E Mathematics Operations & Applications: D. Data Analysis Activity: Data Analysis Rocket Launch

Transcription

1 Science as Inquiry: As a result of activities in grades 5-8, all students should develop Understanding about scientific inquiry. Abilities necessary to do scientific inquiry: identify questions, design an investigation, collect and interpret data, use evidence, think critically, analyze and predict, communicate, and use mathematics. National Council of Teachers of Mathematics (NCTM) Expectations Develop fluency in adding, subtracting, multiplying, and dividing whole numbers. Represent and analyze patterns and functions using words, tables, and graphs. Model problem situations with objects and use representations such as graphs, tables, and equations to draw conclusions. Investigate how a change in one variable relates to a change in a second variable. Collect data using observations, surveys, and experiments. Select and apply appropriate standard units and tolls to measure length, area, volume, weight, time, temperature, and the size of angles. Source: National Science Education Standards 1

2 Science Process Skills: Predicting Inferring Comparing Math Process Skills: Analyzing Comparing Objective: The learner will collect data using observations and experiments. The learner will represent data using tables and graphs. Time: 15 Minutes Instructor Materials: Computer with Excel (or other similar graphmaking software) and PowerPoint Projection system for computer PowerPoint slide, Data Analysis: Sample Graphs Excel file, Data Analysis_Rocket Launch Student Materials: Activity log data table from applicable rocketry appendix Colored pencils (optional; used for creating bar graph) 2

3 Instructor Background Information: Key Vocabulary Constant Parts of the trial that remain the same each time the trial is repeated. Dependent Variable A variable that is measured to learn the effect of one or more independent variables. It is what happens as a result of the independent variable. Independent Variable A variable that is manipulated (controlled) by the researcher and evaluated by its measurable effect on the dependent variable or variables. It is purposely changed so that the effect can be tested. Inference The act of reasoning from factual knowledge or evidence. Mean The average value of a set of numbers. 3

4 Dependent and Independent Variables Scientists often develop experiments to investigate a relationship between particular variables. To test a relationship, a scientist will first identify a dependent variable that he or she wishes to investigate. The scientist will then identify one or more independent variables that he or she thinks might affect or influence the dependent variable. For example, a scientist might want to examine whether a newly developed coating on a car tire increases the friction it produces on a wet road. In this case, the independent variable is the coating on the tire, and the dependent variable is the friction it produces on a wet road. To test this, a scientist would also need to test a control group, which is a group that is not subject to the independent variable. In the example given, the control group would be a tire that does not receive the coating. Reliability The scientific community does not accept data from any experiments that have not been tested numerous times (often by various scientists in varying locations). A single experiment may be subject to extraneous variables for which a scientist did not (or cannot) account. For example, a scientist may observe that a tire with the new coating produces more friction on a wet road. However, it is possible that any single experimental result was affected by unexpected factors. In this example, the scientist might have inaccurately measured the friction on the tire. Repeating experiments makes sure there is a true correlation between the dependent and independent variables (as opposed to a false correlation determined by an extraneous variable). If there is, indeed, a correlation between the dependent and independent variables in an experiment, the results of the experiment should be consistent each time the experiment is performed (within a range of uncertainty). The more an experiment yields the same results, the more reliable the data. In this lesson, the distance the rocket traveled is the dependent variable (vertically for water and solid propellent rockets, or horizontally for straw rockets and CO 2 cars). The independent variables are the applied force and the mass of the rocket. The launch angle was a constant and should have remained unchanged during the rocket launch. Sometimes, there were other variables beyond control, such as wind direction and speed. These extraneous variables could lead to inconsistency and contribute to unexpected results. 4

5 Newton s Second Law of Motion Newton s Second Law of Motion states that the acceleration of an object is dependent upon two variables: the net force acting upon the object and the mass of the object. Commonly stated as, the acceleration of an object increases as the force causing the acceleration increases when mass is constant. Newton s Second Law of Motion can be formally stated as follows, the acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object. We can express this verbal statement in equation form as a = F / m where a is acceleration, F is force, and m is mass. It is customary, however, to rearrange this equation into the more familiar form of F = ma In this arrangement, force is equal to the product of the mass times the acceleration. Consistent with the above equation, a unit of force is equal to a unit of mass times a unit of acceleration. By substituting standard metric units for force, mass, and acceleration into the above equation, we can write the following equivalency. Newton = (kg)(m/s 2 ) Examples of Newton s Second Law are listed below. The greater the force a batter swings when hitting the ball, the greater the ball s acceleration. It s easier to push an empty shopping cart than a full one. A train requires more force to stop than a small car moving at the same speed. 5

