LESSON PLAN

Name: Katie Artzt, Sara Waldrip, and Tom Abraham

Title of lesson: Proportions with Planets

Date of lesson: March 23 and March 30

Length of lesson: 1.5 hours

Description of the class: High-school on-level students

Name of course: Algebra I

Grade level: 9 - 10

Honors or regular: both

TEKS addressed:

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

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

 I. Overview

Using telescopes, students will view models of planets from our solar system. The planets will be at the appropriate distances from each other based on the scale size of each planet. The students will view the planets from the telescope. The students will have previously determined a baseline view through the telescope. This baseline measurement will be used to solve the proportion created from observing the planet at different distances.

II. Performance or learner outcomes

Students will be able to: to use their knowledge of ratios and proportions to figure out the distances of the planets using a telescope. The students will setup proportional equations based on information presented to them about the proportion relationship represented in their observations through a telescope. The students will solve the proportions and present the data in a way that represents their knowledge of proportions.

III. Resources, materials and supplies needed

Built telescopes

Several Boxes of planet and sun models (one box for each telescope)

Maps of Austin

Map of Solar System

Large field (150 m or more)

Measuring device (don’t know what this is called. It is the type that rolls on the ground and will allow the students to tick off the distances the planets are from each other)

Meter stick

Calculators

Clipboards

4 poster boards with orbits all ready drawn.

IV. Supplementary materials, handouts.

Example page of proportions and ratios

Illustration of the ratio used in calculating distances with a telescope

Chart for recording measurements

Possible poster board

Grid paper

V. Safety

The students will be outside. If near the road, the students need to be aware that cars travel at a fast rate down McNeil road. It will also be necessary to keep track of the students and make sure that some of them don’t bolt since they are outside.

The students need to know not to point the telescope toward the sun. Our lesson has all the objects at ground level but a student might become inquisitive. They need to know the dangers of pointing the telescope toward the sun and also be watched to make sure the telescopes are always pointing straight out.

VI. Setup

A predetermined area needs to be chosen. It needs to be long enough that the students can walk the area. A back-up plan needs to be established for rain or mud.

Since this lesson follows another group, it is important to see their lesson plan so that they flow and to know some knowledge of what the students have all ready been exposed too.

Five-E Organization

Teacher Does Probing Questions Student Does

Engage: (5 minutes) Show students maps of Austin and a picture of the solar system. Get the students to start thinking about how the map person (need to look this occupation name up) came up with the drawing size. Also, make sure the students know all the names of the planets. Hold up a ball to represent the sun. Ask the students to choose which object in a box of planets would represent the sun. Next, have them pace the relative distance from the sun	What does this map show? How does the map help you get around town? Are the distances drawn on the map random? Then, how did the person decide how to draw everything on the map? Show solar system What is this a picture of? Can someone name all the planets? How do you remember all the names? Which planet is which? How far is each planet from the earth? Could you draw a map of the solar system just like the map of Austin? What information would you need to do this? I am holding a ball to represent the sun, what object would best represent the earth? How far from the ball would your earth need to be to represent the distance from the sun?	Student should know that the map is a “scale” drawing of Austin. Need to see if the students understand the proportional relationship in developing the map. Katie group: The person teaching before me is supposed to teach proportions and ratios and how it is used to scale maps. This will be a review (hopefully) and a way to transition to the telescope. Some students may know the names and order of the planets. The students should know that there are 9 and that earth is the 3^rd planet from the sun. Students should know that a map is created by measuring with actual measuring devices. Students should begin to wonder how something so far away can be measured without out doing the actual measurement. Students will pick what they think is the appropriate size earth and distance. This will be revisited in the assessment to see if the students have discovered it is MUCH further.
Explain (10 minutes) This lesson is being taught in the 2^nd period of the day. It will be necessary to check previous lessons. If the group before does ratios/proportions with the telescope, then a small review will be needed at this point. If not, an explanation of how to use the telescopes and how to setup up a ratio/proportion will be necessary.	What will you see in the telescope? How do you know how big it is? Does distance away from an object affect what you see? How do you focus on an object? What does the eye piece do?	Students need to know how to measure the viewing area with a meter stick Students need to know the meter stick should be centered. Students should be able to explain how to focus telescope. Students MUST know not to look at the sun.

