Housing Measurement_Section 2_Beg-Numeracy
Housing Measurement: Beginning Numeracy
Section 2: Calculating Perimeter
EL Civics 2011-13
Unit Description:
This unit is divided into three sections with each section having 3 to 5 activities. This
document contains teaching materials for Section 2.
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Section 1: Review Converting Measurements of Length
Section 2: Calculating perimeter
Section 3: Calculating area
Section 4: Calculating perimeter and area of irregular shapes
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Housing Measurement_Section 2_Beg-Numeracy
Why Measure Perimeter? (S2-A1)
What things in life are shaped like squares or rectangles?
square =
rectangle =
1. A book
2. _________________
3. _________________
4. _________________
5. _________________
6. _________________
Perimeter is the measurement around an object.
When do we need to measure the perimeter of an object?
(Teacher’s Note: create a PowerPoint w/ images of when this would be useful.)
1. How many baseboards we need around a floor
2. ______________________________________
3. _______________________________________
4. _______________________________________
5. _______________________________________
6. _______________________________________
7. _______________________________________
8. _______________________________________
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Housing Measurement_Section 2_Beg-Numeracy
Measuring Around vs. Adding sides (S2-A2: Teacher’s Notes)
Materials needed:
 Tape measure (20 ft)
 Measuring tapes for students
 Classroom objects to measure around (book, folder, table, etc.)
Teacher’s Instructions:
Part 1: Hands-on Concept Building: Measuring around an object for perimeter
1. Discuss that perimeter means the measurement around an object.
2. Demonstrate measuring a square or rectangular object such as a table. For a large
object, use a 20 ft tape measure to ensure you can measure the full perimeter with
1 measurement.
3. Share that measurement with the class, for example “144 in”.
4. Now measure each side at a time. Use the words ‘length’ to measure the long side
and ‘width’ to measure the short side. Explain these terms (length = long side,
width = short side) as they will need to know them as they continue forward in this
unit. Write each measurement on the board labeled with length and width. When
you finish, ask the class what to do with the 4 measurements. “How do I know
how much the perimeter is?”~add~.
5. Add up the measurements together, for example “48 in + 24 in + 48 in + 24 in = 144
in.
6. Ask “Why are the measurements the same?” ~measuring all the way around is the
same as adding each side together.
7. Now pass out measuring tapes to each student or pair of students.
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Housing Measurement_Section 2_Beg-Numeracy
Measuring Around vs. Adding sides (S2-A2: Student Handout)
Teacher’s Note: Since measuring tapes often only measure to 60 inches, have students measure only
small items for this activity. Also, make sure they measure at least one square item, such as the box.
1. Measure the perimeter of each object to the nearest inch by measuring
around the object in one measurement.
2. Now measure the perimeter of each object by measuring one side at a
time and adding the measurements together.
Object
Ex. a table
Perimeter in one
measurement
Perimeter measuring each side
144 in
48 + 24 + 48 + 24 = 144
1. a book
____ + ____ + ____ + ____ = ____
2. a folder
3. a driver’s license
4. a square box
5. a TV or computer
screen
Which perimeter is longer for each object, the one with one measurement or
the one measuring each side at a time?
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Housing Measurement_Section 2_Beg-Numeracy
Finding Perimeter of a Square (S2-A3: Teacher’s Notes)
Materials Needed:
 Tape measure to measure objects with sides longer than 60’.
 Measuring tapes for each student or pair
Teacher Instructions:
1. Look at the measurements added together for the square box, #4 on previous
handout. Ask “What do you notice (see) about the measurements of a square?” ~all
four sides have the same measurement~
2. Say “So, if all the sides of a square have the same measurement, how many sides do
you need to measure? ~1 side~ “How do I get the measurement for the perimeter or
all the way around the square?”~multiply by 4 –or- add the 4 sides together~
3. Draw diagrams of two or three squares on the board. Have students come up and
measure one side of each square to the nearest inch. Write the measurements next
to each side measured.
