Astronomy Lesson Plan

Name: Leah Coutorie

Title of lesson: Using a Dobsonian Telescope to find Proportions

Date of lesson: March 23, 2005

Length of lesson: 1 ½ hours

Description of the class:

Name of course: Algebra I

Grade level: 9^th grade

Honors or regular: regular

Source of the lesson:

Optics seminars with Eric Hooper.

TEKS addressed:

§111.32. Algebra I (One Credit).

(a) Basic understandings.

(1) Foundation concepts for high school mathematics. As presented in Grades K-8, the basic understandings of number, operation, and quantitative reasoning; patterns, relationships, and algebraic thinking; geometry; measurement; and probability and statistics are essential foundations for all work in high school mathematics. Students will continue to build on this foundation as they expand their understanding through other mathematical experiences.

(2) Algebraic thinking and symbolic reasoning. Symbolic reasoning plays a critical role in algebra; symbols provide powerful ways to represent mathematical situations and to express generalizations. Students use symbols in a variety of ways to study relationships among quantities.

(3) Function concepts. Functions represent the systematic dependence of one quantity on another. Students use functions to represent and model problem situations and to analyze and interpret relationships.

(4) Relationship between equations and functions. Equations arise as a way of asking and answering questions involving functional relationships. Students work in many situations to set up equations and use a variety of methods to solve these equations.

(5) Tools for algebraic thinking. Techniques for working with functions and equations are essential in understanding underlying relationships. Students use a variety of representations (concrete, numerical, algorithmic, graphical), tools, and technology, including, but not limited to, powerful and accessible hand-held calculators and computers with graphing capabilities and model mathematical situations to solve meaningful problems.

(6) Underlying mathematical processes. Many processes underlie all content areas in mathematics. As they do mathematics, students continually use problem-solving, computation in problem-solving contexts, language and communication, connections within and outside mathematics, and reasoning, as well as multiple representations, applications and modeling, and justification and proof.

(b) Foundations for functions: knowledge and skills and performance descriptions.

(1) The student understands that a function represents a dependence of one quantity on another and can be described in a variety of ways. Following are performance descriptions.

(B) The student gathers and records data, or uses data sets, to determine functional (systematic) relationships between quantities.

(C) The student describes functional relationships for given problem situations and writes equations or inequalities to answer questions arising from the situations.

(D) The student represents relationships among quantities using concrete models, tables, graphs, diagrams, verbal descriptions, equations, and inequalities.

(E) The student interprets and makes inferences from functional relationships.

(3) The student understands how algebra can be used to express generalizations and recognizes and uses the power of symbols to represent situations. Following are performance descriptions.

(A) The student uses symbols to represent unknowns and variables.

I. Overview

This lesson will teach students to use a Dobsonian telescope indoors in order to find angle of view. They will work with measuring lengths and solving for angles to find the field of view. By using the telescopes, the students will be able to make real world connections and use math in real world contexts.

II. Performance or learner outcomes

Students will be able to:

Measure various distances

Solve for angle of view

Measure field of view

III. Resources, materials and supplies needed

1 Dobsonian telescope per group

1 meter stick per group

IV. Supplementary materials, handouts.

Wrap-up Handout

Five-E Organization

Teacher Does Probing Questions Student Does

Engage: I’ll explain that everything we see is in our field of view, which depends on the angle of view. I will ask them various questions about these ambiguous terms and call on them as they raise their hands and listen to them as they call out answers.

1. What do you think our field of view is? 2. Then what is the angle of view? 3. When you look at something up close, do you think the angle of view is smaller or larger than if you look at it far away? Why?

1. Everything we can see, everything that fits in the horizontal distance in which we can see 2. The angle at which sight eaves our eye, this angle (making motions with their arms and hands going from their eyes) 3. The angle gets smaller as the thing moves further away. This is because if something is really close to you it looks wider and so the angle of view gets wider.

Explore: I will have the students explore this idea by finding the angle of view when looking at their own thumb at arm’s length. They will be put into groups (as many as we have telescopes) to try to answer the question of how to find this angle.

1. How will you go about solving for the angle? 2. What did you get for these measurements? What did you get for the angle?

1. Do something with equilateral triangles. Make measurements of the distance from eye to thumb and width of thumb. 2. Answers will vary.

Explain: At this point, I will either choose a group that figured out what to do to present their finding, or explain to them myself how to find this angle.

1. How do you find this angle? 2. How do you put that measurement in degrees? 3. Does this seem about accurate? Why?

1. (theta) = (width of field of view) / focal length) in radians. 2. Multiply it by 360. 3. ES, because it is a pretty small angle and it seems like the angle of view would be pretty small.

Extend / Elaborate: After the formula has been established, I will have them stay in their groups to work with the telescopes. They will go in the hallway and use the telescopes to find the field of view and measure the focal length to find the angle of view.

1. How will you find the field of view? 2. Where will you measure the focal length from and to? 3. How will you find the angle of view?

1. Have someone stand in a designated spot holding a meter stick and have each other person in the group look through the eyepiece and see how many centimeters across of the meter stick they can see. Have multiple people look and take the average just in case there are discrepancies over how much they can see. 2. From about where the primary mirror is in the telescope to the designated spot. 3. Divide the field of view by the focal length to get the angle in radians and then convert it into degrees so that it will make more sense to them.

Evaluate: After they have completed this exercise, if there is time I will have them answer a few questions as a group and then we will discuss the answers as a class. If there’s not enough time for that, I will quickly call on people to answer the questions.

1. What did you do when using the telescope? 2. How did you find the field of view? 3. What was your answer for the angle of view? Show your work. 4. How did the thumb measurements relate to what we found using the telescopes?

1. Make the telescope about parallel to the ground, move the eyepiece up and down to focus. 2. [A variation of the answer above.] 3. Show use of formula to find theta and then convert to degrees. Answers will vary depending on their different focal lengths. 4. The thumb example was what we did with the telescopes on a smaller scale.