Area and
Perimeter Man
MA.C.3.2.1.3.1 and .2; MA.B.3.2.1.3.3
LESSON FOCUS Using counting procedures to determine
perimeter and area of rectangles, squares, and other figures.
COMPANION ANCHORS LESSONS Perimeter; Patterns with
Perimeter; Area; Patterns with Area
MATERIALS
least one other square. Also explain that the
squares should be placed so that the sides match
up evenly and that the squares cannot overlap. You
might model the following example (a trailer
truck), using tiles on the overhead projector.
Excursions student pages 99–106
9 square tiles per student
Rulers or other straight edges
Crayons or markers
Colored construction paper and glue sticks
One-centimeter graph paper
One-inch graph paper
LANGUAGE DEVELOPMENT
area
estimate
perimeter
rectangle
square
square inches
units
◆
As students work on their shapes, circulate to
ensure that they are following the guidelines (no
overlapping, all squares touching another on at
least one side) and to assist as needed. When students have designed their pictures, have them glue
the squares onto the construction paper and title
their pictures.
LESSON OVERVIEW
Students begin by using square units to make a picture. They discover how they can count the sides
of a square figure to determine perimeter and the
number of square units within the figure to determine area. Next, they find and compare the
perimeters and areas of various rectangles and
squares. They then practice estimating the perimeter and area of different figures. Finally, they use
their skills to draw a robot and measure its area
and perimeter.
◆
Next, have students trace the outline of their
picture. Tell them to draw a short tick mark each
time they start to trace a different side. Model this
on the picture of the truck you made.
Truck
SETTING THE STAGE
Create pictures with squares.
◆ Have students turn to My Picture Squares, page
Tell which pictures are larger.
◆ Have students share and compare their pictures.
99, in their Excursions books. Help students cut out
the forty-eight squares. Then distribute a sheet of
colored construction paper to each student.
Ask them which figures are larger than others. Ask,
How could you tell which pictures are larger? (Students
might say that some use more squares; but at this
point, accept any reasonable answers.) Then
explain to students that they are going to find out
about two ways to measure the size of objects.
Finally, display students’ pictures.
◆
Explain to students that they are going to use
the 1-inch squares to create a picture. (They will
use their pictures later in this excursion.) Tell students to arrange the squares on the colored
construction paper so that each square touches at
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TOPIC 3 Area and Perimeter Man
BUILDING CONCEPTUAL
KNOWLEDGE
◆ Explain to students that each side of their tiles, or
the length between two tick marks, can be referred
to as one unit. Then have them count with you the
number of units around the squares they made.
Explain that the perimeter of the square is 8 units.
Find the perimeter.
◆ Distribute four color tiles and a sheet of white
paper to each student, and have students place the
tiles on the paper. Tell students to use the four
small squares (tiles) to make a larger square. Work
along with students on the overhead projector.
Find the area.
◆ Next, write the word area on the board, and
explain that the area of a figure is the number of
square units inside the figure. Tell students that
each tile represents 1 square unit. Then have them
find the area of the square they made. (4 square
units)
◆
Then have students draw short tick marks on
the white paper at each new border of the four
tiles. (They should be familiar with this from the
activity in Setting the Stage.)
◆
Have students next use the four tiles to form a
rectangle and find the perimeter and area of the
rectangle. (Students may continue adding the tick
marks if they find them useful for counting the
sides.) Ask, What is the perimeter of your rectangle?
(10 units) What is the area of your rectangle?
(4 square units)
◆
◆
Write the word perimeter on the chalkboard, and
explain to students that the perimeter of a figure is
the distance around it. Point out to students that
they are going to find the perimeter of the square
they just made.
Point out to students that the areas of the rectangle and the square are the same, but that the
perimeter of the rectangle is greater than the
perimeter of the square. Ask, Why do you think the
Name
Name
Area and Perimeter Man
MEASURE US
MY PICTURE SQUARES
✁
8 inches
Figure A
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© School District of Hillsborough County. Copying this page without written permission of Metropolitan Teaching and Learning Company is illegal.
3 square inches
TOPIC 3 Area and Perimeter Man
99
12 inches
10 inches
Figure B
Figure C
6 square inches
9 square inches
10 inches
Figure D
4 square inches
TOPIC 3 Area and Perimeter Man
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Page 101
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101
TOPIC 3 Area and Perimeter Man
perimeter of the rectangle you made is greater than the
perimeter of the square you made? (more sides
exposed)
BUILDING SKILLS AND
STRATEGIES
Compare areas and perimeters.
◆ Distribute five more tiles to each student. Then
Measure perimeter and area in inches.
◆ Show students how to use a pencil and ruler to
draw a rectangle of 5 units on 1-inch graph paper.
