(Editors NOTE: Perimeter in
this activity is often discussed in terms of number of 'exposed' sides.
Equilateral Triangles could be substituted for the right triangles.)
Objective:
(1) The Objective for this activity
is for students to start investigating the concepts of area, perimeter and
shape. The students should reach their own conclusions -based on this activity-
regarding the variation of area and perimeter based on differences in shape.
They should come to realize that different shapes, regular and irregular,
can have the same areas. They should be able to identify different properties
of the shapes they create, and from those properties, they should be able
to create categories in which they can classify their creations.
Materials:
(9) An overhead projector, triangular
graph paper, graph paper, pencils, paper, equilateral triangle manipulatives,
transparency of triangular graph paper, an overhead scanner, a table top
computer, perimeter-area-shape charts.
Activity:
(10)(11) a) The students will
be given their manipulatives, and asked to create as many shapes as they
can using 1, then 2, then 3 then 4 equilateral triangles.
b) They will then draw their
shapes onto the graph paper.
c) They will then be asked to classify their shapes into categories they create for themselves.
d) They will then fill out their
shape charts. When they have finished their charts, they will be asked to
identify any patterns in each category.
Challenges/Continuations:
(15)
When the students finish their
work with the triangles, they can be asked to try shapes with more than
four triangles. They may also want to try the activity using square manipulatives
and the graph paper.
Closing:
When the students have finished
their exploration of the new shapes, they will share their findings with
the class. They can create a large-scale version of the shape chart in order
to illustrate the entire class findings. The teacher may also want to introduce
the terms 'regular' and 'irregular' shapes, 'closed' and 'open' shapes.
(8)
This Generative Activity is designed
for a sixth grade classroom. the activity will focus on concepts of geometry,
area, perimeter, # sides. The students will be researching shapes
in relation to these concepts. They will be looking at the patterns that
exist in relationship to the perimeter and areas of the shapes that they
create. They will be looking into the possibilities of limitless numbers
of shapes. They will test their classification skills, designing some shapes
that are regular or closed, and others that are irregular and open. They
will make predictions for future patterns, and they may extend the activity
by investigating other shapes and their combination patterns.
(1) The students are given a specific
number of equilateral triangles. They will be given triangular manipulatives
with instructions to create as many shapes as possible with 1, 2, 3 or 4
triangles. They will chart their findings of their new shapes - area, perimeter,
# sides. They will then create categories for classification of the shapes,
based on certain shared properties.
The students will be answering the following questions while they create shapes:
a) How many sides does each shape
have?
b) What is the Area of each shape?
c) Is there a limit to the number
of shapes you can make?
d) What patterns or relationships
do you notice?
e) How can you classify the shapes
you have made? What are the noticeable differences?
(2)
The students must have previous
knowledge of the concepts of ` Area, Perimeter, and Pattern before doing
this activity.
(3) This can be as challenging as
the students and the teacher want to make it. The objective of the lesson
is that the students will see that there is a relationship to the number
of triangles making up the shape, and the area. That they be able to identify
the different types of shapes they are creating, and have a good understanding
of classification. The activity can extend in any number of directions;
creating shapes with other shapes, inventing shape games, challenging peers
to create the same shape based on the description for the shape they have
made, using charts.
(4)
There is a great deal of space in
this project. The students can take it to a number of different places.
They can study the relationship of the number of triangles to the shapes
they create. They can categorize the shapes they create in the categories
they decide upon themselves. The students should note that area never changes,
despite the differing shapes they create with 1-4 triangles as the units.
They can also see that the perimeter and shape can differ drastically. There
is space for a great deal of different responses, and problem solving.
(8)
The following themes should be covered
in the class discussions:\
a) Area - how if structured by the
same size pieces, the shapes' areas will all be equal to the number of units(triangles)used.
b) Perimeter - though the shapes
will all have the same number of building units, the perimeter can be quite
varied.
c) Pattern - classifying shapes
according to particular properties, will bring about a pattern in the shapes
they create. The number of sides in relationship to the type of shape they
have created should be a noticeable pattern. They might also find patterns
related to the number of sides exposed or adjoined.
(12)
This activity should be used for
at least one day, but could last for two or more days depending on how far
the teacher would like to take it. The students could be challenged with
repeating the whole process using another shape or two in the same activity(squares,
diamonds, etc.)
(13) Follow-up activities might
include projects on area, Pattern problems, dissecting shapes, using more
than one type of shape, tessellations etc.
(14) Though I could not locate an
age appropriate student, I did try this out on my neighbor, Jeff, who is
14. He became quite involved with the activity once he was allowed to use
3 triangles. He became preoccupied with trying to figure out how many different
shapes he could make, but was less interested in filling out the chart.
(this leads me to believe that this would be an ideal group project for
tables of kids to work on.) Jeff wanted to try and find a pattern in the
number of sides connected in each shape.
(15)
There are no right or wrong answers
in this activity. However the students will be given the challenge of how
many shapes they can create. It will be hard for them to find all of the
possible shapes, but they should have a great time trying!! There are is
no limit to the number of irregular shapes they will create, however they
may find that it is possible to find all of the regular shapes.
TABLE
# of Triangles Sketch the Shape
Perimeter Area
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
(7) Here are some shapes from Jeff's
experimenting.
