Mean Flight Data Collection. Number of Flights


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1 Mean Flight Data Collection Time in seconds Number of Flights Part 1: A Mean Paper Airplane Flight Students will make a paper airplane, fly it, generate data, collect data, and use this sortie to better understand some selected statistics terms. Students will also learn how to collect, record, organize, and interpret data collected during an experiment. Sortie: Students will make a paper airplane using the instructions for the Square Wing or Basic Dart in Part 4. Students will toss an airplane five times while teammates measure the time of each flight with a stopwatch and record the times on a data collection instrument (sheet at Part 3). Students will organize the collected data and determine the statistical values of range, mean, median and mode from the collected data. Code: SC.5.N.1.1; SC.5.N.1.3; SC.5.N.2.1; SC.5.P.13.1; SC.5.P.13.2; MA.5.G.5.1; MA.5.A.1.1; MA.5.A.1.4; MA.5.S.7.2 The student will determine range, mean, median, and mode from a set of data. Location Coordinates: (, ) Materials in sortie box Box labeled Mean Airplane Flight Inventory sheet is located on the box lid. Boxed Materials include: Materials you bring: 8 stopwatches 1ps pencils Calculator set 1ps data collection sheet 1ps instructions for Square Wing airplane 1ps instructions for Basic Dart airplane 2ps sheets of copy paper Statistics Primer Statistics is the branch of mathematics dealing with the collection, analysis, interpretation, and presentation of masses of numerical data. We hear statistics everyday. Baseball players have batting averages, the number (percentage) of people who will vote during the next election and the grades on report cards are all examples of 1 February 2010
2 how statistics have been used to explain what is happening or how something happened. For example, you allow your class of ten students to have an airplane derby (or race). Ten students construct paper airplanes and each tosses their airplane once. Each time a student tossed an airplane, a timekeeper measures the time of flight with a stopwatch. The ten flight times are shown below: Student: Flight Time in seconds Now use the ten flight times to teach your students a statistics lesson. Statistics Glossary Population A population is any entire collection of people, animals, plants or things from which we may collect data. It is the entire group we are interested in, which we wish to describe or draw conclusions about. In this case, the ten flight times represent our population. Sample Each flight time is a sample. A sample is a group of units selected from a larger group (the population). By studying the sample it is hoped to draw valid conclusions about the larger group. Each of the flight times is a sample of our population (of ten flight times). Data Collection In an experiment, the people who collect and record data may be termed data collectors. The data collector may be student or a teacher. The data can be collected on a blank piece of paper or on a form specifically designed to collect and record the data. The data shown above represents times written in the order they were collected. This is usually referred to as raw data. To be meaningful and useful we need to analyze the data. We will begin to manipulate the data to put it in a form where it can be analyzed and interpreted. The first step is to place the data rank order. The data is arranged in rank order by arranging the flight times in ascending order from the shortest flight time, to the longest flight time (or vice versa). Flight Time (in seconds) Range The range is the length of the smallest interval which contains all the data. It is calculated by subtracting the smallest observations (1.3 second flight time) from the 2 February 2010
3 greatest (3.1 second flight time) and provides an indication of statistical dispersion. The range of our population is 3.1 seconds minus 1.3 seconds or 1.8 (seconds) Mean The mean is a particularly informative measure of the "central tendency." Another name for mean is average. Usually we are interested in statistics (such as the mean) from our sample only to the extent to which they are informative about the population. The larger the sample size, the more reliable its mean. The larger the variation of data values, the less reliable the mean. To find the mean of the flight times, add all scores together (24.6 seconds) and divide by the number of times we added together (10). The mean flight time is 2.46 seconds. Median The median is the number in the middle of all the other numbers. A measure of central tendency, the median of a sample is the value for which onehalf (50%) of the observations (when ranked) will lie above that value and onehalf will lie below that value. When the number of values in the sample is even, the median is computed as the average of the two middle values. Since we have ten samples, the median is found by finding the average of the fifth number (2.7) and the sixth number (2.8) and equals 2.75 seconds. Mode A measure of central tendency, the mode of a sample is the value which occurs most frequently in the sample. In our flight times, the time 2.8 seconds occurs twice. Task: After reading the above passage, read the entire task before you start the activity. 