4. Ask “Now, how do we find the perimeter of each square if we only have the
measurement for one side?~multiply by 4 OR add the measurement 4 x”
5. Demonstrate multiplying the measured side by 4 for each square AND adding the
sides 4 times.
6. Say “Let’s make a formula, an easy way to remember what math to use, to show how
we find the perimeter of a square. We measure 1 side, we can call that side a. We
multiply the side by 4. The formula is 4a = P, where a = 1 side, the 4 in front means
to multiply by 4, and the P = perimeter. 4a = P”
7. Show how the formula represents what you already did to find the perimeter for the
squares on the board.
8. Demonstrate with 2 or 3 square objects step-by-step as above, highlighting the
formula each time.
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Housing Measurement_Section 2_Beg-Numeracy
Finding Perimeter of a Square (S2-A3:Student Handout)
Measure the length of one side of each square to the nearest inch. Write the
measurement on the line. Use the formula to find the perimeter.
1.
Length = ____________
4a = P
4 x ______ = ___________
2.
Length = ____________
4a = P
4 x ______ = ___________
3.
Length = ____________
4a = P
4 x ______ = ___________
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Housing Measurement_Section 2_Beg-Numeracy
Finding Perimeter of a Rectangle (S2-A4: Teacher’s Notes)
Materials Needed:
 Tape measure to measure objects with sides longer than 60’.
 Measuring tapes for each student or pair
Teacher Instructions:
1. Look at the measurements added together in the “Perimeter measuring each side”
column from activity S2-A2. Have students look at the pattern they see from the side
measurements ~a + b + a + b; the 2 measurements of the length are the same & the 2
measurements of the width are the same~
2. Ask “Why are the 2 lengths the same? Why are the 2 widths the same” ~the 2
opposite sides (sides across from each other) are the same length~
3. Discuss how in a rectangle the opposite sides are the same length, the lengths are
equal and the widths are equal. Draw diagrams on the board to explain this.
4. “So, if the lengths are the same and the widths are the same, do I have to measure
all four sides?”~no~ “How many sides do I have to measure?”~2 sides; the length and
the width.~
5. Say “If I measure only one length and one width (demonstrate this using the same
table measured in S2-A2 and then add them together, do I get the perimeter?” ~no~
“Why not?” ~because there are 2 more sides, that’s only half.~
6. Ask “What do I need to do then? I measure the length and I know the opposite side is
the same. So if it is 48 in. on this side, I know it is also 48 in on that side. So, what do
I do with the number 48?” ~multiply by 2 (or add together, but make sure students
see that multiplying by 2 is the same as adding the 2 sides together)~
7. Write on the board 48 x 2 length.
8. Say “I measure the width and I know the opposite side is the same. So if it is 24 in. on
this side, I know it is also 24 in. on that side. So, what do I do with the number 24?”
~multiply by 2~
9. Write on the board 24 x 2 width.
10.Say “I have 48 x 2 length and 24 x 2 width. How much is 48 x 2?” ~96 in.~ “How much
is 24 x 2?” ~48 in.~ Write answers on the board. “What do I do with those 2
numbers?” ~add them together~
11.Write 96 + 48 = ? “What is the answer?” ~144 in.~
12.Write “2 x a (1 side) + 2 x b (the other side) = perimeter” on the board.
13.Compare this formula to what you just demonstrated to the class.
14.Shorten the formula to 2a + 2b = perimeter. Explain that the abbreviated form
means the same thing. Explain that this is called a “formula” or short way to figure
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Housing Measurement_Section 2_Beg-Numeracy
out a math problem. This shows that you don’t have to measure each side, but just
the length and width, multiply each by 2, and add them together.
15.Demonstrate with 2 or 3 more classroom objects step-by-step as above, highlighting
the formula each time. You could use the items they measured in S2-A2 to show that
the answer will be the same.
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Housing Measurement_Section 2_Beg-Numeracy
Finding Perimeter of a Rectangle (S2-A4: Student Handout)
Teacher’s Note: Pass out a measuring tape to each student or pair of students.
