%Unit: Perimeter & Area% %Grade level: 10- Geometry% %Time ...

%Unit: Perimeter & Area%
%Grade level: 10- Geometry%
%Time span: Five days (45 minute classes) %
%Tools used: Geometer’s Sketchpad, Geoboards, National
Library of Virtual Manipulatives, TI-84 Plus%

This portion of the area and perimeter unit should take five days. Topics
include perimeter and area of rectangles and squares, inputting data into the
calculator and then analyzing it.
Day 1:
Review of perimeter.
Discussion of perimeter and area, and their relation to real life situations.
Discussion of an upcoming journal entry.
Development of perimeter formula’s.
Day 2:
A Day in the computer lab with Geometer’s Sketchpad.
Developing a house layout, and then finding the perimeter and area of the house.
Day 3:
Introduction to area with geoboards.
Development of area formulas.
Day 4-5:
Flower Science, given perimeter, find all area possibilities.
Enter data into calculator, graph the data, and what do you notice?
Overall Objectives:
® Students will be able to determine the difference between area and
perimeter.
® Students will be able to use their knowledge of area and perimeter to
handle real life situations.
® Students will develop general understanding for area and perimeter
and they will see where the formulas are derived from.
® Students will use the TI-84 and its graphing functions to see relations
of area.
® The students will further their knowledge of GSP (Geometer’s Sketch
Pad) and measure area and perimeter within GSP.
® Basic introduction of Geoboards (also seen in the National Library of
Virtual Manipulatives).

Title: Intro-discussion.
Objective: This will be a class mainly consisting of discussion. The students will
begin to “think” about math and relating it to real life situations. A journal entry will
also be included in the lesson to encourage the understanding of perimeter vs. area.
The writing of word problems will give the students good practice with writing and
allow them to become creative when it comes to math.
Procedure: After homework is collected and gone over, the students will get into
groups (fellow students they are sitting near). They will then listen to me and
complete the following activity.
Activity:
1) The students will get into groups and they will draw the following on the
provided graph paper:
• A rectangle with length of 5 cm and width 3 cm (P = 16 cm, A = 15 sq. cm).
• A rectangle with height 2 cm and base 8 cm (P = 20 cm, A = 16 sq. cm).
• A rectangle with each side measuring 4 cm (P = 16 cm, A = 16 sq. cm).
*note: answers will not be provided to the students.
At this time, I will have a student from the class designing these rectangles
in the National Library of Virtual Manipulatives- Geoboard section. I will
have my computer hooked up to a projector for all the students to see. I
will be able to use this student’s work as the class progresses and questions
arise.
2) After a quick review/introduction of perimeter, the students will find the
perimeter of each of the rectangles (the students already have previous
knowledge of perimeter, so I will not be spending much time on it).
3) Once the students have recalled perimeter and they have answered the above
questions, the following discussion questions will be asked and discussed:
• To find area, record the number of square centimeter in the interior. Find
the area of each rectangle.
• Do the rectangles with the same area; have the same perimeter (No)?
Why (Different measurements)? *note: this question will be part of a
journal entry that they are going to do for tonight’s homework.
4) After these questions are gone over, we will begin to relate this part of math to
real life situations. We will discuss how the following sorts of questions relate
to math. The questions will consist of:
• How many posters could be placed around Sally’s bedroom? (Perimeter)
• How many tiles does Martha need to tile her bathroom? (Area)
• Mrs. Jacobs wants to put a fence around her house, how much fence will she
need? (Perimeter)
• How much space will the math club’s poster take up when they hang it in the
union? (Area)
5) While still in their groups, the students will think of word problems that only
relate to perimeter. This will help the students to better understand perimeter

vs. area. Once the problems are written, I will have some volunteers read
their problems aloud.
Conclusion: If time permits, we will begin working on actual perimeter examples
(like finding perimeter with measurements). By looking at the rectangles we drew at
the start of class, we will review how we got the actual perimeter of the rectangles (by
adding the sides together). We will begin to develop the formulas to find perimeter,
that is, perimeter of a rectangle = 2(b)+2(h) and perimeter of a square= 4(s).
Development of these formulas will prepare the students for tomorrow’s lesson.
Homework: Journal entry (Do the rectangles with the same area; have the same
perimeter? Why? Also, page 245 (4 - 11).

