Area
and Perimeter with Tanograms(tm)
Overview:
The purpose of this activity is to help
students have a more concrete understanding of the concept of area and perimeter.
The tanogram shapes are there to help students have hands on experience
by using all the pieces to make the different shapes. (10) Students should
be able to realize that the area will not change if all the pieces are used
in constructing the shape. (8) On the other hand, the perimeter should change,
because the more spread out the shape the larger is its perimeter. The appropriate
age for this activity is probably around grades 5-7 as an introductory activity
to the concept of area and perimeter. (3) The students need to have a concrete
understanding of how addition and maybe multiplication (not a necessity).
(2) Mostly, the students will be graphing these figures and counting the
squares. This activity should last at least a day or two depending on how
long the class period lasts. (8) (11) (12)
Suggestions:
While the students are making these shapes, it might be
helpful to demonstrate on the overhead or the chalkboard how to draw the
shape of a square on the graph paper. Make sure to show the students how
to properly record the data. This will be shown on the attached pages with
the different shapes that is possible using the tanogram pieces. You may
want to make a table with all of the class results and have a whole class
discussion on the differences in answers. Your table could look something
like this:
| Shapes | Area | Perimeter |
| Triangle | ||
| Square | ||
| Rectangle | ||
| Trapezoid | ||
| Parallelogram |
For the challenge question, make it become a contest with
the class as a whole to see all the different answers you can get. That
way the students will really want to participate to find the largest perimeter.
Also if the students are having a hard time with this activity at first
constructing the figures, it might be a good idea to have them pair up and
also show an example of one of the shapes. This might give them a better
idea of what they need to do and they won't feel so helpless. (6) (7) (8)
(9) (11) (15)
Extension:
What might also help to show the differences in area and
perimeter concepts is to have the students take one piece (any they choose)
out of the set and then make shapes out of the remaining pieces. Before
they do ask is the area going to change? If so, why would it change. This
will give the students a chance to apply what they have just learned. (1)
(13)
Challenge: What's the Cover
Up?
_ Take out the pieces in the bag. These pieces are called tangrams. Examine the pieces and start to try to make a regular geometric shape using all the pieces.
Regular geometric shape- Objects such as a square,
rectangles, triangles, trapezoids, and
parallelograms. (7)
_ As you are making the shapes graph the shapes on the graph paper. It is easier to place each individual piece on the graph paper and than draw out the piece. At the end of this process you should be able to see the pieces making the big shape. Then gently color in lightly the shape that was just made. This will help you to count all the squares. Finally, measure the shapes by using the squares. (7)
_ The shape total is the area that the shape occupies. (7)
_ The distance around
the shape is the perimeters of the shape. (7)
_ How many different
shapes can you get by using all of the pieces? (1) (3) (4)
(Try really hard to make at least two shapes. That way you will have some way to compare.)
_ Does the perimeter change as the shape changes? Why or why not?
Explain your answer. (5)
_ Does the area change
as the shape changes? Why or why not? Explain your answer. (5)
_ Was there a shape with
a different area? Explain your answer. (5)
_ Look at your shapes again. Do you notice a pattern with
this? Can you make a shape with the largest perimeter? Draw it on the graph.
(5) (8)
_ Can you make a shape with the largest area? Explain your
answer. (5) (8)
_ Create a theory or hypothesis on predicting the outcome
of a shape's perimeter and area using the tangrams. (5) (8)
_ Now make any two shapes you want. See if you still notice
the pattern with area and perimeter with that of the regular shapes. Remember
to graph the shapes you made using the same method you used for the regular
geometric shape. (5) (8)
_ Did your hypothesis hold true? Explain your answer. (5)
(8)
*****************Challenge question****************************
What is the largest perimeter that can be made out of these pieces? Draw it out. You may need more than one sheet of graph paper. How did you know to create this shape? Explain your answer.
(5) (8)
[[You will need graph paper]]
Some Possible Shapes
Example of Student Work:
(14)