Then explain that the side of each unit on the
graph paper measures 1 inch. Explain to students
that when they know the length of a side of each
square unit, they can use that measure to label the
perimeter.
have them repeat the above procedure, forming
rectangles with six, seven, and eight tiles, and a
square and rectangle with nine tiles. Record the
perimeters and areas that students find.
◆
Point out that students could form two rectangles with six tiles (1 ⫻ 6 and 2 ⫻ 3). Ask, How did
the areas of the two rectangles vary? (The areas did
not vary.) How did the perimeters of the two rectangles
vary? (The perimeter of the narrower rectangle was
4 units greater.)
◆
Then find the perimeter of the rectangle you
drew (12 inches) and write it on the board.
◆
Explain to students that because the unit used
for the perimeter is one inch, each square unit is
one square inch. Show students how to find the
area of the rectangle by counting the number of
squares. (5) Ask students how they would label the
area. (5 square inches)
◆
Repeat the questions for the rectangles students
made with eight tiles. Ask, What do you notice about
the narrower rectangles? (They have greater perimeters.)
◆
Finally, distribute the pictures students made in
Setting the Stage, and have them find the perimeter and area. Have them compare their results and
identify the picture or pictures with the greatest
perimeter and area.
◆ Have students turn to Measure Us, page 101, of
their Excursions books. Point out to them that the
side of each square unit is 1 inch. Direct their
attention to Figures A–D and ask the following
questions:
Name
DRAW THE MEASURES
NO SQUARES HERE
Students’ squares and rectangles should reflect
the measures you gave them.
16 inches
Figure A
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7 square inches
102
TOPIC 3 Area and Perimeter Man
16 inches
Figure B
9 square inches
18 inches
Figure C
9 square inches
TOPIC 3 Area and Perimeter Man
Page 102
Page 103
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103
TOPIC 3 Area and Perimeter Man
Which figure has an area of 9 square inches? (C)
Which figure has a perimeter of 8 inches? (A)
Draw a rectangle with a perimeter of 6 inches. (A)
Draw a square with an area of 4 square inches. (B)
Draw a rectangle with a perimeter of 16 inches. (C)
Draw a rectangle with an area of 8 square inches
and a perimeter of 12 inches. (D)
◆
Then, have students work in pairs to find the
area and perimeter of each figure, writing the
perimeter above the figure and the area inside it.
Remind students to label their measurements.
◆
Have students find the areas and perimeters of
their figures and compare their work, discussing
any problems they had completing the figures.
◆
When students have completed Measure Us, ask
them to identify the figure with the greatest
perimeter. (C) Then ask them to describe what is
unusual about Figures B and D. (Though their areas
are different, they have the same perimeter.)
BUILDING MORE SKILLS AND
STRATEGIES
Draw figures with certain perimeters
and areas.
◆ Next, have students turn to Draw the
Find the area and perimeter of different
kinds of figures.
◆ Have students turn to No Squares Here, page
Measures, page 102, in their Excursions books.
Point out that they are again using a 1-inch grid.
Then tell students that you are going to give them
some perimeters and areas and that they are going
to draw rectangles or squares that have these
measurements.
103, in their Excursions books. Explain that they
can find the perimeter and the area of figures that
are not squares or rectangles.
◆
Work with students to find the perimeter and
area of Figure A. Point out that they can use the
same method of counting the sides and squares
that they used to find the perimeter and area of
squares and rectangles. Then have students complete the page, writing the perimeter above the
figure and the area inside the figure.
◆
Have students work in pairs, giving them a few
minutes to complete each figure. Tell them to label
their figures A, B, C, and D as they draw them.
Then say the following:
◆ Ask, Which figures have the same perimeter? (A
and B) What do you notice about figures B and C?
(They have different perimeters but the same area.)
IT’S ABOUT THIS SIZE
Estimate the perimeter and area of each figure.
Estimate perimeter and area.
◆ Explain to students that sometimes a figure may
about 7 inches
Figure A
about 8 inches
1
about 3 or 3ᎏᎏᎏ
2
square inches
Figure B
contain parts of square units. When this is so, they
can estimate to tell about how large the area and
perimeter are. Check to be sure that students
understand that they are not finding the exact
perimeter or area but a measure that is “about” the
actual size.
about 4
square inches
about 12 inches
Figure C
about 8 or 9 square inches
◆
Have students turn to It’s About This Size, page
104, in their Excursions books. Point out that all
the figures contain units that are not complete
squares. Tell students that to estimate the perimeter, they need to look for parts of units, such as
half lines, that make a whole unit. Model for students how to estimate the perimeter of Figure A.
about 13 or 14 inches
Figure D
1
about 6ᎏᎏᎏ or 7
2
square inches
◆
104
Explain that when they estimate area, they also
look for parts of whole square units, such as halves
of squares, that would make up a whole square
unit. Then model how to estimate the area of
Figure A.
