Author:
Sharon Pinkerton
Subject:
Secondary Mathematics
Material Type:
Lesson Plan
Level:
High School
Tags:
Creative Commons Attribution Non-Commercial Share Alike
Language:
English
Media Formats:
Text/HTML

# Google Earth- Law of Cosines and Heron's Formula

## Overview

The purpose of this lesson is to show students how to break up land division and survey their own property.  Students will gain a knowledge of how surveyor's come about dictating property lines.  The lesson gives a greater understanding of Law of Cosines and Heron's Formula.

Image Reference:

Lars H. Rohwedder, Sarregouset - Own work from source files Image:OgaPeninsulaAkiJpLandsat.jpg (GFDL) and Image:Orthographic Projection Japan.jpg (GFDL and CC-By-SA).

# Summary

This was a really fun way to get students involved and use technology to solve problems.  It was also a way to show some a real-world use for these formulas, such as being a land surveyor.

This task should take the whole class period, about 90 minutes, to organize and complete all tasks.  Students will be asked to locate their own homes using Google Earth.  The will calculate total acreage of their property by separating the boundaries into triangles and using Law of Cosines and Heron's Formula with an 85% accuracy.

Instructional Setting:

The classroom is arranged with student's desks all facing multiple whiteboards.  The teacher's desk is off to the side.  The class consists of 10 students, 6 boys and 4 girls.  One student has troubles with social skills but does not have and IEP or 504 plan.  This student takes a bit longer to grasp some concepts but does good with a little extra support.

**This is just my scenario but this just shows that the lesson can differentiated for multiple students.  Your classroom size and environment will differ.

# Background for Teachers

Students will already have a knowledge of Law of Cosines and Heron's Formula.  Students have already learned how to program these formulas into their calculators.  Students will also need to have prior knowledge of geometry and the angles formed by parallel lines. Both the students and teacher will need knowledge of navigating a web page like Google Earth. and the basic tools this program offers.  They will also need knowledge of their geographic location in relations to the town they live in.

The following resources may be helpful to teach this topic:

https://www.docsity.com/en/a-law-of-cosines-cheat-sheet/7230221/

# Step 1 - Goals and Outcomes

Students will be able to apply geometric methods to solve design problem.

Students will work as a class to navigate to their own property and use Google Earth tools to calculate total Acreage.  The teacher will be there to answer operating questions but not give answers.  The students will help each other to navigate the tools and map on Google Earth.

By allowing students to work as a group, students are able to feel more comfortable in contributing their own ideas and strategies.  Students will also gain much needed social interaction skills and knowledge from one another.  If you have a group of students who have struggled in math in previous years but have shown great improvement through activities that get the students involved and collaborating with one another it might be a good idea to group the with more knowledgable students.

# Step 2 - Planning Instruction

After issuing the pre-assessment quiz determine what you need to go back through so students have a clear understanding of the formulas.  I would go through any questions or concerns that the students have about the pre-asessment. I would go over a question on the worksheet just so you know the student's know how to proceed. I then show the students how to use Google Earth by evaluating the boundaries on my own property.  I would then instruct students on how exactly you want them to proceed when accessing Google Earth to evaluate their homes boundaries.

# Step 3 - Instruction

Sequence of Instructional Procedures/Activities/Events (provide description and indicate approximate time for each):

1. Student Prerequisite Skills/Connections to Previous Learning:

Students will need knowledge of navigating a web page like Google Earth.  They will need knowledge of their geographic location in relation to the town they live in.

1. Presentation Procedures for New Information and/or Modeling:

The purpose of this lesson is to show students how to break up land division and survey their own property.  Students will gain a knowledge of how surveyor come about dictating property lines.

When students enter the classroom they will pick up a quiz paper.  They will be given about 10 minutes to complete the quiz.  The quiz will be a short property tax description that the students will need to construct and divide out to calculate the total acreage of property.   They will need to use the concepts they learned from the class before to complete this quiz.  The teacher and students will go through the quiz as a class, answering any questions as needed.  The quizzes will then be handed in.

The teacher will begin the lesson by asking students how they think surveyors come up with calculations and boundaries of property.  The students and teacher will have a discussion on how accurate it would be if we send them out will a basic ruler to measure off the school parking lot and how different elevations come into factor.  They discuss how hard it would be to survey the state of Utah and how the mountain ranges and lakes come into play.  This will connect their learning back to previous concepts.

The students are then asked if they have ever see or used Google Earth before.  Based on their knowledge of the program the teacher will demonstrate how to use the application to find measurements of property.

Students will then come up one at a time and navigate to their own homes.  They will determine on the map where their property lines are and write down the measurements.  Each student will be given a chance to map out his or her own home boundaries.  The students will work together to help determine the best locations for splitting up the property to calculate their total acreage.

With about 20 minutes left before class ends the teacher will gather the students in one last discussion about how they think they can use this knowledge.  The teacher will ask students if their calculations were close to the total acreage that they are billed for on their property taxes each year.  The teacher will demonstrate on Google Earth how the application takes into account the varying elevations into its calculations.  The students will then revisit the question they did on the pre-Assessment about the total acreage of Utah.    They will Google their answer and recalculate the measurements on Google Earth to see how close they get.

1. Guided Practice:

The teacher will demonstrate how use Google Earth and it tools to calculate total acreage using his/her own property.

1. Independent Student Practice:

Students will work as a class to navigate to their own property and use Google Earth tools to calculate total Acreage.  The teacher will be there to answer operating questions but not give answers.  The students will help each other to navigate the tools and map on Google Earth.

1. Culminating or Closing Procedure/Activity/Event:

With about 20 minutes left before class ends the teacher will gather the students in one last discussion about how they think they can use this knowledge.  The teacher will ask students if their calculations were close to the total acreage that they are billed for on their property taxes each year.  The teacher will demonstrate on Google Earth how the application takes into account the varying elevations into its calculations.  The students will then revisit the question they did on the pre-Assessment about the total acreage of Utah.    They will Google their answer and recalculate the measurements on Google Earth to see how close they get.

Instructional Strategy (or Strategies):

The teacher involves the students in group discussion so that the students will be able to express their own thoughts and ideas.  The teacher will create an atmosphere that is open and accepting so students will feel safe and comfortable in the classroom.  The teacher will use this discussion to gage the student’s knowledge of the concept.  She/he will also gain an understanding of the student’s abilities to navigate and run the Google Earth application.

The teacher will also use modeling as an instructional Strategy.  The teacher will give the students an example of how to calculate his/her own property boundaries using the tools that the students will need to be familiar with in their own calculations.

Differentiated Instruction Accommodations:

By allowing students to work as a group, students are able to feel more comfortable in contributing their own ideas and strategies.  Students will also gain much needed social interaction skills and knowledge from one another.  This group of students all have struggled in math in previous years but have shown great improvement through activities that get the students involved and collaborating with one another.  By grouping these students they are able to fill in the gaps of their knowledge through interaction with one another.

Use of Technology:

Technology is used in this lesson by exploring the many uses and tools in the Google Earth Pro application.

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# Step 4 - Assessments

Student Assessment/Rubrics:

The teacher will know that students have met the objective when they have successfully navigated to their respective properties and accurately calculated the acreage of land.