather your stuff and let's go out in the field.
    So we went outside, we had it organized for our first session of the student-made rocket launching.
    Alpha! We'll be launching at a PSI of 40, an angle of 40, a rotation of 0.
    We thought about the essential pieces of data we needed to collect while we were outside doing this experiment. Those were launch start time, start and stop, the true distance, how far east and west then how far north and south of the target that the rockets landed.
    Male: 144 and that was 3 inches.
    Female: No!
    Tom: DNF, did not finish.
    Some of these rockets actually blew up on the launch pad.
    All right, let's try the other one. These are wound really tight.
    Initially, there can be a sense of failure.
    1, there we go. That's all right, you'll get good data, because that's why you have a lot of other data sets.
    As long as educator you create that culture that's part of the learning process, then by the time you get to the end of the year, they understand and they roll with the punches.
    This one's going to be good.
    Female: Oh, and I made this one.
    Female: Are we keeping everything the same, though?
    Female: Yeah.
    Tom: Fortunately, one group, out of their 3 launches, the first 2 were DNF's but then their 3rd one was extremely close to the target.
    Nice. Good job.
    Female: 14 feet. Then 150.
    Tom: I was impressed that you could tell that they used their data to make informed decisions. In fact one of our groups actually was able to hit the moon with their 3rd rocket.
    So you manipulated angle that time and you're going really far. What should you manipulate ...
    Female: PSI. So let's do 30. 30, 30.
    Tom: Okay. 3, 2, 1. Whoa. That's easy enough to measure, isn't it?
    At the end of about 45 we had this wonderful sheet of data that the students gathered themselves.
    From the preliminary launches, how did that data drive your decision? Were there specific pieces that made you say, hey this is a trend I noticed, or this is something. Your rockets were wildly successful yesterday in my opinion. As you're wrapping up, please draw your individual design.
    For the final launch day, we allowed each team 2 launches towards the engineering design challenge.
    Once you've discussed it as a group, pull together a group design of which we're going to make 3 rockets with the intent of launching the best 2 and we're going to take the average distance from the moon to determine the champion on this.
    Again, individual design, group design, build, test, reflection. It's a cyclical process.
    Female: This one was the one that hit the wind. The blue one had a 40 degree angle where as the other one's had 30 degrees.
    Female: So probably if we made that lower, that would probably be more accurate.
    Female: We could drop it down to 35.
    Tom: All right, so you're on line, that's good. Why is it that you think that you guys have to use more PSI than the other groups?
    Female: Because we don't have any mass.
    Tom: So what PSI are you going to use?
    Female: How about 43?
    Tom: 43. Go. Well done, good job.
    Their results this time were much closer than before and they applied what they learned in the past and what they observed.
    Male: When I changed the PSI to 40 and the angle to 40, on the one that hit, they had 40 degrees on the angle, and we probably could have hit it if we would have had their angle.
    Tom: One of our groups made sure that the clay was fixed in 2 different spots on the rocket. I think their average was around 5 feet away.
    3, 2, 1. What do you guys want? The same? Oh.
    Male: 4 foot, 2 inches.
    Female: We need to keep 30 30 PSI, because that's what we've had success with.
    Tom: Then the anomaly from the whole day was from the team that re-used the same rocket from launch day 1 that actually hit. Then they made 2 rockets based upon that design.
    Tyna: What did you change?
    Male: I put 0.5 more grams, just because if you look out, there's no more wind. So if we change that, it could go too far.
    Female: Maybe we should just keep it exactly this.
    Male: Yeah.
    Tom: 3, 2, 1. That went really far. So that was the same rocket yesterday.
    Female: Yeah, went way farther.
    Tom: Any factors that might have played into that?
    Female: There was less wind today, but that wouldn't help, that would just hinder it.
    Male: Well, the rocket we're going to shoot now is heavier.
    Female: Should we ... 30 30. You think we should lower the angle or the PSI?
    Male: What's the difference?
    Male: PSI.
    Female: Lower it to 20? 27 PSI.
    Tom: 27, is that what you want.
    Male: We have to have enough to make it.
    Tom: 3, 2, 1.
    Male: See, way too much.
    Male: I don't know, this is just disappointing after we hit it yesterday. I don't know what the big factor could be.
    Tom: It was kind of neat and it caused a really interesting conversation later to see how the same design one day could have a different result on the back end.
    Tyna: All right, we need to average the 2 distances.
    Tom: When it came to thinking about the final presentations, one of the things that I always have the students do is think about the process from start to finish. This is a practice that you have to build within your class that the students quickly become accustomed to.
    Let's go ahead and please talk about your design and what brought you to this point.
    Male: We started off with a PSI of 40 as well as our angle of attack.
    Tom: They have the expectation that they're going to use the engineering design process and they're going to show how their product changed with each iteration and how they used what they learned to improve their product.
    Male: So, in the future, we had the exact same design, but we moved the angle up 2 degrees because we were a little short.
    Female: We decided to make a rocket with no mass.
    Tom: What did you guys need to do that other groups didn't have to do.
    Female: PSI needed to be greater.
    Female: It didn't get enough momentum so we added a gram.
    Tom: I think that I have my students comfortable enough to where they can get up in front and talk about their failures in an open way.
    Male: We overshot by like 70 feet on each one.
    Tom: So what are our theories?
    Male: How it was launched.
    Tom: Sometimes we learn more through those failures and trying to explain the unexpected then we do when things occur as we expect them to.
    Female: When I was them, I made sure to have one fin vertically down, like a Y kind of.
    Tom: Do you think that could have generated any kind of lift?
    It became open dialogue with the class.
    Female: My theory is these rockets are built similar to arrows and ...
    Tom: Other students chimed in and offered their theories. I thought that was such a huge learning moment.
    Male: The one that we did hit is an outlier, if you think about it. Because our other 2, they went over 200 ...
    Tom: So, the prize for winning the contest ... What was your average distance away from the moon?
    Male: 5 feet 6 inches.
    Tom: You guys literally win the moon as your reward.
    I think if we did this rocket unit when I was in school, it would've still been cool. But the fact that we theme this, we tie in a career connection, and the students, they're part of that iterative design process to achieve a goal, I think that makes it much more rich and much more impactful.

School Details

Greenon High School
3950 South Tecumseh Rd
Springfield OH 45502
Population: 510

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greatschools

Teachers

Tom Jenkins
Tonda North

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