Math And The Olympics 2008

MATH AND THE OLYMPICS: How to use math in an Olympic Context Websites Summer Olympic Sports

Summer Olympics Wikipedia

Summer Olympic Sports Flash Video 1. Student-generated list of how math is used in the Olympics.

How is math used in the Olympics? Some of the answers maybe…. • • • • • • • • • • •

scoring points for medals averaging scores time - more than 1 run distance speed "hang time" height of jump height/weight/ age of athletes integers - hockey - goals/penalties statistics

2. Olympic unit initial survey.

How is each sport judged in the Olympics?

Kidawson Olympic Math 2008

3. Olympics Unit Survey: Place on monkey survey on-line to collect and analyze data Answer each of the questions below. Please take the time to answer every question carefully as we will be using your responses to help us develop the unit to include your interests! 1. What Summer Olympic sports do you enjoy watching? 1. 2. 3. 2. Tell us about a Summer Olympic sport that you know a lot about (the athletes, the sport itself, etc.) 3. If you were a sport reporter assigned to the Summer Olympics, what questions would you be interested in investigating and reporting about? 1. 2. 3. 4. For a final project for this unit, you will be working with a partner to investigate a question that you have about the Summer Olympics, List TWO people below that you could work with on this project. (NOTE: This project will require you and your partner to spend time together outof-class to work on it.)

4. "Warm-up ask for some conversions in the context of speed in sprint kayaking and

running or other sports

5. "Warm-up" ask students to compare the size of various kinds of kayaks, canoes,

rowing boats, sculls

Kidawson Olympic Math 2008

6. Handout guiding students’ initial estimation of what sport is “fastest” Who’s the fastest? With your partner order the following sports by their speeds from fastest to slowest in the chart provided. Then estimate the top speed attained in each sport by kilometres p/h Rowing-Single Scull rower Canoe Kayak Single sprint kayak 500m Aquatics-Swimming 100m freestyle Sports of your choice (4)

Cycling Canoe Slalom- one run Athletics-Hurdles 100m

Name(s)……………………………………………………………………………………. SPORT

TOP SPEED Estimate in kilometres p/hour

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

Kidawson Olympic Math 2008

ACTUAL SPEED in kilometers p/h

ACTUAL SPEED In metres p/ minute

What is the range of the top actual speeds? I.e. the difference between the fastest and the slowest 7. Record of a class discussion on what learned about speed (including a conceptual Technical Mark Tally

Frequency

Composition and Style Tally

Frequency

map created by the teacher based on students' input) 8. Reading on scoring criteria in gymnastics Handout created to help students organize the tabulation of the scores assigned by each student Who wins? From the data collected in class of your sport (gymnastics, diving, trampoline etc), complete the above frequency table SPORT…………………………………. Types of averages 1. 2. Kidawson Olympic Math 2008

Name (s)……………………..

3. Other 9. Statistics National Flags Each country has its own defined flag representing its country. Choose at least 10 countries participating in the Olympics and analyze the colours of their flags Graph you results. Research into the colour that is most prominent for your finding s and give at least three reasons based on research for your finding Country Red

Blue

White

Flag Colours ?

?

Design criteria 1-3 for analyzing 10 flags you chose e.g. most appealing colour etc. And place a mark 1-15 beside your ten flags. Find the score for each flag Criteria 1 Criteria 2 Criteria 3 Criteria4 Criteria 5 Country

Criteria 1

Kidawson Olympic Math 2008

Criteria 2

Criteria 3

Score

10. "Warm-up" ask students to order and find various averages using data from the

Men's track events race or other sports 11. 12. Excerpt from an article explaining key elements of the pentathlon Modern Olympics In addition to the modern pentathlon, there has also been an athletics pentathlon event for men and women in the modern Olympic Games. The first Olympic competition for the men was at the 1912 Summer Olympics in Stockholm and for women was at the 1964 Summer Olympics in Tokyo. The events of the pentathlon, in order, were: 1. 110/100 meter hurdles 2. Shot put 3. High jump 4. Long jump 5. 1500/800 meters The javelin and the 800 meters were added in the 1984 Summer Olympics to create the women's heptathlon. The hurdles race also became 100 meters.