Explore: (45 min – 1 hr) Before going outside give students clipboards with the assigned problem. Break the students into 4 groups; which is the number of telescopes. Discuss with the class how they will get the baseline ratio using the meter stick and help explain field of view. Have the students explain to you what they will record on the data sheet (see below). Reinforce the message that they must NOT point the telescope up while outside. Do the students need to take the telescopes outside or will they all ready be there? Make sure students have a clipboard each and a calculator for each group. Once outside, have the students hold a meter stick and get a baseline measurement. Then have the students use a large ball at the same distance out. Have them estimate the size of the diameter relative to the size of the viewing area. Have them put the yard stick back and see how close they are. Repeat with a smaller object at the same distance. Now have the students move further away from the telescope. Have the students calculate the viewing diameter. Then have them look at the same objects. Begin the same process with the planets. There are 4 groups to share the planets. Since each group is quite large, students can be calculating the field of view while another group is walking out the distances. Teacher must walk around and make sure the students are taking turns. Teacher should observe strategies that each group is using. Teacher should let the students know that they will have to show their strategy for their solution to the class. Return to class Instruct students to put their solutions on the poster board. If time is short, this activity needs to be removed. Instead, students will just present their data solutions.

How can I use this meter stick to determine the field of view? What does the field of view mean? Why do I need to know the field of view at xx meters? When you look at the planets, will the planet take up the whole view or do you think it will only take up part of the view? What do you need to record about each planet as you look at it? Is it important to have a clear focus on the object? How will you find an object that is so small and far away? Is it important to center planet to make size estimation? Why? What are you trying to measure when you look at the planet? What does the meter stick say? Do you need to calculate the size? How many balls can you lay next to each other in the field of view? Can you lay more of the balls in the field of view at a greater distance?

If the students have used the telescope in the previous lesson, they should know that the (field of view)/(distance from object) equals the baseline. Students should know to record distance, use distance to calculate field of view. Students may mistake field of view for planet size. Students will pace out planets and mark of with stakes. They will do this as if they can see each one from the sun. Students need to show they know diameter of planet equals the percent of view across middle. Students need to make sure they center planet in the viewing area. Students should know they are looking for the diameter of the planet or the length across the center. Students will take a planet and walk the distance away from the telescope. The student will face the telescope and the other students will view the student and planet through the telescope. Students will use the same strategy they used above to figure out the planets diameter. Students need to take turns pacing out the planet. All students need to look at the planet and come to an agreement on the size. Students will need to return to the class with 20 minutes left to finish discussing the results.

Explain: (10 – 15 min.) (Wrap up explore) Each group presents their strategies their poster. They will be required to show how they calculated their results. All posters will be visible. Teachers should guide the students to discuss and compare each student’s poster. If time is short, class will discuss results as a group.

What results did you get? Was it hard to estimate the size of the planet? Did anyone get a different size for any of the planets?

Expected Student Responses/Misconceptions Each group will explain results and debate will begin about different answers.

Extend / Elaborate: Teacher guides students to calculate the orbit around the sun based on distance. Assumption should be made that the orbits are circular.

What shape is a planets orbit? Do we have the right information to calculate the orbit of the planets? What do we need to find? What formula is used to determine the size of the circle?

Students should use the distance from the sun to calculate the circumference of each orbit. If this were a 2 day class. I would have the students prepare a poster with the orbits and the correct scale size of the planet.

Evaluate: Teacher will collect students tally sheets. Teacher will revisit it initial exercise. The students will pace off the distance from the sun in the classroom

Students will turn in completed tables to evaluate their understanding.

Group Members:

Base view

Distance

Meter stick measurement

Body	Distance from earth	Calculated view	Size of planet in view	Calculated size of planet
Mercury
Venus
Mars
Jupiter
Saturn
Uranus
Neptune
Pluto

The scale used in our models is 1km = xxx m

	Diameter	Surface area
Mercury
Venus
Mars
Jupiter
Saturn
Uranus
Neptune
Pluto