1. Make sure each student has a copy of the pattern or instructions (from Part 4) to fold a Square Wing paper airplane. 2. Direct students to fold the Square Wing paper airplane. 3. Divide students into teams of three or four students. 4. Assign students roles as timekeeper, spotter, pilot, and data collector. Students may be assigned more than one role. 5. The timekeeper will use the stopwatch to time the flight of the pilot s airplane. The spotter will stand away from the pilot and retrieve the airplane after each toss. The data collector will record the time the timekeeper calls out on the SLOF after each flight. The pilot will toss the airplane five times. 3 February 2010
4 6. The pilot will throw their paper airplane five times. Each time the pilot throws it, the timekeeper will use a stop watch to time how long it stays aloft. Round the time of flight to tenths of a second (0.0). 7. The data collector will record the time for each flight in Column B of the pilot s data collection sheet. After the pilot makes five tosses, roles should be exchanged so each student ends up assuming each of the roles. Students will use the data on their data collection sheet to complete the data questions. A B C D Flight Time of Flight (sec) Rank ordered Flight Times Conclusions 1 Mean: 2 3 Median: 4 5 Mode: Total Flight Time 8. First have students rank order their flight times from the shortest to longest in Column C. 9. Direct students to find the Mean of the flight times. Students will find the mean by adding all the flight times and divide by 5. Record the answer in column D. 10. Direct students to determine the Median of the flight times. Record the answer in Column D. 11. Direct students to find the Mode of the flight times. Record the Mode in Column D. 12. Direct students to find the Range of the flight times. Record the Range in Column D. 13. Make certain each student has included their name on the SLOFs they turn in. Extension 1. Ask students to suggest other paper airplane flight aspects that could be studied using the scientific method and this data collection and analysis method. 2. Challenge students to think of another type of activity that could be studied using the scientific method and this data collection and analysis method. Post Activity Direct teams to collect the stopwatches and calculators and to store them in the appropriate Sortie Bin marked Mean Flight. Teams should collect their paper airplanes, data collection sheets and personal materials and prepare to move to the next sortie. 4 February 2010
5 Sortie Juliet: Mean Flight New Generation Standards for Science and Math: Grade 5 SC.5.N.1.1 Define a problem, use appropriate reference materials to support scientific understanding, plan and carry out scientific investigations of various types: such as systematic observations, experiments requiring the identifications of variables, collecting and organizing data, interpreting data in charts, tables and graphics, analyze information, make predictions, and defend conclusions. SC.5.N.1.3 Recognize and explain the need for repeated experimental trials. SC.5.N.2.1 Recognize and explain that science is grounded in empirical observations that are testable; explanation must always be linked with evidence. SC.5.P.13.1 Identify familiar forces that cause objects to move, such as pushes or pulls, including gravity acting on falling objects. SC.5.P.13.2 Investigate and describe that the greater the force applied to it, the greater the change in motion of a given object. MA.5.G.5.1 Identify and plot ordered pairs on the first quadrant of the coordinate plane. MA.5.A.1.1 Describe the process of finding quotients involving multidigit dividends using models, place value, properties and the relationship of division to multiplication. MA.5.A.1.4 Divide multidigit whole numbers fluently, including solving realworld problems, demonstrating understanding of the standard algorithm, and checking the reasonableness of results. MA.5.S.7.2 Differentiate between continuous and discrete data and determine ways to represent those using graphs and diagrams National Science Standards: Grades 58 Content Standard A: Science as Inquiry As a result of activities in grades 58, all students should develop abilities necessary to do scientific inquiry and understandings about scientific inquiry. Content Standard B: Physical Science As a result of their activities in grades 58, all students should develop an understanding of properties and changes of properties in matter; motions and forces; and transfer of energy. Content Standard F: Science in Personal/Social Perspectives As a result of activities in grades 58, all students should develop an understanding of personal 5 February 2010
