| Lessons |
Lesson Summary
|
| For
virtual manipulatives for geometry, please see: http://matti.usu.edu/nlvm/nav/grade_g_3.html |
| Geom
5.1 Areas of Triangles, Parallelograms, Trapezoids
PDF
*Worksheet
*PDF
|
Students
use 3x5 cards to develop the formulas for finding the areas
of triangles, parallelograms, and trapezoids. First they
find the area of the 3x5 card. Then they relate the area
of two triangles with the same base and height as the card
(another card is cut to make these triangles). Then they
do the same with parallelograms and trapezoids. They develop
the formulas for finding the areas of these shapes using
their own reasoning and understanding. *Access worksheet. |
Geom
5.2 Regular Polygon Area
PDF
|
Students
develop a formula for finding the area of a regular polygon
by constructing a hexagon, observing the triangles, and then
reasoning to write the formula. |
Geom
5.2b Amusements Assessment
|
Students
Assessment |
Geom
5.3 Geometric Probability
PDF
|
This
lesson contains several activities that use area and length
to model probability. The first activity asks students to
calculate the probability of landing on a given area within
a shape. The next activity gives students possible sides of
triangles and asks the probability that they would create
a triangle. Students must understand the triangle inequality
for this activity. The final activity uses geometric area
and expected value to answer questions involving a game. |
Geom
5.4 Examining Geometric Solids
PDF
|
Students
build different solids using a choice of different materials.
They analyze the characteristics and record them on a graphic
organizer (see below or access the associated link). Next,
the students access a Web site to find out about Platonic
Solids, build nets for the solids and derive Euler’s
formula relating faces, edges and vertices of polyhedrons.
|
Geom
5.5 Measuring Prisms and Cylinders
PDF
*Origami
box directions
*PDF
|
Students
examine the concepts of volume and surface area by first making
a net out of a cereal box. Then, in the activity “Packing
the Packages,” they find the maximum volume and related
surface areas for different sized boxes (created by cutting
the corners out of graph paper and folding up the sides.)
*Access origami box directions. |
Geom
5.5b Measuring Cylinders
PDF
|
Students
do an activity similar to 5.5a.which uses cylinders. Then
they do a fun activity called “Will you be Wet or
Dry?”
|
Geom
5.6 Measuring Cones, Pyramids, Spheres
PDF
|
Students
derive the formulas for volume of cones, pyramids and spheres
by relating the volume of a cone to a cylinder of the same
base and height, a pyramids to a prism of the same base and
height, and a sphere to a cube of the same base and height.
In a second activity, students find the maximum cone volume
using a paper circle with a radius slit. |
| Geom
5.6b Maximum Cone Volume PDF |
Continued
from 5.6 above |
| Geom
5.6c Constructed Response Assessments |
Constructed
response items. |
Geom
5.7 Revolving Solids
PDF
|
Students
first rotate two dimensional figures across the x and y axes
and compare areas. Then they rotate two dimensional figures
around the y axis to create 3 dimensional figures. They compare
volume and surface areas. |
| Geom
5.8 How Much Skin Do You Have (Assessment) PDF |
Students
estimate the surface area of their body. |
| Geom
5.9 Splitting Bananas |
Students
estimate the volume of a banana. Groups present their methods
to the class and then write a comparison about the different
groups’ methods. |
