See how they run!: The 100 meter dash

Middle level students will collect times as they run the 100 meter dash. These times will be depicted through various graphic representations (bar, circle, histogram). Times will be compared to current world records for the 100 meters. Students will decide which Math class ran fastest and support that choice in short essay form. They will also try to determine the faster gender based on the data collected.

This lesson plan is a unit filled with related lesson plans. One or two parts of this project could be completed as a stand-alone lesson, or the entire set of activities and extensions could be completed for an involved, integrated unit.

A lesson plan for grades 6–8 Mathematics

By Holly Smith

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• NCDigIns Help students become proficient in mathematics with this formative assessment diagnostic tool.

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Related topics

• Learn more about data analysis, data collection, graphing, mathematics, and problem-solving.

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Learning outcomes

Students will:

• accurately collect measurements to the most appropriate decimal place.
• order and compare decimal representations correctly as well as relate these decimals to the closest equivalent fractions.
• practice subtraction with decimals.
• choose appropriate graphic representations for the collected data and graph their findings.
• draw interior angles in circle graphs. They will review angle types and angle pairs.
• use calculators to derive class percentages based on times run. Ratios will be discussed and used.
• research the history of world record performances in the 100 meters.
• prepare a short essay supporting which class ran fastest, using collected or derived data computed during class trials.

Teacher planning

Time required for lesson

Two weeks

Materials/resources

• The 100 meter dash will need to be measured carefully in a spacious outdoor area. Ideally, a middle or high school track would be preferred, but it is not an absolute necessity.
• Three or four stopwatches or student watches with a stopwatch function will be essential. The physical education department will often have stopwatches that may be used.
• Pencil, notebook paper, graph paper or white drawing paper (9″ X 12″ or “12″ by “18″), colored pencils, fine-tipped markers, protractors, calculators, and rulers are needed for data collection and creating graphic representations.
• Current world almanacs are necessary to research world record times. The most current times should also be checked via the internet.

Technology resources

• Calculators
• Computers with internet access may be used to help check world records.

Pre-activities

Students need to have basic knowledge of percent, the connection between fractions and decimals, and ratios/proportion.

