Olympic records through time

SCORE Mathematics

Standards Connections

Olympic Records Through Time

Introduction: Are we faster, stronger, better than we used to be? Compare the records of gold medal Olympic winners for the last 100 years and decide.

Prior Knowledge: You will need to have beginning graphing skills.

Grade Level: 4-7

Task: Produce a graph/chart which shows performance in a particular event over time. If possible, find an equation which describes the trend in performance. Write/discuss the possible causes for the change.

Resources:

Olympics Results <http://www.ex.ac.uk/cimt/data/olympics/olymindx.htm>
Olympic records <http://www.hickoksports.com/history/olympix.shtml>
The Olympic Sports <http://abc.net.au/olympics_1996/sportspg.htm>
USA Swimming Olympics <http://www.usswim.org/olympics/olymedme.htm>

Student Worksheet (html) / (pdf)

Process: First, go to above URL and choose an event. Second, make a table/graph of year and record (time, distance, speed, what's appropriate depends on the event). Third, make note of any trends in performance. Lastly, discuss/write about the trend and speculate on its cause. Can you make an equation that describes the trend? Remember, staying the same is also a trend (y = c).

Learning Advice: I recommend a chart/graph with the year on the horizontal axis and the record(time, distance, etc.) on the vertical. Will you start at zero? Choose a scale appropriate to your data.

Evaluation: Two items will be evaluated. First, data plot/graph (accuracy). Second, essay/discussion of trends and causes. (quality of work--rubric)

Extensions: Some sports give a time and a distance. It would be good to give each student 1 year and have them compute a per unit rate so that different years could be compared. This way the whole class does one sport rather than letting each student choose their own event. The teacher could print out one set of medalists at home and have the class all do the same one if Internet access is limited.

Conclusion: You have had practice organizing and analyzing data. You may have had practice creating equations of lines. You will have done critical thinking in speculating at the causes of the results you observed.

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California Mathematics Academic Standards:

Grade 4:
Algebra and Functions
1.0 Students use and interpret variables, mathematical symbols, and properties to write and simplify expressions and sentences.
1.4 use and interpret formulas (e.g., area = length x width or A = lw) to answer questions about quantities and their relationships

Grade 5:
Algebra and Functions
1.0 Students use variables in simple expressions, compute the value of the expression for specific values of the variable, and plot and interpret the results.

1.1 use information taken from a graph or equation to answer questions about a problem situation
1.2 use a letter to represent an unknown number; write and evaluate simple algebraic expressions in one variable by substitution

Mathematical Reasoning
1.0 Students make decisions about how to approach problems.

1.1 analyze problems by identifying relationships, discriminating relevant from irrelevant information, sequencing and prioritizing information, and observing patterns

2.0 Students use strategies, skills and concepts in finding solutions.

2.3 use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning

Grade 6:
Mathematical Reasoning
1.0 Students make decisions about how to approach problems.

1.1 analyze problems by identifying relationships, discriminating relevant from irrelevant information, identifying missing information, sequencing and prioritizing information, and observing patterns

2.0 Students use strategies, skills and concepts in finding solutions

2.3 estimate unknown quantities graphically and solve for them by using logical reasoning and arithmetic and algebraic techniques

Grade 7:
Algebra and Functions
1.0 Students express quantitative relationships using algebraic terminology, expressions, equations, inequalities and graphs.

1.1 use variables and appropriate operations to write an expression, an equation, an inequality, or a system of equations or inequalities that represent a verbal description (e.g., three less than a number, half as large as area A)

Mathematical Reasoning
2.0 Students use strategies, skills, and concepts in finding solutions.

2.3 estimate unknown quantities graphically and solve for them by using logical reasoning and arithmetic and algebraic techniques

NCTM 5-8:

STANDARD 1: MATHEMATICS AS PROBLEM SOLVING
STANDARD 2: MATHEMATICS AS COMMUNICATION
STANDARD 3: MATHEMATICS AS REASONING
STANDARD 4: MATHEMATICAL CONNECTIONS
STANDARD 7: COMPUTATION AND ESTIMATION
STANDARD 8: PATTERNS AND FUNCTIONS
STANDARD 9: ALGEBRA
STANDARD 10: STATISTICS

NCTM 9-12:

STANDARD 1: MATHEMATICS AS PROBLEM SOLVING
STANDARD 2: MATHEMATICS AS COMMUNICATION
STANDARD 3: MATHEMATICS AS REASONING
STANDARD 4: MATHEMATICAL CONNECTIONS
STANDARD 5: ALGEBRA
STANDARD 10: STATISTICS
STANDARD 12: DISCRETE MATHEMATICS