The Arizona STEM Acceleration Project

Angles in Navigation

Angles in Navigation

A 8th-10th grade STEM lesson

Author: Karen Larsen

Date: 11/04/2023

Notes for teachers

​

• This lesson is built as part of a module where the concepts of linear pairs are taught. A brief explanation of what linear pairs are may be in order.

​

• The activity of looking through the sextant at the sun requires you to use the shades for safety, if you are worried about this you can just have them pick an object like a billboard or flag and use the object as if it were the sun.

​

• You are welcome to modify the lesson in any way as this idea can be used in many other settings.

​

List of Materials

• Sextant ( more than one if possible so that more students can be using them at once).
• Sextant Use Chart: Davis Sextant Guide
• Assignment: Sextant Activity
• Graph paper or white boards

AZ Mathematics

Standards

Content

• G.CO.7 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.

​

• G.CO.10 Prove theorems about triangles.

​

• G.SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

Practice

• All Standards for Mathematical Practice will be addressed in this module.

​

• ​
• ​

Science Core Ideas

• U1: Scientists explain phenomena using evidence obtained from observations and or scientific investigations. Evidence may lead to developing models and or theories to make sense of phenomena. As new evidence is discovered, models and theories can be revised.

​

• U2: The knowledge produced by science is used in engineering and technologies to solve problems and/or create products.

​

​

Objectives: Apply knowledge of angles to the idea of navigation and the earth.

Today:

• Students will discover how angles can be used in navigation.
• Picture and understand the planet in mathematical terms.
• Relate their position on the globe to time and the position of the sun.
• Apply this knowledge to other’s experiences around the world.

Agenda (1 or 2) 55 minute periods

Set-up and Concepts

1. (5-15 minutes) Review the concept of angles, congruence and linear pairs. Point out how to make two congruent triangles on a coordinate plane in the 1st and 2nd quadrant centered at the origin.
2. (10 minutes) Demonstrate how to use a sextant and explain what it does simply with room for more in depth discussion.

Activity

3. (10 minutes) Go outside and setup sextants if they have a stand.

4.(25-60 minutes) Do the activity in the document Sextant Activity which asks the students to measure the angle of the sun from the horizon and then to use this information to discover the approximate time and what time it would have to be to make a congruent angle on the other side of the sky by using noon as the 90 degree y axis.

​

Scenario: Stranded in the desert

​

​

Imagine this: You’re in an ATV wreck where your phone is damaged and you need to get back to camp. How long do you have until it gets dark. How can you find your way back to the crash?

Answer: Angles.

Hands-on Activity Instructions

• Here is the activity instructions that I built Sextant Activity
• The best Group Structure is 3-4 if you have enough materials.

​

• The activity has 2 parts and can actually be done interchangeably so that you don’t have people standing around too much.

​

• The first activity in the document is learning to use the sextant and just find the basic angle of the sun from the horizon.

​

• The second activity is to graph this angle as a triangle on the cartesian plane and using it to find the approximate time of day. Then drawing what other congruent triangle would be on the opposite quadrants. What other time of day would have the same angles.

​

​

​

Here are some different examples of student drawings to show their work

Assessment

• Quiz based on the mathematical content
• Report on sextants and their uses
• Repeated Trial of the Activity

Differentiation

• Only do the second activity and have students count divide the total number of degrees on the horizon (180) by the number of fists they count to find the approximate degrees per fist .

​

• If there is still time help them see how this can relate to degrees the sun moves per minute.

Remediation

Extension/Enrichment

• Extend the idea of sextants with the guide to what sextants can tell us and the beginner guide to sextants:Davis Sextant Guide.

​

• If time permits use this knowledge to help them approximate their position on the globe and how those same angles could be used in a different quadrant to show another place on the globe.