Llama 1
posted December 1, 1999 as a Math Forum EPoW

Introduction: In the Llama puzzle series, students explore the relationship between area and perimeter by experimenting with an applet. In this part of the series, students resize a llama pen and try to find the lengths that will give the maximum area with a certain perimeter.

Where's the Math: This problem challenges students to estimate, hypothesize, experiment and draw conclusions using geometry, ratio/proportion and measurement sense. Students encounter concepts of maxima as they experiment with various heights and widths of the lama's pen. Open-ended questions encourage students to revisit their assumptions, targeted questions encourage directed exploration, and process oriented questions encourage students to rethink their answers. Standards: Measurement, algebra, geometry, data analysis & probability Role of Components: The Llama problem series uses Geometer's Sketchpad allow students to interact with a simulated barn and pen. Height and widths are inputted via number entry fields (labeled with ESCOT labels) and triggered by a button panel. Instructions are displayed via the HTML viewer, and solutions are entered in a text entry box. Logoscript handles communication among components.

 Try the applet!

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Sample submitted solution:

From: Landon, age 14
School: Issaquah Middle School, Issaquah, Washington

1. What did you expect to happen?
I expected the largest area to be a rectangle with the long end to the barn because that the barn is free fence space!

2. What was the width and height that gave the largest area? Explain how you figured it out.
9 height, and 18 width. I figured it out by making estamates with large spaces in between. When the area started to get smaller I went knoch by knoch till I got the highest area.

3. Is there just one answer? Explain your thinking.
No, because you can always get more specific with decimals so the area could always get slightly bigger but with a fence you probably want to stick with .5's.

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