First Semester Pre-calculus Project

Elliptical Templates

The Problem: A carpenter friend of yours needs some templates that he can use to produce the correct holes in the roof. Your group is to produce the correct template for each pipe-and-roof combination below.

Create two elliptical templates using a method determined by your group. Make sure to indicate, in order, all of the following on your template:

  • a = 1/2 of major or minor axis.
  • b = 1/2 of major or minor axis.
  • c = distance from center to foci.
  • p = pipe diameter.
  • m = pitch of roof.
  1. Work/steps must be shown, on front side of template, for the process used to find all the values. No work shown for any one item will result in a letter grade drop. Neatness counts.
  2. Make sure to round only at the last step when solving for specific lengths.
  3. Cut the hole for the elliptical template. The template should be made from a file folder and should lay flat until needed. Do not include loose materials that can be lost.
    Use Microsoft Word to assist in drawing the proper template. (I will show you this later on).
  4. Each template should come with "pitch" triangles that can be used to slant the template at the proper slope. Do not include loose materials that can be lost.

The following table shows the template number, circumference of pipe, and pitch of roof.

Template / Circumference
(in mm) / Pitch
(rise:run) / Template / Circumference
(in mm) / Pitch
(rise:run)
A(1) / 246 / 3:12 / B(1) / 145 / 3:12
A(2) / 246 / 4:12 / B(2) / 145 / 4:12
A(3) / 246 / 6:12 / B(3) / 145 / 6:12
A(4) / 246 / 8:12 / B(4) / 145 / 8:12
C(1) / 162 / 3:12 / D(1) / 127 / 3:12
C(2) / 162 / 4:12 / D(2) / 127 / 4:12
C(3) / 162 / 6:12 / D(3) / 127 / 6:12
C(4) / 162 / 8:12 / D(4) / 127 / 8:12

You will work on this project with one other person specified below. This person can help you brainstorm ideas about how to solve the problem. Your group will have two folders to make. Each person makes one to turn in. You may NOT talk to anyone about this project except Mr. Bosma and your partner. It IS considered CHEATING to talk to anyone else about the project. If discovered, you will receive the necessary penalty.

Here are the group assignments:

Group / Templates / Group / Templates
Tyler, Chalsey / A(1), A(2) / Lindsay, Inez / B(3), B(4)
Nico, Heidi / B(1), B(2) / Adam, Carson / C(3), C(4)
Mason, Justin / C(1), C(2) / Burr, Mark / D(3), D(4)
Abby, Josh / D(1), D(2) / Brittany, Eric / A(1), A(2)
Blake, Parker / A(3), A(4) / Cody, Andreas / B(1), B(2)

The project will be due Wednesday, December 12.

The grading rubric for the project can be found on the following sheet.