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Building Dog Houses
CHECK the HOW TO pages from doglinks for more ideas
by Hilda
Hamilton
Grade: Grade Eight area
Subject Area: Math, Science, Computer Skills
Time required: I have a 75 minute class period. This lesson and
the evaluative activities would require 2 to 3 class periods.
Materials needed: centimeter grid paper run on colored paper, isometric
dot paper, centimeter cubes, bulletin board paper, computer, teachermade
spreadsheet.
Lesson Objectives:
Students will create polygons with
equal areas, but different perimeters.
Students will evaluate the effectiveness of their polygon creations.
Students will create rectangular prisms with equal volume, but different
dimensions.
Students will evaluate the effectiveness of their prism creations.
Students will explore the effect that doubling, tripling, etc. dimensions
has on perimeter, area and volume with grid paper and centimeter cubes.
Students will explore the effect that doubling, tripling etc. dimensions
has on perimeter, area and volume using a teachermade spreadsheet.
PreActivities:
Students have had experience with
the concepts of perimeter, area and volume.
Students have previously drawn polyhedrons on isometric dot paper.
Students have had experience working with spreadsheets and a desktop
publishing program.
Activities:
Teacher challenges students to create
as many floor plans for a dog house as possible, if they were only told
that the dog house must have 10 square feet. (Let 1 cm = 1 ft. on cm
grid paper.)
As students create floor plans,
they cut them out and tape them to a piece of bulletin board paper displayed
in the classroom.
Items of discussion should include:
Which floor plan has the greatest perimeter? the smallest?
How many possible floor plans are there?
How can you be sure that you have thought of all possibilities?
What are the advantages to creating a dog house with the smallest perimeter?
the greatest?
Teacher asks students to write
a reflection in their notebook on what they discovered. Is there a way
to ensure finding the polygon with the greatest perimeter? the smallest?
Students pair up to share their reflections.
In pairs, students are given 24
centimeter cubes. They are asked to create dog houses with a volume
of 24 cubic feet (Let 1 centimeter cube =1 cubic foot.)
The dog houses should be rectangular prisms.
Students draw their creations on isometric dot paper, cut out drawings
and tape them to another piece of bulletin board paper displayed in
the classroom.
Items of discussion should include:
Which prism is tallest? shortest? widest? least wide? How many possible
prisms can be created? Are there specific advantages/disadvantages to
any of the dog houses?
Teacher asks students to write
a reflection in their notebook on what they discovered. Is there a way
to ensure that all possible dog houses have been created with a given
volume?
Students pair up with someone other
than the partner they built dog houses with, to share their reflections.
Teacher chooses one of the dog
house floor plans and students redraw it on their grid paper by doubling
the length of each side. What happens to the perimeter? What happens
to the area? Why does the area quadruple when the perimeter only doubles?
Teacher creates a dog house with
4 centimeter cubes and asks students to do the same. Teacher asks students
to double each dimension of the prism.
What happens to the perimeter of each face? What happens to the area
of each face? What happens to the volume of the prism? Why is the volume
8 times as large when the sides were only doubled in length?
Teacher lets students continue
to explore this concept using a teacher prepared spreadsheet. Students
manipulate the data to explore what happens when dimensions of a rectangle
and a rectangular prism are doubled, tripled, etc.
In pairs, students develop pattern
charts to help others visualize their discoveries.
Measures/Evaluations:
Students create other floor plans
and structures when given required area or volume (i.e. a dollhouse)
Using a desktop publishing program,
students prepare a report for a "customer", informing them
of all the ways to create a certain floor plan or structure and reasons
why some would be preferable over others.
Students verbalize the effect of
doubling, tripling, etc. the dimensions of a rectangle or a rectangular
prism.
In pairs, students create a pattern
chart that shows their understanding of the effect of doubling, tripling,
etc. dimensions of a rectangle and a rectangular prism.
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