6 health; populations, resources and environments; natural hazards; risks and benefits; science and technology in society. Content Standard G: History and Nature of Science As a result of activities in grades 58, all students should develop understanding of science as a human endeavor; nature of science; and history of science. 6 February 2010
7 Mean Flight Data Collection Time in seconds Number of Flights Part 2: A Mean Airplane Flight Students will make a paper airplane, fly it, generate data, collect data, and use this sortie to better understand some selected statistics terms. Students will also learn how to collect, record, organize, and interpret data collected during an experiment. Sortie: Students will make a paper airplane using the instructions for the Square Wing or Basic Dart in Part 4. Students will toss an airplane five times while teammates measure the time of each flight with a stopwatch and record the times on a data collection instrument (sheet at Part 3). Students will organize the collected data and determine the statistical values of range, mean, median and mode from the collected data. Location Coordinates: (, ) Materials in sortie box Box labeled Mean Airplane Flight Inventory sheet is located on the box lid. Boxed Materials include: Materials you bring: 8 stopwatches 1ps pencils 8 calculators 1ps data collection sheet 1ps instructions for Square Wing airplane 1ps instructions for Basic Dart airplane 2ps sheets of copy paper Task: After reading the above passage, read the entire task before you start the activity. 1. Make sure each student has a copy of the pattern or instructions (from Part 4) to fold a Square Wing or Basic Dart paper airplane. 2. Follow instructions to fold the Square Wing or Basic Dart paper airplane. 3. You should be organized into teams of three or four students. 1 February 2010
8 4. Assign team members roles as timekeeper, spotter, pilot, and data collector. Students may be assigned more than one role. 5. The timekeeper will use the stopwatch to time the flight of the pilot s airplane. The spotter will stand away from the pilot and retrieve the airplane after each toss. The data collector will record the time the timekeeper calls out on the SLOF after each flight. The pilot will toss the airplane five times. 6. The pilot will throw their paper airplane five times. Each time the pilot throws the airplane; the timekeeper will use a stopwatch to time how long it stays aloft. Round time of flight to tenths of a second (X.X) 7. The data collector will record the time for each flight in Column B of the pilot s data collection sheet. After the pilot makes five tosses, roles should be exchanged so each student ends up assuming each of the roles. Use the data on their data collection sheet to complete the data questions. A B C D Flight Time of Flight (sec) Rank ordered Flight Times Conclusions 1 Mean: 2 3 Median: 4 5 Mode: Total Flight Time Once you have each filled in the table on your data collection sheet, follow the steps below. 8. Rank order your flight times from the shortest to longest in Column C. 9. Calculate the Mean of the flight times. You can find the mean by adding all the flight times and divide by 5. Record your answer in column D. 10. Determine the Median of the flight times. Record the answer in Column D. 2 February 2010
9 11. Determine the Mode of the flight times. Record the Mode in Column D. 12. Calculate the Range of the flight times. Record the Range in Column D. 13. Make certain your name and your teammates name(s) are written on the SLOFs you turn in. Extension 1. Think of other paper airplane flight aspects that could be studied using the scientific method and this data collection and analysis method. 2. Think of another type of activity that could be studied using the scientific method and this data collection and analysis method. Post Activity Teams should collect the stopwatches and calculators and to store them in the appropriate Sortie Bin Marked Mean Flight. Teams should collect their paper airplanes, data collection sheets and personal materials and prepare to move to the next sortie. 3 February 2010
10 Part 3 MEAN FLIGHT SCIENCE LAB OBSERVATION FORM (SLOF) Timekeeper: Spotter: Pilot: Data Collector: Procedure  This is what I will do: Prediction  This is what I think will happen: Data Collection A B C D Flight Time of Flight (sec) Rank ordered Flight Times Conclusions 1 2 Mean: 3 Median: 4 Mode: 5 Range: Total Flight Time Observation  This is what I saw happen: Evaluation  This is why I think it happened, and this is what I learned: February 2010
11 The Classic Dart This one is the most well known plane in the world. Not good as a fast plane, but it s a good plane to learn from, both from the point of view of just folding the plane and from learning to modify designs to meet your own needs. Here goes... Fold a piece of A4 paper lengthways Make two 45 degree folds into the center and open out again. Now make two more folds into the center. Fold the airplane in half along the fold made in step I.
