## "Marathon Graphing" Teacher Support

Marathon Graphing Archived PoW || Student Version

Marathon Graphing is no longer the current ESCOT Problem of the Week. The student version allows teachers to use the problem with their students without giving the students access to the archived answers. Teachers can use the link to the archived problem to get ideas of student thinking.

[Standards]  [Activities]  [Lessons]  [Dr. Math]  [Vocab]  [Other Resources]

Marathon Graphing asks students to think about models of real-life linear relations, including world record times for the men's and women's marathon. In addition, students are helped to understand the meaning of x- and y-intercepts, slopes, and how to use linear models to predict past and future events.

This ESCOT PoW could be used as an exploration of linear relations, x- and y-intercepts, and slope.

If you have something to share with us as you use any of the links or suggestions on this page (something you tried and changed or a new idea), we would love to hear from you. Please email us.

Alignment to the NCTM Standards - Grades 6-8

Algebra
- identify functions as linear or nonlinear and contrast their properties from tables, graphs, or equations
- explore relations between symbolic expressions and graphs of lines, paying particular attention to the meaning of intercept and slope
- use graphs to analyze the nature of changes in quantities in linear relations
- model and solve contextualized problems using various representations, such as graphs, tables, and equations

Geometry
- use visualization, spatial reasoning, and geometric modeling to solve problems

Data Analysis & Probability
- select and use appropriate statistical methods to analyze data

Problem Solving
- solve problems that arise in mathematics and in other contexts

Communication
- communicate mathematical thinking coherently and clearly to peers, teachers, and others
- use the language of mathematics to express mathematical ideas precisely

Connections
- recognize and apply mathematics in contexts outside of mathematics.

Possible Activities:

Pre-Activity
The activity Least squares fit line by ExploreMath (requires Shockwave plug-in) can be done informally and for fun. Students use the slider bars to create a line, and then press the line of least squares to test how well they have done.

Students collect and analyze data by passing a hand squeeze around a circle. Details for this activity have been written by Cynthia Lanius in The Hand Squeeze Problem.

Plot simple linear relations from tabular data, and identify the x- and y-intercepts as well as the slope. Investigate how the slope changes if the x- (or y-) intercept is increased or decreased, and vice versa. Construct a table of data that has a slope parallel to the first line.

Post-Activity
Use a graphing calculator (or Excel) to see whether the marathon data are really linear. Explore non-linear relations and compare to linear ones.

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Related Lessons Online:

Lessons Online - Interpreting Graphs:

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Resources to use with students:
- Math Terms - Ask Dr. Math FAQ

- Best Line Fit: Least Squares
- Domain and Range
- Finding the Equation of a Line
- Function Machine
- Geometric Objects and Properties using Algebra
- Mapping Functions in the Real World
- Natural Domain of a Function
- Range and Domain of a Graph
- Slope
- X- and Y-Intercepts

Vocabulary
- axis
- domain
- function
- graph
- line
- line of best fit
- range
- slope

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Other Resources
Graphing:
- Chameleon Graphing
- General Coordinates Game
- Graphing a line
- Graphing a linear equation using y=mx + b
- Maze Game
- Meeting Lulu
- Plotting points