STINKY FEET

Height Vs. Shoe Size

"The Shoe Salesman's Question"

A Webquest for Math 105/214

Introduction

Poor old Al Bundy, the world famous shoe salesman, needs your help with his shoe sales job. Long-story-short, he'll pass out if he sees another cheese-encrusted, wrinkle-toed, stinky foot. He is calling upon you to help him determine if he can sell shoes based on a person's height!

Task

In this web-quest students will collect data (shoe size & height in inches). Students will then be taken through various steps designed to analyze their data. In the end, students will be asked to answer the question, "Do you think it would be reasonable to sell shoes by a person's height?"

The project should be conducted individually. But use your class mates to collect the data. You will be given one week to conduct your research and write your essay based on your analysis.

Process

You can cut and paste this "Process" into Word, if you don't want to rewrite each step.

HERE WE GO:

Record your shoe size and height in inches on a slip of paper.

** Because sizing is different for men and women, female students will need to record the corresponding men's size if they know it or subtract 1.5 from their women's size.

Record the results from the class in a table similar to the one below. The Predicted Shoe Size and Amount of "miss" will be filled in later (step 10, below). You can print this one if you would like to (or copy & paste it into Word):

Height (x)	Shoe Size (y)	Predicted Shoe Size	Amount of "miss"

Now, on a sheet of graphing paper, plot each person's coordinates...
(x, y) = (height, shoe size) as points on the grid. Label your x-axis "height" and y-axis "shoe size".
Do most of the points seem close to falling on a line? One way to tell is to draw as narrow an oval as possible around the points. The narrower the oval, the closer the points are to lining up. The more circular the oval, the less so.
Draw a line through the middle of your scatter plot. The line should also run through the middle of your oval.
Your line is a geometric model for the relationship between height and shoe size.

You can use your model to estimate your shoe size. Find your height on the horizontal scale and trace upward until you come to the line. Then trace to the left until you come to the vertical scale. Read your predicted shoe size.

What shoe size was predicted?________

How does the predicted shoe size compare with your actual shoe size?_____________________
Choose two points on your line whose coordinates are integers. They do not have to be points of your original data but should be fairly far apart. Record the coordinates of the points below:

______________

______________
Use these two points to find the slope of the line.

Slope = _______
Use your slope and one of your two points to find the y-intercept,
(0, b) of the line. Write the y-intercept and the equation of the line.

y-intercept: ______________

equation: ________________
Your equation is an algebraic model for the relationship between height and shoe size.

Use this model to calculate your predicted shoe size. Do this by substituting your height for x in the equation and rounding the shoe size to nearest 0.5.

What shoe size was predicted? ________

How close is the predicted size to your real shoe size? _______
Use your equation to calculate the predicted shoe size for each member of your class. Be sure to round to the nearest 0.5. Record the results in the third column of the table, "Predicted Shoe Size".
In the fourth column, record the amount the predicted size missed the real size for each student (the difference).
Compare your misses with those of another student. Whose line did the best job of predicting shoe sizes for the members of your class? Why?
a. According to the Guinness Book of World Records, the tallest person who ever lived was Robert Wadlow, who was 8 feet, 11 inches tall.

What shoe size does your equation predict for him? ________

b. The tallest woman is Sandy Allen at 7 feet, 7 inches.

What shoe size does your equation predict for her? ________
What shoe size does your equation predict for a person who is 50 inches tall? ________

Do you think this prediction is reasonable? Why or why not?
Write a short essay (1 PAGE) on why or why not it would be reasonable to sell shoes by a person's height.

Evaluation

Grades are based on the following criteria and rubric:

Correct Equations: 5 pts
Correct Graphical Representation and Solution: 5pts
Correct Solution by Substitution: 5pts
Correct Solution by Elimination: 5 pts

Rubric for Essay: 35 points

	Beginning	Developing	Accomplished	Exemplary
Meaning: the extent to which the response exhibits sound understanding, interpretation, and analysis of the task and text(s)	~convey a confused or inaccurate understanding of the research ~alludes to the research but makes unclear or unwarranted connections 1 pt	~convey a basic understanding of the research ~makes superficial connections between information and ideas in the research 3 pts	~convey a thorough understanding of the text ~make clear and explicit connections between information and ideas in the research 5 pts	~reveal an in-depth analysis of the research ~make insightful connections between information and ideas in the research 7 pts
Development: the extent to which ideas are elaborated using specific and relevant evidence from the text(s)	~are incomplete or largely undeveloped, hinting at ideas, but references to the research are vague, irrelevant, repetitive, or unjustified 1 pt	~develop some ideas more fully than others, using relevant and specific details from the research 3 pts	~develop ideas clearly and consistently, using relevant and specific details from the research 5 pts	~develop ideas clearly and fully, making effective use of a wide range of relevant and specific details from the research 7 pts
Organization: the extent to which the response exhibits direction, shape and coherence	~lack an appropriate focus but suggest some organization, or suggest a focus but lack organization 1 pt	~establish, but fail to maintain an appropriate focus ~exhibit rudimentary structure but may include some inconsistencies or irrelevancies 3 pts	~maintain a clear and appropriate focus ~exhibit a logical sequence of ideas but may lack internal consistency 5 pts	~maintain a clear and appropriate focus ~exhibit a logical and coherent structure through skillful use of appropriate devises and transitions 7 pts
Language Use: the extent to which the response reveals an awareness of audience and purpose through effective use of words, sentence structure, and sentence variety	~use language that is imprecise or unsuitable for the audience or purpose ~reveal little awareness of how to use sentences to achieve an effect 1 pt	~rely on language from the research or basic vocabulary, with little awareness of audience or purpose ~exhibit some attempt to vary sentence structure or length for effect, but with uneven success 3 pts	~use appropriate language with some awareness of audience and purpose ~occasionally make effective use of sentence structure or length 5 pts	~are stylistically sophisticated, using language that is precise and engaging, with a notable sense of voice and awareness of audience and purpose ~vary structure and length of sentences to enhance meaning 7 pts
Conventions: the extent to which the response exhibits conventional spelling punctuation, paragraphing, capitalization, grammar, and usage	~demonstrate a lack of control of the conventions, exhibiting frequent errors that make comprehension difficult 1 pt	~demonstrate emerging control of the conventions exhibiting occasional errors that hinder comprehension 3 pts	~demonstrate partial control of the conventions, exhibits occasional errors that do not hinder comprehension 5 pts	~demonstrate control of the conventions with essentially no errors, even with sophisticated language 7 pts

Conclusion

By completing this project, students should learn how to create a linear model based on collected data. They will also see that height will not always be an indicator of shoe size. Sometimes we need to go above and beyond a simple linear model to predict things. The methods used in this webquest are an important start to understanding data collection and mathematical modeling. We will discuss these topics further in class!

Most Recent Update: May 14, 2004