Lesson Review
| Author: | Kevin Jordan |
| ETP Title: | Geometry Through a Sundial |
| Organization: | |
| ETP Type: | |
| Grade Level(s): | 10 |
Subject Areas
- Mathematics
California Standards
7.0 Students prove and use theorems involving the properties of parallel lines cut by a transversal, of quadrilaterals, and of circles.
7.0 Students prove and use theorems involving the properties of parallel lines cut by a transversal, the properties of quadrilaterals, and the properties of circles.
Lesson Abstract:
The purpose of this project is to introduce students to one of the most ancient methods of telling time in the world, the sundial.
In working through this project students will
1. Do research online and answer questions based upon your research
2. Complete exercises which involve the geometric principles upon which sundials are
based
3. Construct a Geometer’s Sketchpad dynamic model of these geometric principles
4. Learn what True North is, why it is important for Sundial Operation
5. Locate True North for your own sundial.
6. Construct an Equatorial Sundial Faceplate using Geometer’s Sketchpad
7. Compute the dimensions required to make your Equatorial Sundial operate accurately
8. Assemble and orient your working Equatorial Sundial.
9. Produce a picture or poster report of your efforts.
The needs this ETP will fulfill in the classroom, teaching or school:
The connection between the ETP and Fellowship. :
Outline:
Need:
Students often go through geometry as a set of exercise which have little "real world application". This project is intended to bring together several differing geometric and scientific concepts in a manner that is engaging and self-verifiable.
a) Additional Standards:
Math 8.0 Students know, derive, and solve problems involving the perimeter and circumference of common geometric figures.
Math 18.0 Students know the definitions of the basic trigonometric functions defined by the angles of a right triangle.
Math 19.0 Students use trigonometric functions to solve for an unknown length of a side of a right triangle, given an angle and a length of a side.
b) Connection to fellowship--My fellowship position at Santa Clara University had me participate in the design and construction of a sustainable solar home as part of the Dept. of Energy's Solar Decathlon. Orienting Solar panels to achieve maximum efficiency requires they be positioned at a specific angle to the sun. Understanding the movement of the sun across the sky and throughout the year and being able to predict the sun's elevation in the sky is central to being able to determine this optimum angle.
c) Learning Objectives:
1) Students will be able to identify basic parts of a sundial
2) Students will be able to identify at least three different types of sundials
3) Students will be able to explain the difference between Local apparent time and
Mean Solar Time
4) Students will be able to identify the times of the year when their sundial will give accurate time and when it will not.
5) Students will learn how to locate True North
6) Students will know how to orient their sundial using True North
7) Students will construct and assemble a fucntional sundial
8) Students will identify and summarize the geometric concepts which they used and which they must know in order to build a sundial and understand how it works.
d) Materials/Resources
1) URL: http://www.mysundial.ca/tsp/tsp_index.html
URL: http://en.wikipedia.org/wiki/Solar time
2) Geometer's Sketchpad-- students will need individual access to this software
3) Paper/ wood or metal-- depending upon student ambition
e) General Overview
This project is intended as an "application" of multiple concepts students have learned over the course of the year. After students have learned through traditional lecture and practice the vocabulary of circles, right triangles and trigonometric functions or right triangles, they will construct a functioning sundial and explain how it works using the appropriate geometric concepts of circles, parallellism, and right triangle trigonometry.
f) Evaluation Method
This project consists of seven exerices which students will work through prior to the assembly of their dial. these exercises can be piggybacked on assignments given in class or, in the case of the faceplate lab, completed as an in class dynamic geometry lab assignment. Successful completion of each exercise will allow students to continue to the next.. Once the faceplate lab is successfully completed, the student will be ready to build his/her dial.
g) Possible Timeline-- can vary according to how much class time is devoted to ths project (ie whether or not it is piggybacked onto existing class assignments)
1) Day 1 & 2: Intro to sundials powerpoint. Students to read/research sundial terminology, operation and variety. Complete Background Info questionnaire
2) Day 3 Sundial Geometry Exericise Handout
3) Day 4: Sketchpad lab-- make a model of Sundial Geometry- demonstrate result
4) Day 5 : Determine True North -- Part 1
5) Day 6-- (do over a weekend) Determine True North Part 2
6) Day 7 -- In class Lab: Make an Equitorial Sundial Face Plate
7) Day 8- Assembly Handout
Depending upon teacher interest-- a concluding assessment project could be to have the student make a poster to include the basic geometric concepts used in making a sundial, and to have a picture of their sundial in its position at home (next to a magnetic compass to indicate that it's facting approximately the appropriate direction ** note that magnetic north is NOT the same as TRUE north)
h) uploaded files :
Sundial Sundials.ppt 11168k 1-Intro 1a GeoThru Sundial Intro.pdf 48k 2-Research 2 Sundial Questions.pdf 56k 2a-Research Solns 2b Sundial Questions solns.pdf 63k 3-Geometry of Sundial 3 Sundial Geo Ex.pdf 597k 3a-Geo of Sundial Solns 3bSundial Geometry Table-soln.pdf 40k 3b-Making a Sketchpd model 3cMkng Sktchpd Mdl Geo.pdf 147k 4-Finding True North 4 Finding True North.pdf 17k 4a-Finding True North Soln 4a Finding True North-soln.pdf 30k 4b-Finding True North -2 4b Finding True North--2.pdf 35k 5-Making Sundial Plate 5Mkng Sktchpd Face Plate.pdf 364k 5b- Sundial Plate 5bEquatorial Sundial Plate.pdf 33k 6-Assy of Sundial 6Assy of Equatorial Sundial.pdf 719k
Objectives of the ETP:
Types of assessment or evaluation that will accompany this ETP:
Bibliographic or other resources your used in creating this curriculum:
Supply List:
Attachments:
