GOOGLE EARTH GEOMETRY LESSON By Casey Sneider

CONTENT  Grade Level: 6-9  Students will use technology and their knowledge of algebra to take measurements and compute volume and surface area in order to make connections between 3-D solids in a real world setting and mathematics.

STANDARDS  This software meets ISTE standards, which are the following:  Creativity and Innovation: Students demonstrate creative thinking, construct knowledge, and develop innovative products and processes using technology. Students can use the models and simulations in Google Earth to explore various terrains, ancient civilizations, the solar system, etc.  Communication and Collaboration: Students use digital media and environments to communicate and work collaboratively, including at a distance, to support individual learning and contribute to the learning of others. Students can interact and collaborate with peers in order to communicate information and ideas effectively to multiple audiences using Google Earth.  Research and Information Fluency: Students apply digital tools to gather, evaluate, and use information from Google Earth to explore various topics in science, history, and technology classes.  Technology Operations and Concepts: Students demonstrate a sound understanding of technology concepts, systems, and operations. They can use Google Earth to explore computers, tablets, etc. and learn how to use them properly.

PREREQUISITES  Students should have had a lesson on volume and surface area prior to this lesson, in order to know the formulas.  Students should have used or seen a teacher use Google Earth before.

INSTRUCTIONAL OBJECTIVE  Finding the volume and surface area of geometric solids using a formula.

INSTRUCTIONAL PROCEDURES  Before  Students will receive a lesson on polyhedrons, 3-D geometric solids with flat faces and straight edges, and on finding the volume and surface area of polyhedrons, such as spheres, prisms, and pyramids.  Students will need to have knowledge of the following formulas.

SURFACE AND LATERAL AREA FORMULAS  Surface Area of a Cube – SA=6a 2 (a is the length of the side of each edge of the cube)  Surface Area of a Rectangular Prism – SA=2ab+2bc+2ac (a, b, and c are the lengths of the three sides)  Surface Area of a Sphere – SA=4 π r 2 (r is the radius of the circle)  Surface Are of a Cylinder – SA=2 π r 2 +2 π rh (h is the height of the cylinder, r is he radius of the top)  Lateral Area of a Pyramid – SA=(1/2)pl (p is the perimeter of the base, l the slant height)

VOLUME FORMULAS  Volume of a Cube – V=a 3 (a is the length of the side of each edge of the cube)  Volume of a Rectangular Prism – V=abc (a, b, and c are the lengths of the three sides)  Volume of a Sphere – V=(4/3) π r 3 (r is the radius of the circle)  Volume of a Cylinder – V= π r 2 h (h is the height of the cylinder, r is the radius of the circle)  Volume of a Pyramid – V=(1/3)bh (b is the base of the pyramid, h is the height of the pyramid)

INSTRUCTIONAL PROCEDURE  During  Students will be able to work in groups and use Google Earth to solve volume and surface area problems that will appear three dimensionally on the computer.  Demonstrate how to view and pan around these solids.  Have the students go to each geometric solid, which contain a placemark icon that includes the necessary dimensions students need to complete a Geometric Solids Worksheet they will be given. (Formulas will be given on the worksheet to grades 6-7)

INSTRUCTIONAL PROCEDURE  After  Once the students finish the worksheet, have each group demonstrate to the class how they computed the surface area and volume of one of the geometric solids on the worksheet using the Google Earth dimensions.  After the presentations, go over any of the problems that the students struggled with.

MATERIALS AND EQUIPMENT  Computers with access to Google Earth for each group of students  Geometric Solids Worksheets for computations  Calculators for each group of students for making calculations

ASSESSMENT/EVALUATION  Students will be graded based on their Geometric Solids Worksheet and the presentation their group gives to the class on how they found the volume and surface area of a specific geometric solid on Google Earth.  Each building problem will be worth 10 points  5 points for calculating the correct area  5 points for calculating the correct volume  Points will be deducted if the answers are not labeled with feet, inches, centimeters, etc.  The presentation given by the group will be worth 20 points.  Full credit will be given to those groups that show they have a clear understanding of the material and are able to communicate effectively to their classmates how they solved their problem.

DIFFERENTIATION  For ELL’s and/or students with disabilities, individualized attention will be given or they will be assisted in using the computers to find each solid on Google Earth.  The students can also help one another in their groups.

TECHNOLOGY  This lesson calls for each group of students to have access to a computer with Google Earth.  They will use Google Earth to explore different geometric solids in the world and use their measurements to solve math problems.

SELF-ASSESSMENT  The value of this lesson will depend on the performance of the computers available and if the Internet is working properly.  Take note of whether or not the students had difficulties working with Google Earth and how long it took them to solve each problem.  Find out if there are any other places the students would of liked to explore and learn about.

NEEDS STATEMENT  It is important that all students have an understanding of basic geometry concepts, especially in 8-9 grade when students typically begin to learn more advanced geometry that uses theorems, postulates, and proofs. To be able to understand the wonder of the world’s shape and appreciate it, students need to be able to understand and have knowledge of spatial use. In other words the areas related to space and the position, size, and shape of things in it. When students know how to apply and understand the relationship between shapes and sizes, they will be better prepared to use them in their everyday lives. Geometry will assist them in doing that, because it provides the knowledge of how to deal with measurements and relationships of lines, angles, surfaces and solids.