6 Instructor Preparation: üü üü Set up instructor computer station and projection system as necessary. If using Excel, install file Data Analysis_Rocket Launch. You may want to launch this file in advance, make any label changes as necessary, and minimize it until it is needed in step 5. You may also want to do the same for the PowerPoint slide Data Analysis: Sample Graphs (used in step 3). 6

7 Lesson: Activity 1. Draw the students attention to their data tables from the rocketry appendix activity log. The tables asked for them to make two predictions: A. What will happen to the distance traveled (speed in the case of CO 2 dragsters) by the rocket as they increase the mass on the rocket but keep the applied force the same? B. What will happen to the distance traveled (speed in the case of CO 2 dragsters) by the rocket as they increase the force on the rocket but keep the mass the same? 2. Ask: Now that you ve collected the data, how can you analyze it to measure against your prediction from the rocketry lesson? Using a visual representation, how can you determine the ways in which mass and force influenced the distance traveled by the rocket. (Lead a brief discussion, guiding students to conclude they should graph the results, comparing the rocket launches. [It may help to recall the lesson Introduction to Graphing & Analyzing Data. ]) 3. Display the PowerPoint slide Data Analysis: Sample Graphs. This slide contains four different types of graphs: bar, line, area, and pie. 4. Ask: Which type of graph would provide the best visual representation of the data we collected, allowing us to easily and quickly answer the two predictions? (While one could argue that all could work one way or another, the best, however, is the bar graph. The students should eventually come to this conclusion.) Note: You may want to use the Excel file, Data Analysis_Rocket Launch, to project a representation of the graph, filling in the labels and data that are applicable for the chosen rocket appendix. Graph: Mass as Independent Variable 5. Use the activity log page in this lesson and lead an interactive discussion, having the students complete the graphs, starting with Mass as Independent Variable. A. Label the X-axis: Mass of Rocket Add the applicable unit labels. This will vary with each rocket appendix. The mass of the water rocket, for instance, will be much greater than the mass of a straw rocket. Label the units accordingly. 7

8 Note: The number of data groups presented on the graph will primarily depend on how the launch was managed. If, for instance, each student conducted three launches, each with varying mass, you may want them to only graph their data, using three data groups; or you may elect to find the class mean for each launch and represent the data groups so they reflect the class as a whole. If, however, students conducted launches as groups, such as eight, you may want to graph all the groups, providing eight data groups. The options are flexible. Just ensure the students can make the correct inference from the data groups. B. Label the Y-axis: Distance Traveled ( Speed for CO 2 cars) These unit labels will also vary, depending on the chosen rocket appendix, so label as is applicable. C. Fill in the blank for the constant, the force applied. Depending which rocketry appendix the students conducted, this will vary. For instance, if using a solid propellent rocket, the force applied may be the rocket engine size (A8-3, B6-4). If using a CO 2 dragster, it may be the cartridge size (8 gram, 4 gram). If launching straw rockets, it may be the scale printed on the clear plunger tube. D. Graph, using the data from the straw rocket appendix data table. 6. Ask: With the data graphed, what can we infer about how increasing the mass of an object, while keeping the force applied to the object the same, influences the distance the object travels? (The greater the mass of the object, the shorter the distance it will travel.) 4 Check for Understanding: What are some other examples that represent this part of the law? (Answers will vary, but students may suggest things like not being able to throw a heavy object, such as a bowling ball, as far as a baseball.) Note: Did the data provide unexpected results that don t support Newton s Second Law? If so, this is a great opportunity to discuss unaccounted variables which might have influenced the data (winds, faulty engine, CO 2 cartridge, or launcher, etc.). Good science rarely relies on just a few simple tests but often uses hundreds, or even thousands, of trials conducted, in some instances, over many years. Correlate this to Newton s Second Law of Motion. 7. Ask: If mass is the independent variable, what is the dependent variable? (The distance the rocket traveled. The mass of the rocket is inversely proportional to the total distance traveled by the rocket.) Graph: Force as Independent Variable 8. Move to the next graph on the activity log: Force as Independent Variable. Lead a similar discussion as you did for the previous graph. A. Label the X-axis: Force Applied Add the unit labels that are applicable for the selected appendix. 8

