Unit of Instruction: Three-Dimensional Polyhedrons
Noah Kadre
Ed Tech 506
Fall 2011
Unit Goals
The Unit goals of this project cover standards addressed in the NCTM standards for Geometry Curriculum, as found on the state of Idaho education website (listed below). This unit covers specific year-long standards Geometry (a., b.), as well as many other standards which the students will encounter in other units. The focus of the unit is on three-dimensional shapes, their properties, and how to apply mathematical problem solving to the shapes.
The unit consists of eight lessons:
1: introduction to 3-d shapes, faces and edges of polyhedrons
2: vertices and face shapes of polyhedrons
3: calculating surface area of rectangular prisms
4: calculating volume part 1
5: calculating volume part 2
6: platonic solids
7: irregular polyhedrons, and real world relationships
8: hands-on modeling of crystalline structures
Lesson 1: Introduce 3-d shapes, specifically polyhedrons. Define and count edges and faces of polyhedrons.
Objectives:
1. When shown a 2-d and 3-d shape, the student will identify which is the 3-d shape.
Standards: Geometry (a,b), Problem Solving ( a,b,c ), Communication (a)
2. When shown a polyhedron the student will identify and count the number of shape edges to 80% accuracy.
Standards: Geometry (a,b), Problem Solving ( a,b,c ), Communication (a)
3. When shown a polyhedron the student will identify and count the shape faces to 80% accuracy.
Standards: Geometry (a,b), Problem Solving ( a,b,c ), Communication (a)
Lesson 2: Define and count vertices of polyhedrons and identify the face shape.
Objectives:
1. When shown a polyhedron the student will identify and count the shape vertices.
Standards: Geometry (a,b), Problem Solving ( a,b,c ), Communication (a)
2. When shown a polyhedron the student will identify the face shape to 80% accuracy.
Standards: Geometry (a,b), Problem Solving ( a,b,c ), Communication (a)
Lesson 3: Calculating the surface area of a rectangular prism.
Objectives:
1. When given a rectangular prism with dimensions, the student will calculate the surface area to 80% accuracy.
Standards: Geometry (a,b), Problem Solving ( a,b,c ), Communication (a)
2. When given a rectangular prism with dimensions, the student will display the logical steps to calculating the surface area.
Standards: Geometry (a,b), Problem Solving ( a,b,c ,d), Communication (a)
Curriculum Standards
NCTM STANDARDS from Idaho.gov
https://www.sde.idaho.gov/site/humanities/docs/curriculum/17%20NCTM%20STANDARDS.pdf
GEOMETRY
a. Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.
b. Use visualization, spatial reasoning, and geometric modeling to solve problems.
PROBLEM SOLVING
a. Build new mathematical knowledge through problem solving.
b. Solve problems that arise in mathematics and in other contexts.
c. Apply and adapt a variety of appropriate strategies to solve problems.
d. Monitor and reflect on the process of mathematical problem solving.
COMMUNICATION
a. Use the language of mathematics to express mathematical ideas precisely.
Learner Characteristics:
Here are the required characteristics of the intended audience:
Cognitive Characteristics:
The student must be able to gain information from graphics and read and write at a 7th grade level.
(See below for specific prior knowledge requirements.)
Physical characteristics:
The student must have appropriate sensory perception.
Affective Characteristics:
The student must be willing to learn and apply effort to these lessons.
Social Characteristics:
The student must be willing to work with peers and the instructor.
Prior Knowledge
The student will need the prior knowledge of passing Algebra, and its requirements, and be current in the class curriculum in Geometry. Specifically, students must be able to solve one-step algebraic equations.
Classroom Environment:
The classroom layout will be a traditional classroom, with one student to each desk, all within view of the media screen. An optional online version will be made available for online students.
Introduction Procedure:
The introduction of the unit will be 2-d and 3-d examples of images, and will ask the student to consider what properties a 3-d shape has that a 2-d shape does not. The introduction will also include an overview of the unit.
Technology Requirements:
The unit will need a standard computer with a multimedia projector, capable of running PowerPoint or Adobe Presenter. A standard copying machine or printer will be needed to print the notes and worksheets.
Graphics:
I will present the following static graphic visuals for this unit:
1. 2-d and 3-d Shapes
2. Typography Overview: 2-d/3-d, edge, surface area, volume
3. Polyhedron faces and edges
4. Polyhedron vertices and face shape
5. Surface Area 1
6. Calculating Surface area: breakdown prism
7. Calculating surface area: orientation of prism sides
8. Calculating surface area: Your turn!
Assessment:
Lesson 1 will have a formative worksheet assessment, including identifying unique characteristics of 3-d shapes and counting faces and edges.
Lesson 2 will have a formative worksheet assessment, including counting vertices and identifying face shapes of polyhedrons.
Lesson 3 will have formative worksheet assessment, including calculating the surface area of five different rectangular prisms.
Lesson 1: Introduce 3-d shapes, specifically polyhedrons. Define and count edges and faces of polyhedrons.
Objectives:
1. When shown a 2-d and 3-d shape, the student will identify which is the 3-d shape.
Standards: Geometry (a,b), Problem Solving ( a,b,c ), Communication (a)
Assessment worksheet will have unlabeled 2-d and 3-d shapes, which the student must classify as 2-d or 3-d.
2. When shown a polyhedron the student will identify and count the number of shape edges to 80% accuracy.
Standards: Geometry (a,b), Problem Solving ( a,b,c ), Communication (a)
Assessment worksheet will have 5 polyhedrons, which the student must count the number of edges.
3. When shown a polyhedron the student will identify and count the shape faces to 80% accuracy.
Standards: Geometry (a,b), Problem Solving ( a,b,c ), Communication (a)
Assessment worksheet will have 5 polyhedrons, which the student must count the number of faces.
Lesson 2: Define and count vertices of polyhedrons and identify the face shape.
Objectives:
1. When shown a polyhedron the student will identify and count the shape vertices.
Standards: Geometry (a,b), Problem Solving ( a,b,c ), Communication (a)
Assessment worksheet will have 5 polyhedrons, which the student must count the number of vertices.
2. When shown a polyhedron the student will identify the face shape to 80% accuracy.
Standards: Geometry (a,b), Problem Solving ( a,b,c ), Communication (a)
Assessment worksheet will have 5 polyhedrons, which the student must identify the face shape.
Lesson 3: Calculating the surface area of a rectangular prism.
Objectives:
1. When given a rectangular prism with dimensions, the student will calculate the surface area to 80% accuracy.
Standards: Geometry (a,b), Problem Solving ( a,b,c ), Communication (a)
Assessment worksheet will have 5 rectangular prisms, which the student must calculate the surface area.
2. When given a rectangular prism with dimensions, the student will display the logical steps to calculating the surface area.
Standards: Geometry (a,b), Problem Solving ( a,b,c ,d), Communication (a)
Assessment worksheet will have 5 rectangular prisms, which the student must display the logical steps to calculating the surface area.