Directions: Measure the length and width of the objects to the nearest inch
and write the measurements in the chart. Use the formula you practiced to
find the perimeter.
Formula: _________________________________
Object
Ex. Table
Length Width
48 in.
Perimeter:
2a + 2b = Perimeter
2 x 48 + 2 x 24 in. =
96 + 48
= 144 in.
24 in.
1. your table
2. your paper
3. the whiteboard
4. the TV or
computer screen
5. the map
6. the window
7. the door
8. the top of the
cabinet
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Housing Measurement_Section 2_Beg-Numeracy
Perimeter in Feet & Inches (S2-A5: Teacher’s Notes)
Materials Needed:
 Tape measures for measuring objects in feet and inches. (Ideally, 1 tape measure
for each group of 3 or 4 students.)
Teacher’s Instructions:
1. Explain that when we measure a longer length and width, we would use a tape
measure. A tape measure gives us the measurement in feet and inches.
2. Measure a large square object in feet and inches. Demonstrate that all 4 sides are
the same.
3. Write the measurement of one of the sides of the square on the board. If neither
length nor width have extra inches, you should measure an object that does.
4. Now apply the formula (4a = P) to the measurement. Show how we multiply each
unit by four.
Ex. 3 ft 4 inches
X4
12 ft 16 inches
5. Now explain that 16 inches is larger than a foot so we need to “convert” it to feet
(and inches). “How much is 1 foot?” ~12 inches~ What do we do when we change
inches to feet?” ~divide~ “So, 16 ÷ 12 = ? How many times does 12 go into 16? ”
~1~. “How many extra inches are there?” ~4 inches~ “How do you know that?”
~Multiply 12 by 1 = 12 inches. Subtract 12 inches from 16 = 4~
Ex.
1 ft 4 inches
12 x 1 = 12
12 16
Subtract 12 from 16
-12
Remainder 4 inches
4
6. Now measure the length and width of a rectangular object, such as the table. Write
the length & width on the board in feet and inches. If neither length nor width
have extra inches, you should measure an object that does.
7. Write: (for example) Length (side a) = 3 ft. 11 in. width (side b) = 1 ft. 11 in.
8. Apply the formula 2 x (3 ft 11 in). Review how to multiply ft. and inches.
Ex.
3 ft 11 inches
1 ft 10 inches
X2
12 22
6 ft 22 inches
-12
10 inches
6 ft + 1 ft. 10 in. = 7 ft 10 in
9. Repeat with 2 x (1 ft. 11 in.) Then add the answers together.
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Housing Measurement_Section 2_Beg-Numeracy
Perimeter in Feet & Inches (S2-A5a:Student Handout)
Teacher’s Note: Pass out a tape measure to each student or pair of students.
Directions: Measure the length and width of the objects in feet and inches to
the nearest inch and write the measurements in the chart. Use the formula
you practiced to find the perimeter.
Formula: _________________________________
Object
Length
Width
Ex. Table
3 ft. 11 in.
1 ft. 11 in.
2a = 2 x 3 ft. 11 in =
3 ft 11 inches
1 ft 10 in.
X2
12 22
6 ft 22 in.
-12
10 in.
6 ft + 1 ft. 10 in. = 7 ft 10 in
Perimeter:
2a + 2b = P
2b = 2 x 1 ft. 11 in =
1 ft 11 inches
1 ft 10 in.
X2
12 22
2 ft 22 in.
-12
10 in.
2 ft + 1 ft. 10 in. = 3 ft 10 in
1 ft 8 in
7 ft 10 in + 3 ft 10 in = 10 ft 20 in.
12 20
10 ft. + 1 ft. 8 in. = 11 ft. 8 in.
-12
8 in.
1.
Your Table
Perimeter:
2a + 2b = P
2.
Whiteboard
Perimeter:
2a + 2b = P
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Housing Measurement_Section 2_Beg-Numeracy
Perimeter in Feet & Inches (S2-A5b:Student Handout)
Directions: Use the measurements you took for the activity before. Now you
will calculate perimeter by converting to the smallest measurement first,
finding the perimeter, and then converting back to feet & inches.