Activities

1. The instructor will explain that traditionally the world’s record holders of the 100 meter dash are considered the world’s fastest humans.
2. Students will be asked to estimate these current records. They may check these records via the most current almanac or the internet.
3. Have students estimate how quickly they think they could complete the same task.
4. Place students in appropriate groups to run the 100 meters. This could be done according to student preference. The instructor could assign groupings according to student assessment of speed. Asking students to name children who are fast runners in PE class may help to determine suitable pairings. Body build and general weight could be another guideline. Gender could also be considered. Certainly the number of stopwatches available will be a limitation. It is often easier to time two or three students than a group of four or more.
5. The day before the 100 meter trials are run the instructor will need to remind students to wear appropriate shoes and attire. Loose, comfortable clothing used for physical education classes and comfortable athletic shoes are necessary for safety as well as for collecting valid times.
6. To avoid confusion and loss of time, be sure to select helpers before students go to the track to run. One student will be responsible for lining up each group at the starting line and for signaling the teacher that the group is ready to run. This student will need a list of student groupings to assist the process. Two or three students with stopwatches will be needed to time individual students as they cross the finish line. Select one student to time first place finishers, one student to time second place finishers, and so on.
7. On the day that the 100 meters is run be sure to have students warm up with appropriate stretches to avoid muscle pulls and strains. Check the track to be sure that there are no obstacles (a small pebble, loose sand or dirt, a small stick) that might cause a runner to slip or fall.
8. Once a heat has been run, the teacher will call for the time for each finisher. Runners are then directed to the center of the track to cheer other students who will be running.
9. After the initial heats have been completed, the teacher may offer a chance for interested students to run a second heat (time permitting). Students who wish to run are then paired with students who have similar times. Students who do not care to run a second time are instructed to stay at the finish line (inside of the track) and cheer for those who have chosen to run a second time.
10. With organization and student cooperation, running the 100 meters will take approximate 30-45 minutes.
11. Once back in the classroom, the teacher will share the results with students. Have them comment on what they discover as they study student times. This is an important task and does not need to be rushed. Have students order runners according to what they consider important criteria (ex. time, gender, second interval). This could be an individual task for homework or could be accomplished in class with partners. Having students list ( in full sentences) 5 to 10 significant observations about class or individual times is also an important task.
12. The time and subsequent tasks needed to accomplish and enrich important objectives depend on how in-depth an instructor wishes to extend this activity. Listed below are activities I have used to integrate NCSCOS objectives and NCTM standards.
• Have students create appropriate graphic representations of the data collected. Question students as to what type of graph might be used to display their class data. It is crucial that students participate in the process of discussing the features of each graph and when that type of graph should be used. Students might choose to complete bar graphs, histograms, or circle graphs. With each graph there are decisions to made as to which data to use and how to organize that data. For example, will the graph show boys’ times, girls’ times, or both? Will world record times be included as well? Will this graph be completed on grid paper? If so, what size grid will be chosen and what interval will be used to display time? If drawing paper is used, what measurements will be used to determine the intervals? What will be used as a key? A title?
• Another graph choice could be a histogram. Having students complete this graph would delineate the differences between a histogram and a bar graph. Histograms are used when data components could be any value in a range--for example, times run in the 100 meters. The bars of a histogram touch each other. There are numbers on the horizontal axis as well as the vertical axis. Shared boundary values are assigned to the bar on the right. Histograms may be used to graph absolute values as well as percentages.
• If a circle graph is used, student knowledge of percent will need to accessed. Most of the time math class student counts are not necessarily percent friendly. Instead of having 20 pupils in one class and 25 students in another, my classes might have the following numbers: 23, 19, 27, and 15. Before attempting to convert ratios into percents using these numbers, I work with a fictitious class of 25 students. We group students by second intervals: 15..00-15.99, 16.00-16.99, 17.00-17.99 etc. Together we consider how a class of 100 students would have run if those runners had similar results. Ex. 4/25 = 16/100 = 16%.Once these proportions are determined, the class will work with calculators to determine what percentage might be used to represent a less compatible ratio, ex. 4/23 = ? % (100 /23 x 4).When students reason that this method will work and that it is easily explained,they can help others who are having difficultly. This reinforces what these students already know and helps create many instructors instead of only one adult on stage.
• At this point the students are using protractors to practice creating circle graphs that have equal divisions. Have each student split one circle into halves, quarters, eighths, and sixteenths. Another circle could be divided into thirds, and another tenths. With each circle students need to create a table to contain ratios, percent, and degrees. Ex. 1/2 = 50/100 = 50% = 180 degrees. Students practice drawing these interior angles to get a sense of wedge size and the accompanying percents. This also allows students to draw angles in a meaningful context.
• Once the practice circles are completed, the teacher asks students how to determine the number of degrees allowed per student if a class had 22 students instead of 20 or 25 students. Generally a child will suggest dividing the 360 degrees in a circle by the number of students in the class. When this has been decided, students add or multiply to determine how many degrees would be allotted for two students, three students, four students, etc.
• At this point, students can work together or on their own to construct circle graphs to accurately portray class results. They may also complete circle graphs for other classes. This can also be an opportune time to introduce or review angle types and angle pairs (supplementary and complementary angles).
• Another method for creating a circle graph is to use adding machine tape to determine the size of each pie wedge. Depending on student experience, this technique might be an excellent introduction to making circle graphs. Based on the width of the tape, have students determine the size of a rectangle that could represent each student runner. For example, suppose the tape was 2 inches wide, a 2″ by 2″ square or a 2″ by 3″ rectangle could represent one runner. If there are 25 students in a class a length of 2″ by 50″ (2″ by 2″) or 2″ by 75″ ( 2″ by 3″) would represent the entire set of runners. Using colored pencils or crayons assign a specific color per second interval (orange = all runners in the 15 second interval). Three orange rectangles would represent 3/25 runners whose times ranged between 15:00 - 15:99 seconds. Continue using different colors to account for each second interval run in that class. Again, each small colored rectangle will represent one runner. Once the entire set of runners is color-coded, cut the adding tape. Loop the two ends of the tape together and staple with the colored side facing the center of the circle. Use colored yarn to create radii to mark the sides of each wedge. This will make a large hands-on circle to represent the class effort. A key could then be created to label the different wedges and a title would define the data.
13. Once these graphs have been completed, children may decide which class or which gender might be considered faster based on the data they have gathered and displayed. When a viewpoint has been embraced, arguments may be constructed to write a persuasive short essay to present this belief. This assignment is an excellent opportunity to establish a collaborative effort with the language arts teacher. Rubrics may be written and papers graded according to the rubric designed.
14. An important part of this assignment would be to determine if the sample size is suitable to support such a position. Students will come to recognize the need to ask the following questions: Is the sample size large enough? Is the sample truly random, or does it need to be more diverse in nature?
15. Additional problem solving situations may be created involving world record speed. For example, if Florence Griffith Joyner consistently ran at her world record speed (10.49/100 meters), would she break the speed limit in downtown Beaufort, North Carolina (25 mph)? Another problem might center on the maximum speeds of other animals. For example, at maximum speed how fast could a cheetah, a lion, or a pig run the 100 meters?
16. Remember, this math activity is only limited by the scope of the instructor’s flexibility and the time constraints that exist.

Assessment

• Teacher designed rubrics can be used to access the correctness and effectiveness of graphs.
• Student essays may also be evaluated according to teacher-created checklists.
• Based on teacher-supplied data, students may produce a suitable graph and answer teacher-designed questions.
• Student observations about class data may be assessed for correctness and importance.
• Presented with different sets of data, students can select appropriate graphic representations and present arguments to justify why one type of graph is more suitable than another.

Supplemental information

Friel, Susan N., et. al. Navigating through Data Analysis in Grades 6-8, National Council of Teachers of Mathematics. 2003.

Comments

I have used this lesson/unit with gifted students as well as those with special needs. The major difference in presentation is pacing and in depth exploration of the topics and activities presented.

Also, creating spreadsheets for class times and graphing the data in various forms could be used as an extension of this set of activities.