Download Exploring the Properties of Rectangular Prisms 2

Project AMP
Dr. Antonio Quesada – Director, Project AMP
Exploring the Properties of Rectangular Prisms
Key words: polygon, interior angles, vertices, translation, faces, base, three-dimensional,
rectangular prism
Existing Knowledge:
Students should be familiar with the Cabri Geometry II program.
They should have some understanding of measuring length in metric units, calculating area
of rectangles, recognizing perpendicular, parallel, diagonal lines, and identifying
the translation, reflection, and rotation of a figure.
NCTM Standards:
Students will analyze characteristics and properties of two and three-dimensional geometric
shapes and develop mathematical arguments about geometric relationships.
Learning Objectives:
The students will –describe, classify, and understand the relationships among two
and three-dimensional objects.
- identify congruent parts of figures
-examine the relationship between the angles, side lengths, areas
and surface area
Materials:
1.
2.
3.
4.
5.
Cabri II
Lab worksheet
Pattern blocks
Math text (as resource)
Prism
Key words: polygon, interior angles,
vertices, translation, faces,
base, three-dimensional,
rectangular prism
Procedure:
þ Students should be placed in groups of 2-4.
þ The teacher will place a drawing of a box that represents a student bedroom on the
chalkboard. Ask, “If you are going to paint the walls of a room in your home, how
would you know how much paint would be needed?” Allow time for student
responses, but do not reveal an answer at this time. Tell students that they will
investigate some geometric ideas before giving a final answer.
þ The Cabri II program does not have the full potential to present three-dimensional
figures. Therefore, some adaptation may be needed in using the measurement tool.
þ Distribute the worksheets and instruct students to begin the Cabri II program.
Project AMP
Dr. Antonio Quesada – Director, Project AMP
Exploring the Properties of Rectangular Prisms
Lab Worksheet
Part I
Team Members:
____________________
____________________
File Name:
____________________
*Regular polygons must have equal sides and equal angles.
1.
Construct a triangle, rectangle, pentagon, and hexagon.
2.
Write the number of sides and interior angles for each figure.
Figure
# of sides
# of int. angle
Triangle
Rectangle
Pentagon
(Regular polygon tool)
Hexagon
3.
What is the relationship between the number of sides on a figure and the number of
interior angles?
_________________________________________________________________
4.
Measure the angles on each figure.
Figure
Meas. of angle
Triangle
(Angle tool)
Rectangle
Pentagon
Hexagon
5.
Explain the relationship between the number of sides and the measurement of the
angles.
__________________________________________________________________
__________________________________________________________________
__________________________________________________________________
6.
Draw the diagonals on each of the figures.
7.
How do the number of diagonals on each figure relate to another property of each
geometric shape? ___________________________________________________
___________________________________________________________________
___________________________________________________________________
.
(Segment tool)
Project AMP
Dr. Antonio Quesada – Director, Project AMP
Part II
1. Construct a regular four-sided polygon.
(Use regular polygon tool)
2. Draw vector.
(Use vector tool)
3. Translate the polygon.
(Use translation tool)
4. Draw sides by connecting the corresponding vertices of the 1st and 2nd rectangle.
(Use segment tool)
5. Label the vertices of the front face of the figure as A, B, C, D,
starting from bottom left and moving clockwise.
(Label tool)
6. Trace the front face by using segments. Measure the length and width of this face.
(Use segment, distance and length tool)
7. Move the labels and numbers to a convenient place on the screen. (ex: AB=2.36)
(Use numerical edit tool)
8. Grasp the vector by one end and move it. What changes are taking place?
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
9. Label the vertices on the back face EFGH, starting from bottom left.
(Label tool)
10. Find the length of each edge of rectangle CDGH.
CD = ______ DH =_____ HG =______
CG =_______
(Use distance and length tool)
11. Find the area of CDGH. __________. Name the congruent faces on this figure.
______________________________________________________________________
12.
Explain how to find the surface area for this figure, a rectangular prism._______________
______________________________________________________________________
______________________________________________________________________
______________________________________________________________________
Bonus: You must paint the walls and ceiling of a 15’x12’x8’ room. How many square
feet will you paint?