13. Give a measuring task designed to help students better understand what is involved

in the pentathlon

Kidawson Olympic Math 2008

14. Discussion on medal rankings and alternatives

Olympic Statistics Medals Wikipedia medal Counts Look at the medal counts by country

Kidawson Olympic Math 2008

Rank

Nation

Gold

Silver

Bronze

Total

1

United States (USA)

36

39

27

102

2

China (CHN)

32

17

14

63

3

Russia (RUS)

27

27

38

92

4

Australia (AUS)

17

16

16

49

5

Japan (JPN)

16

9

12

37

6

Germany (GER)

13

16

20

49

7

France (FRA)

11

9

13

33

8

Italy (ITA)

10

11

11

32

9

South Korea (KOR)

9

12

9

30

10

Great Britain (GBR)

9

9

12

30

11

Cuba (CUB)

9

7

11

27

12

Ukraine (UKR)

9

5

9

23

13

Hungary (HUN)

8

6

3

17

14

Romania (ROU)

8

5

6

19

15

Greece (GRE)

6

6

4

16

16

Brazil (BRA)

5

2

3

10

17

Norway (NOR)

5

0

1

6

Kidawson Olympic(NED) Math 20084 18 Netherlands

9

9

22

2

1

7

19

Sweden (SWE)

4

Kidawson Olympic Math 2008

• •

• • • • •

Look at the above medal count. What would happen to the table if only the total was taken into account? Compare between two alternative medal counts – gold medals and country totals. Why are they different? What do you think is more fair and why? Think of another way of ranking data you think would be even fairer. What would happen to the medal table if Gold=3 Silver=2 Bronze=1? What would happen if countries were grouped by size and the number of athletes competing? What if % were used?

15. Background Information and Ideas about measurement within the Olympics

Issues about measurement and its history -- What, how and why we measure WHY THINGS ARE MEASURED: •

•

•

mostly, it is a (usually preliminary) step to determine who wins an event and to rank the other participants -- (NOTE: in most sports, the ranking ends up being "complete", but not always -- ex: hockey; but this is a point may be to consider more when I think about the issue of order) measurements necessary to prepare the right conditions to play the game (ex: length the speed skaters have to cover in each specific event; position of poles in slalom; dimensions of hockey field and exact position of "goal door" -- (NOTE: I realize I am lacking a lot of precise sport terminology! the need to use precise terminology here could provide an interesting analogy with the use of precise terminology in math -- something worth thinking about...); etc.) in a sense, we could also talk of the use a person can make by knowing his/her competitors "measures" in an event (what do they need to do in order to "beat him/her" or win, how it compares with their "average" or "best" performance (NOTE: this could actually lead to some statistics and probability considerations... worth thinking about)

WHAT IS MEASURED? Kidawson Olympic Math 2008

• • •

• •

time taken to complete an event (ex: most athletics, canoeing swimming (not relevant in: pole-jump, hockey) Speed (average? instant?) (ex: running) Accuracy of performance -- this could be more or less objectively determined; objective ex: number of targets made/ missed in pentathlon (?) -- subjective ex: artistic score in rhymic gymnastics distance -- ex: how far one jumps with long jump ; what a sprint kayaker has to paddle; medals won by a country (notice here how gold, silver and bronze are essentially not comparable, unless we explicitly create "ways" to do so)

NOT SURE IF "WHAT" OR "HOW": • •

"Scoring" used to combine target shooting and speed in pentathlon (?) measuring of time, etc. when participants go in "batches" (ex: 2 speed skaters a time)