9 B. Label the Y-axis: Distance Traveled Add the unit labels that are applicable for the selected appendix. C. Fill in the blank for constant. Here, it is the mass of the rocket. D. Graph the data. 9. Ask: What inference can we make from this graph? How does an increase in force relate to the distance rockets of the same mass will travel? (When more force is applied to rockets of the same mass, the rocket receiving the greater force will travel a further distance.) Correlate this to Newton s Second Law of Motion. 4 Check for Understanding: What are some other examples that represent this part of the law? (Answers will vary, but they may relate it to something like billiards. When playing billiards, one can hit a ball vary hard with the que stick, sending the ball racing across the table, or they can tap the ball lightly, making it move only a few centimeters.) 10. Ask: If force is the independent variable, what is the dependent variable? (The distance the rocket traveled. The amount of applied force is proportional to the distance traveled by the rocket.) Conclusion 11. Review with students the skills they used to conduct their investigations: predicting, measuring, presenting data in tables and graphs to correlate to a scientific law, and determining the reliability of data. Emphasize that these skills are frequently used in the workplace as well as to solve everyday problems. 12. This lesson is complete. Return to the step from where you left off with the associated rocketry appendix. 9

10 Data Analysis Rocket Launch Activity Log Distance of Rocket Launch: Mass as Independent Variable Type of rocket launched: Constant: Dependent Variable: Y-axis: (unit of measurement: ) X-axis: (unit of measurement: ) Data Analysis When applying an equal amount of force, the rocket with greater mass will travel a distance further than less than the rocket with less mass.

11 Data Analysis Rocket Launch Activity Log Distance of Rocket Launch: Force as Independent Variable Type of rocket launched: Constant: Dependent Variable: Y-axis: (unit of measurement: ) X-axis: (unit of measurement: ) Data Analysis When launching rockets of equal mass, the rocket that has a greater amount of force applied to it will travel further than less than the rocket which has a smaller force applied to it.

12 Data Analysis Rocket Launch Activity Log Distance of Rocket Launch: Mass as Independent Variable Type of rocket launched: straw rocket Constant: force (set to 60 on launcher) Dependent Variable: distance traveled Y-axis: Distance Traveled (unit of measurement: Meter ) X-axis: Mass of Rocket (unit of measurement: Gram ) Data Analysis When applying an equal amount of force, the rocket with greater mass will travel a distance further than less than the rocket with less mass.

13 Data Analysis Rocket Launch Activity Log Distance of Rocket Launch: Force as Independent Variable Type of rocket launched: straw rocket Constant: mass (3.5 grams) Dependent Variable: distance traveled Y-axis: Distance Traveled (unit of measurement: Meter ) X-axis: Force Applied (unit of measurement: scale on clear launcher tube ) Data Analysis When launching rockets of equal mass, the rocket that has a greater amount of force applied to it will travel further than less than the rocket which has a smaller force applied to it.

14 Data Analysis Rocket Launch Assessment Suggested Final Assessment Questions 1. Why are tables and graphs useful in organizing data to solve a problem and justify a conclusion? 2. If another class of students repeated this investigation, would you expect them to get similar results? Use the graph below to answer the two questions that follow: Wind-Up Car Investigation 100 Distance Traveled (cm) Car A Car B Car C Car D (10) (25) (40) (65) Number of Winds 3. In general, as the number of winds increases, the distance the car travels. a. Decreases b. Increases c. Remains the same d. Doubles 14

15 Data Analysis Rocket Launch Assessment Suggested Final Assessment Questions 4. Which car s data does not fit the general pattern shown in the graph? a. Car A b. Car B c. Car C d. Car D 5. Why should the mean results be used instead of using results from only one trial? 15

16 Data Analysis Rocket Launch Assessment Suggested Final Assessment Questions Comprehension 1. Why are tables and graphs useful in organizing data to solve a problem and justify a conclusion? Possible answer: Tables and graphs organize data and provide a visual representation of the data. Application 2. If another class of students repeated this investigation, would you expect them to get similar results? Possible answer: Yes, if consistent procedures are followed, they should obtain similar results. Use the graph below to answer the two questions that follow: Wind-Up Car Investigation 100 Distance Traveled (cm) Car A Car B Car C Car D (10) (25) (40) (65) Number of Winds Application 3. In general, as the number of winds increases, the distance the car travels. a. Decreases b. Increases c. Remains the same d. Doubles 16

17 Data Analysis Rocket Launch Assessment Suggested Final Assessment Questions Analysis 4. Which car s data does not fit the general pattern shown in the graph? a. Car A b. Car B c. Car C d. Car D Analysis 5. Why should the mean results be used instead of using results from only one trial? Possible answer: The mean gives a more accurate representation of the entire data set and not just a single trial. 17