Formula: _________________________________
Object
Ex. Table
Length
3 ft. 11 in.
Width
1 ft. 11 in.
2a = 2 x 3 ft. 11 in =
3 ft 11 inches
X 12
36 in + 11 in. = 47 in.
2 x 47 in = 94 inches
Perimeter:
2a + 2b = P
94 in + 46 in = 140 in.
P = 11 ft 8 in.
1.
Your Table
Perimeter:
2a + 2b = P
2.
Whiteboard
Perimeter:
2a + 2b = P
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2b = 2 x 1 ft. 11 in =
1 ft 11 inches
X12
12 in. + 11 in. = 23 in.
10 in.
2 x 23 in = 46 inches
11 ft 8 in
12 140
-12
20 in.
-12
8 in.
Housing Measurement_Section 2_Beg-Numeracy
Perimeter Activity (S2)
Home Decorating Project: You bought curtains for your living room. You like
the curtains but you want to make them prettier. You decide to sew a border
of ribbon all around the curtains to add color. Look at the diagram of the
curtains on the next page. Now follow the directions.
1. What color curtains did you buy? Note: Think about the color of your
living room. What color would look nice?
2. What color ribbon do you want to add? Note: Think about the color of the
curtains. What color would look good with this color? This is called an
“accent” color.
3. Color the diagram with the colors you chose. Use markers, crayons, or
colored pencils. If white, leave blank.
4. Now measure the windows in feet (and inches if extra inches). You can
measure the windows in your living room and bring those measurements
to class or you can measure the windows in your classroom to use as an
example. Note: Your curtains need to be long enough to cover the top and
bottom of the window frame. They need to be wide enough to cover both
the left and right of the window frame.
5. Write your measurements on the diagram and worksheet.
6. Now think about how much ribbon you need to buy. Look at the diagram.
Curtains are not just 1 piece of fabric. They come with 2 “panels” or
pieces of fabric. The ribbon must go around each panel.
7. Calculate the perimeter of one of the shapes.
Square: 4a = P
Rectangle: 2a + 2b = P
8. There are 2 curtain panels. So how much ribbon (in feet and inches) do
you need in total? Round your inches
9. Ribbon is sold by the yard. You need to convert your measurements to
yards. First, round your inches up to the next foot. Then convert to yards.
Remember: 3 feet = 1 yard
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Housing Measurement_Section 2_Beg-Numeracy
Curtains Diagram (S2)
1. Color the inside of the curtain panels
2. Color the ribbon border of the curtain panels.
3. Measure the window(s) and write the measurements on the diagram.
Curtain
Panel 1
½ Window Length: ______________
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Curtain
Panel 2
½ Window Length: ______________
Window Height ____________________
Window Height ____________________
Window Length: _______________________
Housing Measurement_Section 2_Beg-Numeracy
Perimeter Activity Worksheet (S2)
1. Curtain Fabric Color: __________________________
2. Curtain Ribbon Color: _________________________
3. Window Length: __________________________
4. ½ Window Length _______________________
5. Window Height: __________________________
6. Calculate the perimeter of one of the curtain panels:
7. My curtain panel is a square rectangle. (Circle one)
The formula I will use is: (Circle one below)
Square: 4a = P -OR- Rectangle: 2a + 2b = P
My Calculations:
Length = ___________ Height = ___________
Perimeter = _________ ft and ______ inches
8. You will need ribbon for 2 curtain panels. Multiply the perimeter by 2:
__________________ x 2 = _______________________
1 panel Perimeter
2 panels Perimeter
9. I will need a total of _________feet ______ inches of ribbon.
10. Round the inches up to the next foot. Note: You need to make sure to
have enough ribbon so rounding down is not a good idea.
I will need ___________ feet of ribbon.
11. Ribbon is sold by the yard. You need to convert feet to yards:
Remember: 3 feet = 1 yard
________ = ? yards
Total feet
3 feet = 1 yard
Divide down
I will need ________ yards _______ (extra) feet of ribbon.
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