HOW IS MEASURED -- i.e., what UNITS are used: • • • •

TIME: hours, minutes, seconds, 1/100th of second (NOTE: scores are "mixed numbers") DISTANCE: miles/ km / m etc. (when would you choose one versus the other? why? how do you convert?) SPEED: miles/hour; kilometers/hour; meter/sec. (why these "compounded" units? when would you choose one versus the other? why? how do you convert?) many things are measured in whole numbers, by just counting

HOW IS MEASURED -- i.e., what TOOLS and APPROACHES are used: • •

• •

• •

speed -- requires actually measuring distance and time; average vs. instant How can a skier time really be measured? (Technology used, etc.; it may be quite different for a cross country biker or a slalom paddlers; also, you probably have two different people and instruments measuring at "beginning and end" -- how can those be coordinated?) "elimination rounds" (ex: hockey) (how do they really work? when are they necessary/ useful in a sport) Competitors going one at the time (ex: slalom), in groups of 2-n (ex: speed skating), altogether (some cross country skiing, perhaps?) -- Why? How different is this from having elimination rounds? how are borderline cases decided (ex: bullet hitting the target on line) averaging several runs (ex: bob, sled)

WHAT IS COMMON IN PREVIOUS EXAMPLES: •

•

Essentially all measurements end up being expressed in some kind of number (is it really true all the time? is it really necessary and if so why?) (NOTE: it might be interesting to consider what kind of numbers are or not represented -- ex: no irrationals!) In all the "objective" measurements, you use the same process (choose a unit, etc.)

Kidawson Olympic Math 2008

WHAT IS DIFFERENT IN PREVIOUS EXAMPLES? • •

•

some measurements use whole units (ex: goals in hockey; targets in shooting; scoring in figure skating), others a continuum (distance) Competitors going one at the time (ex: slalom), in groups of 2-n (ex: speed skating), altogether (some cross country skiing, perhaps?) -- Why? How different is this from having elimination rounds? Some events use "elimination rounds" and others don't (why?)

OTHER QUESTIONS/ ISSUES THAT COULD BE RAISED: • • • • • • • •

How do different events deal with ties? Are there events when ties are just NOT possible? Were any of the events measured differently in the past? If so, why/ why was it changed? How did people come up with criteria to measure more subjective things (ex: figure skating)? How "precise" the measurements taken really are? How can these imprecision’s affect the events? What can be done to make those measurements more "precise"? What is already done to make measuring more "fair"? What else could be done? (ex: figure skating -- dropping highest and lowest mark) What is the "fastest" winter sport? (NOTE: one should also consider the speed of sportsman who are not measured on speed -- ex: skating speed of hockey players) How would you judge who is the "best" skier? Or even the "fastest" skier? How would you judge whether the winner won by a large margin or not? (Difference? ratio? why? how do you compute each of those?)

Kidawson Olympic Math 2008

16. Olympic Project Some Ideas for independent, group, and class work

Record of teacher's modeling how the proposed framework for the project could be used to summarize the results of their inquiry around "Who's fastest?"

Kidawson Olympic Math 2008

Quest: A question in your area of interest. Who’s fastest? Graphs and Tables- bar graphs on sports, flags, participation numbers, countries attending historically, speed factors, medal counts Data gathering: research, newspaper articles, timed events, Drawing conclusions: analyzing data and reporting in different ways. Are the results always the same?

OLYMPIC UNIT PROJECT You are a math reporter covering the Summer Olympic Games in Norway. Your assignment is to write an article about an aspect of the Summer games that involves mathematics. Your project will have 5 parts worth the following points: QUEST - A question in your area of interest (5 points) DATA - From magazines, newspapers, T.V., etc. (10 points)

Kidawson Olympic Math 2008

GRAPHS AND TABLES - Frequency table and 2 graphs (choose from bar, line, pictograph, or circle graph) (25 points) BEHIND THE SCENES: What factors effect your data? Identify and provide information about the story behind the data. (10 points) CONCLUSIONS - Written in newspaper article form with headline and any supporting graphs or pictures. This article should include mean, median, mode and range, if appropriate to your data, in order to help you draw your conclusions. (30 points)

Kidawson Olympic Math 2008