Shoelaces 2
posted March 15, 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. In this part of the series, students explore issues of scale and the meaning of y-intercepts. 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.

(The applet for this problem is currently unavailable) 

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Sample submitted solution:

From: Scott, age 13
Josh, age 12
School: Issaquah Middle School, Issaquah, Washington

1. What length of ribbon do you need for a box with a dimensional sum of 3cm?
about 25cm

2. What length ribbon do you need for a box with a dimensional sum of 70cm?
about 168

3. Polly is willing to wrap packages with dimensional sums ranging from 3cm to 70cm. What maximum X and maximum Y values would you use on a graph to help her employees choose ribbon lengths for packages? Explain how you chose this scale.
70 and 170 I put the max values she could wrap on the x axis then i put the line of best fit on. then i made it big enough to see.

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