TOPIC 3 Area and Perimeter Man
Page 104
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TOPIC 3 Area and Perimeter Man
LANGUAGE ARTS CONNECTION
◆
Then have students work in pairs to estimate
the perimeter and area of Figures B, C and D. Have
students write the perimeter above the figure and
the area inside it. When they have finished, have
them compare their work.
Write a robot story.
◆ Have students write a short story about the
adventures of their robot and share their stories
with the class.
◆
To extend this activity, you could have students
draw squares and rectangles on any size graph
paper and estimate the perimeter in units and the
area in square units.
HOME CONNECTION
Find perimeter and area.
◆ Students use Home Connection: Measure Up!,
PUTTING IT INTO ACTION
pages 105–106, in their Excursions book to measure
the perimeter and area of a table in their home.
The page is used as the unit of measure. You might
want to model how to flip the page around your
desk to measure the perimeter. Show students how
they could use sheets of notebook paper to cover
the area of the desk. Then have students practice
using Home Connection: Measure Up! to find the
perimeter and area of surfaces in the classrooom
before they try it at home.
Make Area and Perimeter Man.
◆ Distribute a sheet of 1-cm graph paper to each
student. Tell them that they are going to use
squares and rectangles to create pictures of robots.
◆
Explain to students that all the lines must be
drawn along the grid lines. They should include a
head, eyes, nose, mouth, torso, arms, hands, legs,
and feet.
Calculate the perimeter and area of the
robot.
◆ When students have completed their robot pictures, have them calculate the perimeter of the
figure. Then have them calculate the area of each
body part and add them together to find the area
of the robot. Point out to students that they may
need to estimate the perimeter or area, depending
on their picture. (Students can express their measures in units and square units or centimeters and
square centimeters.)
◆
Have students name their robots and compare
the areas and perimeters of their drawings. Finally,
display their completed robots in the classroom.
76
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Name
Area and Perimeter Man
MY PICTURE SQUARES
TOPIC 3 Area and Perimeter Man
99
100
© School District of Hillsborough County. Copying this page without written permission of Metropolitan Teaching and Learning Company is illegal.
Name
MEASURE US
8 inches
Figure A
Figure B
Figure C
Figure D
TOPIC 3 Area and Perimeter Man
101
DRAW THE MEASURES
Students’ squares and rectangles should reflect
the measures you gave them.
102
TOPIC 3 Area and Perimeter Man
© School District of Hillsborough County. Copying this page without written permission of Metropolitan Teaching and Learning Company is illegal.
Name
NO SQUARES HERE
16 inches
Figure A
Figure B
Figure C
TOPIC 3 Area and Perimeter Man
103
IT’S ABOUT THIS SIZE
Estimate the perimeter and area of each figure.
about 7 inches
Figure A
Figure B
Figure C
Figure D
104
TOPIC 3 Area and Perimeter Man
Name
HOME CONNECTION: MEASURE UP!
Dear Parent or Guardian:
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Your child has been learning how to find areas and perimeters. To do so,
he or she has been drawing figures on grid paper and finding the area of
each figure by counting the squares within it. Here is an example of how
your child has been using counting to find area and perimeter:
Area is found by
counting the
squares inside the
figure. The area is
17 square units.
Perimeter is found by
counting the sides.
The perimeter of this
figure is 20 units.
Now, your child is going to find the area and perimeter of a table in your
home, using this page as a measuring tool.
You can help your child while participating in his or her learning
experience. Because your child will be using only this page to measure
the perimeter and area, he or she will have to move it around the surface
of the table and count the number of pages. You can help your child
keep track of the number of "pages" it takes to measure the perimeter
and cover the area. If you have extra notebook paper in your home, your
child could use it to cover the table and then just count the sheets to find
the area.
If not intrusive, your child can also use the page to find the perimeter of
a room in your home.
TOPIC 3 Area and Perimeter Man
105
Measure the Perimeter
• Use this page to measure the perimeter and area of a table in your
home.
• First lay the page lengthwise along the edge at one corner of the table.
Place your finger along the edge where the page ends. Then flip the
page over your finger. Be careful to keep the page along the edge.
• When you get to the next corner, turn the page lengthwise and move
down the next side.
• Move around the table this way and count each time you flip the page.
When you get back to where you started, the number you have
counted will be the perimeter.
The perimeter of my table is
Measure the Area
• You can also use the page to find the area. This time, move back and
forth across the table from one end to the other. The point is to find
out how many pages it takes to cover the table.
The area of my table is
Use the page to measure the perimeter and area of other surfaces in your home.
Use the space below to record the measurements.
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TOPIC 3 Area and Perimeter Man