Title: Designer for the Day.
Objective: The students will be designing a layout and estimating measurements
in relation to height. Then, they will find the area and perimeter of the layout, seeing
that math can be handy and helpful. The students will be using yesterday’s perimeter
formulas and the definition of area that we also went over yesterday.
Procedure: For today’s class, we will all be heading to the computer lab (or we
could just meet in the computer lab). Each student will have their own computer
and once they enter the lab, their computer will be “locked” (by me) until directions
are gone over.
Activity:
1) Once the students have entered the lab and are settled down, I will
begin the lesson. For today’s class, we will be finding the perimeter
of one story in the student’s house (the story that their bedroom is
located on) using GSP.
2) Since the students already have so much experience with GSP, no
much explanation of the program will be needed (they will have
many notes and handouts on the program from previous classes).
3) I will begin by showing the students a floor plan for my studio
apartment (the entire demonstration of my apartment can be found
in appendix).
4) I expect the student’s layout to be in some sort of ratio, for
instance, one foot = one centimeter (like my layout is). I want
them estimate the size of the room’s in their house in relation to
their height. For example, let’s say that a student is five feet tall,
how many of that student (lying down) could fit along a specific
wall?
5) I want the perimeter of each room/closet/hallway/etc and the area
of each if we have time. The perimeter of each room is something
that must be completed using the formulas that we used yesterday.
Conclusion: Once the students have completed the project and handed it in,
they will be starting their homework until the bell rings.
Assignment: Page 245 (12- 20 and 22, 23). Also, answer the following question:
Why would we need to know the area of your living room or bedroom (so we could
put in carpet or tile)?

Title: “How would you define area?”
Objective: After this lesson is complete, students will have the general
understanding that area is the number of units that fit within a figure. From these
observations, students will be developing formulas based upon their discoveries.
Procedure:
We shall begin the class by discussing area. I will be asking the students such
questions as, “How would you define area?”, “What kinds of things have area?”, and
having the students distinguish the differences between perimeter, area and volume.
I will ask the students to recall the definition of area that we discussed on day 1.
After I feel that students generally have an idea of area, we shall begin the activity.
Activity:
1) Nailing Down Area: An introduction activity to the geoboard
to help students to better understand the meaning of area.
2) Students will get with a partner (the student sitting beside
them), and each pair will be given a geoboard (including rubber
bands), and geoboard paper (a piece for each student). As a
class we will quickly review the rules of the geoboard.
3) I will give the students about five minutes to “play” with the
geoboards. This will allow to students to see how they can
form different shapes and such with the rubber bands and the
pegs.
4) While the students are “playing” with the geoboards, I will be
putting a few questions on the black board. These questions
will consist of:
‣ Create a triangle whose area is half of a unit.
‣ Create quadrilaterals whose area is exactly 1 unit.
‣ Create quadrilaterals/triangles whose area is larger than
1 unit.
5) The students will now begin to work on the questions that I
have written on the board. The students will also begin to
generate some formulas for the area of quadrilaterals. Once
students have generated a formula for quadrilaterals I will then
encourage them to use that information to develop a formula
for triangles. As a class we will review the student’s
observations and their formulas they have developed. I will be
asking for volunteers to come to the overhead and present their
findings.
Conclusion: As a closing to this activity, I will be putting a picture of an
arbitrary shape on the overhead. I will ask the students to tell me what the closed

shape area would be (I will present the size of the unit to the students as well). This
closing part of the activity will allow students to get a better understanding that the
“unit” can very in size depending upon the shape. This will prepare students to do
their homework and for the upcoming activity.
Homework Assignment: In the text book, page 245-248 (24-33,35-42).

