Cooperative Manufacturing Module

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## Overview

Depending on the level of the math class, you might need to review with the class how to calculate circumference and, similarly, how to find the arc length of a quarter circle. They might also need a review (or supplementary lesson) on applying the Pythagorean theorem and using trig functions or ratio of side lengths in a 30-60-90 triangle.

A couple other activities that might be beneficial to the class before beginning the actual base plate project involves the Cartesian coordinate system and communicating in mathematical terms. The sample assessment item attached could be used for the students to complete individually. The other activity is for students to perform in pairs. Sitting opposite each other with folders (or other dividers) standing upright between them, one students has a piece of graph paper with geometrical figures on it while the other has only a blank sheet of graph paper. With both students unable to see the other person's paper, they try to duplicate the original. The "communicator" uses the coordinate system to describe where each figure is located and the "grapher" plots accordingly. (Note: Even the two axes are missing and must be communicated at the very beginning.)

After practicing some of the mathematical skills needed for the base-plate project, the class is ready to go to the computer lab and download the project from the Internet. (They can break up in groups of two, three, or four students depending on the size of the class and the number of computers available.) The teacher provides the URL and lets the students read the entire description of the project. At this point, discussion of the objectives is important and if the students have further questions already, they can be encouraged to e-mail those inquiries to the students and staff at Davea. Next, the students will need to print a copy of the blueprint of the base plate and perhaps the objectives and suggested approach to the problem as well.

After the students have read about the project and before they spend the remaining time in class starting to compute the lengths of the missing dimensions (labeled A-J) on the blueprint, the teacher should show the brief video made at Davea which explains the milling process in more detail. (A TV-VCR should be in the computer lab so that the students can watch the tape right after reading the project's description.)

The students will probably need more time at the beginning of class working in their groups to finish calculating all the missing lengths on the blueprint. The teacher can check that they are handling the arc lengths okay and the two missing sides of the 30-60-90 triangle.

As students finish finding all the missing dimensions, they can begin using those lengths to transfer the blueprint to graph paper and identify the coordinates of the critical points around the base plate. (Teacher should have a discussion with the class about which points are needed to include in the instructions for the plate to be milled correctly. Remind them not to forget about the screw holes!)

It is probably better for each student to create his/her own graph of the base plate rather than only making one per group. After all group members agree on what the graph should look like and what the correct coordinates are, they can collaborate on the final write-up. These milling instructions should contain a list of all the important coordinates around the base plate and a description of the curves involved. Each of these three arc lengths will need to be described by the center and the radius of the circle of which it is a part. Again, remind the students not to forget to also describe the center and the radius of each of the two screw holes.

Depending on the availability of computers and the program Geometer's Sketchpad, the students might also plot the points of the base plate on the computer. If using Geometer's Sketchpad, the students should bring up a new sketch and proceed as follows:

1) Choose "Show Grid" from the Graph menu.
2) Choose "Plot Points" from the Graph menu and input all the coordinates they calculated around the edges of the baseplate, starting with the origin and then going around the figure in order. Click "Plot" to see all the points plotted on the grid.
3) To automatically connect all the points, choose "Segment" from the Construct menu. (Notice however that the endpoints of the arcs will have been connected with diagonal lines rather than curves.)
4) Delete the three diagonal lines where curves should be, locate the centers of the circles, and construct the circles with the given radius lengths.
5) Construct the three arcs (quarter circles) on the circles and then use "Hide Objects" to conceal the original circles.
6) Draw the two screw holes by plotting the centers of those two circles and one radius.

Groups will be continuing at their own paces. Again, if they have questions as they are working, they should be encouraged to correspond via e-mail with the students at Davea. Once a group has completed finding the coordinates and verifying them on a sketch, the group members can use the form on the project's homepage to send their results to Davea.