Shoelaces 1
posted March 1, 2000 as a Math Forum EPoW

Introduction: In this problem, students use graphing skills to help store customers choose the best shoelace length and giftwrappers the best ribbon length.

Where's the Math: The problem series encourages students to make predictions and develop generalizations from data represented on a graph. Standards: Data analysis and probability, measurement, algebra Role of Components: The Shoelaces problem uses the PEN component overlayed on top of a SimCalc graph to provide scafolding to students new to point plotting. Positive feedback is given in the form of a green circle that appears on the graph when the student moves the mouse over a point in a given list. The second part of the EPoW used PEN with simple function to fit a line to the set of plotted points. Students experiment with the y-intercept using a swing slider. Graph instructions are displayed via the HTML viewer, and solutions are entered in a text entry box. Javascript handles communication among components.

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Sample submitted solution:

From: Jeni, age 12
School: Issaquah Middle School, Issaquah, Washington

1. What length shoelace will best fit a shoe with 18 eyelets?
170cm

2. You are going to display this graph in the shoelace department of As the Shoe Fits. Write clear directions for customers which describe how to use the graph to determine which length of shoelace to purchase. When choosing your shoelace length, you can look at this graph to help you find the perfect length.
Take a look at your shoes. Count how many eyelets you have on 1 of your shoes. Then, look at the graph, and find your amount under the "eyelets" axis. Then, continue to go up the line of where your eyelets is plotted, until you reach the line shown on the graph. Once you stop at the line shown, look at the horizontal line that intersects with it. The number written next to it under the "lengh" axis is the perfect length for your shoelaces! I found this works because it shows how many eylets you are going to have to shoelace, and how much lace you will need. It also gives you shoelace left over to tie a decent knot.

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