How fast does the sphere grow?

Subject: geometry



Unit and Topic:






Geometry of Earth


Grade/Level:



Time Allotment:
6 – 8 grade



90 min





Pre-Requisite Skills:
Students must have basic computer skills; know how to use
formulas to solve problems using the concepts of radius, circumference, volume and surface area of sphere.




Objective(s):
The students will be able to: use VRML program to create a simple 3-D image of sphere and wrap a picture of earth around it. They will also be able to explore the change of circumference, area, volume, and surface area as the radius of the sphere changes. Given radius of the earth, students will be able to find the circumference, surface area and volume of the earth.




Summary:
The purpose of this lesson is to use computer technology to help students visualize the change of a sphere’s surface area, circumference, and volume as the radius doubles or triples.




PREPARATION



Instructional Materials
LCD project, laptop, computer with VRML and text-pad, Cortona Viewer, pencil and paper,
blackboard, and calculators.




Resources:
Internet connection, Google search.




IMPLEMENTATION



Introduction/Motivation:
Teacher starts the lesson by asking students how they can draw a 3-D image of a sphere with just a computer,




Learning Context :
Students should follow directions and work on the computer independently. They will also be able to consult the student seats next to them should they have any questions.




Procedure:
1. Introduction of the lesson: agenda and expectations are given at this point using power point presentation.

2. Students follow step by step directions to create a 3-D image of a sphere ( red, radius of 1 unit, and locate in the center of the screen)

3. Students explore the changes of the image (circumference and volume) as the radius changes.

4. Use pencil, paper, and calculator to find the changes of the sphere’s volume, surface area, and circumference as the radius doubles in size, triples, or ½ the original size, and record their findings in the chart.

5. Summarize their findings

6. Continue with step by step instruction to show students how to wrap a picture of earth around the sphere.

7. Give earth’s radius on board

8. Use calculator to find the surface area and volume of the earth.

9. Summarize the lesson: students record their findings in their chart and teacher summarizes their answers.


Differentiated Instruction:
Accelerated learner:

They can create 3-D images of a cone, cylinder, or box with 3-D images of a cone, cylinder, or box different colors.

Justify the reason as the radius doubles, the circumference doubles, the area 4-times, the volume 8-times the original size.



Pair fast learner with slow learner and allow slow learners to use calculators.




Sample Student Products:
Students’ 3-D images will be stored on teacher’s jump drive. Math calculation part will be done on paper and pencil and collected at the end of the class.




Collaboration:
This lesson can be collaboratively taught with science teacher in the subject of earth science.




Author's Comments & Reflections:
Surface area and volume of a sphere is a somewhat abstract concept for students to grasp, and we often don’t have a tangible model to show to students, especially if we want to demonstrate the change of volume as the radius of the sphere changes. With VRML program for students to use, they get the instant 3-D image. Students can manipulate the image, change its radius and see the instant change of the volume, which in turn makes the lesson more interesting and attention catching.




STANDARDS & ASSESSMENTS




WV CONTENT STANDARDS AND OBJECTIVES:

M.O.8.4.1.

Select and apply an appropriate method to solve, justify the method and the reasonableness of the solution of problems involving volume of spheres.



USA - 21ST CENTURY LEARNING SKILLS & ICT LITERACY

Standard 3: Geometry
Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the field of mathematics, students will analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships, specify locations and describe spatial relationships using coordinate geometry and other representational systems, apply transformations and use symmetry to analyze mathematical situations, and solve problems using visualization, spatial reasoning, and geometric modeling.



NATIONAL STANDARDS:

NM-MEA 6-8.2

Use formulas to determine the circumference and area of circles. Use formula to determine the volume of spheres.




RUBRIC

contents
Excellent
Good
Fair
Poor



3-D image
The image of sphere with wrapping is created with the correct color, size, and located at the right quadrant
3-D image with wrapping is created with correct color, size, and located at the right quadrant
3-D image with wrapping is created with correct color and size
3-D image does not show or wrapping is not shown

Math reasoning
The reasoning is clear and convincing with concise wording
The reasoning is somewhat clear convincing with little vagueness
The reasoning is confusing but on the right track
The reasoning is confusing and wrong

Calculation
Calculation is accurate with no mistakes
Calculation is accurate with ignorable mistakes
Calculation has some mistakes
Calculation is wrong

Neatness of work
The work is neat with step by step work showing.
The work is neat with step by step work showing.
The work has some steps missing
The work is illegible