12 Fold down wings, this is normally done so the wings are the same size as the fuselage, but larger wings make the plane more of a floater, with more lift, and smaller wings make for a faster dart, that flies a smaller distance. Just experiment! Open out into plane shape. Experiment with wing angles for best results. A good starting angle is just above level. A number of variations of this plane exist. A good place to start with modifying this design is to make adjustments the back of the wings as you would to correct its flight, but actually folding (see below) so that the extent of the lift causes the plane to loop the loop. If you fold the flaps upwards, it will loop upwards, and vice versa. If you fold one upwards on one downwards, the plane will spiral through the air, although not for very long.
13 The S93 This plane has firmly established itself as a fine lecture hall plane, floating down right to the front many a time. Hence we have given it the name S93 as this is (or rather, was) our academic year's name. Apparently it's known as the "floater plane" in Israel. Here goes... Take a piece of A4 paper, and fold l lengthways (hotdog fold), and open out. It helps if you make this fold both ways, that is, fold it towards you once, then unfold and fold away from you, and then open out. This will help in the later stages. Make 45 degree folds to center Fold down the top as shown, the gap between the folds made in II and the new fold is about 2cm. Now make 45 degree folds again.
14 There should now be a small triangle of Now fold the plane back on itself. paper sticking out; fold this upwards to along the fold made in step I. seal the folds made in IV. Fold down as shown to make wings. You should make the wings he same size as the fuselage, by folding them down to it. The wings can now be folded out to plane shape. The wings should be above level to make the plane fly. (or lots above level for flights starting from a height, like a lecture hall.
15 Part 5 A Mean Flight TEACHER OBSERVATION / SUGGESTION / REVISION FORM Teachers who visit the USAF Armament Museum with their students should provide feedback to the OCSD Curriculum office. This feedback is important in assessing the quality of the materials and activities for our teachers and students. Teachers may use this form for recording any observation, making comments, or suggesting revisions and additions to the activities. Comments may be anonymous but by including identification, we may contact you to ask for additional details. Identification will also allow us to advise you whether we need more information to implement your suggestion(s). Teacher: School: Telephone: Date of Visit: Which activity did you enjoy best? Which activity did your class enjoy best? Is there an activity you would like to have added to address a L DOE NG SSS? If necessary, continue Observations, Comments and Suggestions on reverse Observations: Comments: Suggestion(s): Overall rating: Outstanding Above Average Fair Poor February 2010
16 Tips on making and throwing Paper Airplanes The most important thing when making a plane is not making the folds in exactly the right place, although this is important. More important is making each fold well. To do this, make the folds on a table, pressing down onto the paper with a finger, then go over this with a ruler or pen on its side. DO NOT use your finger nails to make a fold, this makes more than one fold in a small area, and the fold will tend to move about as you make the rest of the plane. Another important thing is the angle of the wings, they should be tilted upwards. Once thrown the only way the plane can keep up speed is to lose height gradually. If the wings are level, this loss in height will not occur and the plane will try to climb, thus losing speed and stalling. By putting the wings in a Y shape, this is overcome. Now you ve made the plane it s time to test it out and fine tune it. Throw the plane and observe its actions: Veers left or right Most planes have some sort of fuselage, or at least part of the plane is vertically orientated. Gently bend the back of this in the opposite direction to the way it veers. (for example) If the plane veers right, gently bend the vertical part to the left, and throw again. Flies straight into the ground Here you have 2 options to try: Gently bend the back of the wings (on both wings), or any horizontal part of the plane, upwards, or Make the angle of the wings flatter, so they are more level with the ground. Both these should add to the lift the plane has. Climbs rapidly, then falls out of the sky This is the opposite top the above, so the 2 options are: Gently bend the back of the wings downwards, or Make the angle of the wings greater, so the are less flat to the ground. 1
17 Both these decrease the lift, and allow the plane to fly better. All the bends above are very small. They are NOT folds, a slight bend can make a surprisingly big difference, and you can always bend a bit more if it doesn t work enough. Example A dart flies straight into the ground, so you decide to bend the back of the wings upwards, as shown below: 3D view Side view 2
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