Title: Flower Science
Objective: Students will be applying all their knowledge of area and perimeter to a
real life situation. From their knowledge of the calculator, they will be inputting
their data and then graphing it as well.
Procedure:
Class will begin by reviewing the formulas that we went over yesterday and
the previous days as well. The students will be expected to have a formula page
within their notebook and this is where the formula for area (and perimeter) will be
written out. We, as a class, will do a quick review of what we discovered yesterday
(area formula for rectangles and triangles) and we will be writing them in their
notebook, if they are not already in there.
Activity:
1) After we have discussed the formulas, I will be handing out the
worksheet that the students will be doing in class today (see
Appendix for the worksheet and its answers). Graph paper
will also be handed out.
2) After a quick overview of the worksheet, the students will begin
their work. The students will be asked to complete the entire
problem (all parts) and then asked to graph their findings. The
directions of the activity are on the actual worksheet.
3) For the rest of the class, the students will just follow the
directions on the worksheet until it’s complete. There is a lot of
data on the worksheet, and I do expect it to take two days. The
first day (day 4) the students will be completing the chart. The
chart is quite long and should take an entire class period.
4) On day 5, I will be doing a quick review of inputting data into
the calculator and then graphing it (the transparency will be
used and can be found in the Appendix).
Conclusion: At the end of day five, once the chart is complete and the data is
graphed, the students will be asked to graph their findings (in more detail) on graph
paper for homework. They can begin this once the worksheet is complete.
Homework Assignment: Finish the worksheet, if it’s not already done,
and graph Flower Science in greater detail.

Appendix
Day 2
This is my presentation of my apartment. This is what I will be expecting of the
students. I’m not looking for the students to have tabs or buttons like mine does,
but I do expect them to include the measurements (lengths, area and perimeters)
of the following things:
Bedrooms
Bathrooms
Closets
Entire floor
Kitchen, etc.
This is the first picture that the students will see. This is the general outline of my
apartment. For this picture, 1 cm= 1 foot. To see the actual measurements, just
press the button.
Show Distance Measurements
A
D
H
F
E
I
C

After you have pressed the button, this is what you will see:
Hide Distance Measurements
A
D
AD = 17.99 cm
DC = 12.04 cm
AE = 12.01 cm
H
FH = 4.52 cm
F
IH = 6.03 cm
E
I
C
EC = 17.99 cm
CI = 4.50 cm
Now, we will press the tab (at the bottom of the sketch) to see the next page. Here,
we have found the perimeter of the apartment:
A
D
AD = 17.97 cm
AE = 12.01 cm
Perimeter of entire apartment = 59.95 cm
DC = 12.01 cm
DC = 12.01 cm
H
FH = 4.52 cm
F
IH = 6.03 cm
E
I
C
EC = 17.97 cm
CI = 4.49 cm

If you click on the next tab (page 3), it will show us the perimeter of the bathroom:
A
D
AD = 17.97 cm
AE = 12.01 cm
Perimeter of entire apartment = 59.95 cm
DC = 12.01 cm
DC = 12.01 cm
H
FH = 4.52 cm
F
IH = 6.03 cm
Perimeter of Bathroom = 21.08 cm
E
I
C
EC = 17.97 cm
CI = 4.49 cm
The next tab (page 4) will then show you the area of the entire apartment:
A
D
AD = 17.97 cm
AE = 12.01 cm
Perimeter of entire apartment = 59.95 cm
DC = 12.01 cm
DC = 12.01 cm
Area of Entire Apartment = 215.80 cm 2
H
FH = 4.52 cm
F
IH = 6.03 cm
Perimeter of Bathroom = 21.08 cm
E
I
C
EC = 17.97 cm
CI = 4.49 cm

Lastly, tab 5 will show you the area of the bathroom:
A
D
AD = 17.97 cm
AE = 12.01 cm
Perimeter of entire apartment = 59.95 cm
DC = 12.01 cm
DC = 12.01 cm
Area of Entire Apartment = 215.80 cm 2
H
FH = 4.52 cm
F
IH = 6.03 cm
Perimeter of Bathroom = 21.08 cm
Area of Bathroom = 27.29 cm 2
E
I
C
EC = 17.97 cm
CI = 4.49 cm
This is the end of my apartment presentation.

Worksheet for Day 4-5, the answers are provided in RED.
Appendix
Flower Science
Name: _______________
Jon has 32 yards of fencing. Jon wants to make a garden for his mom for her
birthday. He knows that if he doesn’t put a fence around the garden, that the deer
will eat all of her tomatoes. Jon wants to make a rectangular garden for his mother.
What are the dimensions of the garden to result in the maximum area?
Draw some possible rectangular gardens and find their area.
Dimensions
(yards)
Students will be asked to generate a chart like the following one:
Base
Height
(16-b=H)
Amount of
fencing
(perimeter)
Area
(square yards)
15 x 1 1 15 32 yards 15
14 x 2 2 14 32 yards 28
13 x 3 3 13 32 yards 39
12 x 4 4 12 32 yards 48
11 x 5 5 11 32 yards 55
10 x 6 6 10 32 yards 60
9 x 7 7 9 32 yards 63
8 x 8 8 8 32 yards 64
7 x 9 9 7 32 yards 63
6 x 10 10 6 32 yards 60
5 x 11 11 5 32 yards 55
4 x 12 12 4 32 yards 48
3 x 13 13 3 32 yards 39
2 x 14 14 2 32 yards 28
1 x 15 15 1 32 yards 15
After the chart is complete, make a graph of it (in your calculator). Graph the values
of the base on the horizontal axis and the values of the area on the vertical axis (see
graphing transparency for directions on inputting lists into the calculator and then
graphing them).

Answer the following questions:
1. Where does the maximum area occur? The maximum area occurs when the
base is 8 and so is the height. The maximum area is 64 square yards.
2. To have the maximum area for his mother’s garden, what should his
dimensions be? 8 x 8.
3. If you decided to put the garden along the garage, so you would only need to
fence three sides, how would this affect your area? It would make my area
bigger because I could use the same amount of fencing but I would only need
it for three sides instead of four.
4. Jon wants to buy his mother some seeds so she can plant them in her garden
as well. One package of seeds costs $1.59 and covers three square yards.
How many packets of seeds will he need and how much will it cost him? He
will need 22 packets, because three goes into 64 21.33 times, and we round up
so he will have enough seed. He will be spending $34.98 on seeds for his
mother’s garden. We got the price by multiplying 22 times $1.59.
For homework: Draw the graph on graph paper in more detail. Be sure to include labels and
titles.

Appendix
Transparency for Day 5 (Steps on inputting the chart into their calculator and creating a graph
of the information they gathered- what the students will actually see on their calculator is
provided).
Using the TI-84 we begin inputting our data into our calculator by naming our list 1
our base column and our list 2, our area column.
Step 1: Go to List and hit ENTER(or hit 1 on the key pad).
Step 2: This will bring up a screen to enter your data into list 1, list 2, etc. We will
begin by highlighting list 1, hitting clear and then enter. This will clear out any
information that is already in list 1. We should do the same for list 2 as well.
Step 3: Begin to type your data into list 1 (your base answers will be entered here).
Simply hit enter after each entry. Once you have done this, do the same for list 2 but
enter the area answers here. Be sure the correct area matches up with right base.

Step 5: Now, choose Stat Plot.
Step 6: Choose Plot 1 by hitting enter. Highlight ON, select the desired graph, and
a marker of your choice.
Step 7: Now, choose Zoom, and highlight 9: ZoomStat.
Step 8: Now, simply hit enter, and the graph will appear on your screen.