Mathematics
Grade 5
Develop Formulas for Area,
Perimeter, and Volume
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Dear Parent or Guardian:
Your son or daughter is currently learning to use patterns to find
formulas that can be used to find the perimeter, area, or volume of
geometric figures. Here is your chance to help him or her practice
this important skill.
In this PAL Packet you will find a short activity for you and your
son or daughter to do. Please do the activity and The Back Page
this evening. Then sign your name on The Back Page and have your
son or daughter return it tomorrow.
Thanks for your help.
Sincerely,
_________________________
Your son or daughter’s teacher
Grade 5 – Develop Formulas for Area,
Perimeter, and Volume
© 2004 Evans Newton Incorporated
1
Last printed 9/7/04
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PATTERNS
Parent Pointer —
Patterns are found all around us. Ceiling and floor tiles, sidewalks, and
the windows of buildings all have a pattern. Architects use patterns to
make their designs pleasing to the eye. Businesses use patterns to
determine the storage area needed for boxes of finished products.
Learning to recognize patterns in geometric figures will prepare your
son or daughter for higher-level mathematics.
Math in the Home, on the Go, and for the Fun of It —
DIRECTIONS: Read and discuss the What Are We Working With?
reference sheet with your parent or guardian. There are groups of
geometric figures on the Find the Formula from the Pattern
worksheet. With your parent or guardian, fill in the tables to identify
the patterns. Then answer the questions below the tables.
Talk about It —
After you have finished the activity, turn to The Back Page to show
what you know.
Now go have some fun with the activity! (
Grade 5 – Develop Formulas for Area,
Perimeter, and Volume
© 2004 Evans Newton Incorporated
2
Last printed 9/7/04
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WHAT ARE WE WORKING WITH?
Terms to Know
Area – The number of square units inside a figure
8 square units
Formula – An equation that can
be used to find the
answer when working with
the same kinds of figures
Area = base × height
Perimeter – The distance around a figure
Volume – The number of cubic units inside a figure
12 cubic units
Types of figures
Quadrilaterals -
Prisms -
square
cube
rectangle
rectangular prism
Right triangle Grade 5 – Develop Formulas for Area,
Perimeter, and Volume
© 2004 Evans Newton Incorporated
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FIND THE FORMULA FROM THE PATTERN
1. The perimeter of each rectangle is written inside the figure.
3
P=8
6
4
1
P = 12
A
2
P = 20
4
B
C
Length
Width
Perimeter
A
B
C
What pattern do you see for finding the perimeter?
Based on the pattern, write a formula for finding the perimeter of a
rectangle.
_______________________________
Draw and label another rectangle to show that the formula works.
Grade 5 – Develop Formulas for Area,
Perimeter, and Volume
© 2004 Evans Newton Incorporated
4
Last printed 9/7/04
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FIND THE FORMULA FROM THE PATTERN
(continued)
2. The right triangles below have their areas written beside them.
H
I
A = 6 cm2
4 cm
3 cm
6 cm
J
A = 12 cm2
A = 22 1 cm2
2
9 cm
4 cm
Base
Height
5 cm
Area
H
I
J
What pattern do you see for finding the area?
Based on the pattern, write a formula for finding the area of a right
triangle.
_______________________________
Draw and correctly label another right triangle to show that the
formula works.
Grade 5 – Develop Formulas for Area,
Perimeter, and Volume
© 2004 Evans Newton Incorporated
5
Last printed 9/7/04
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FIND THE FORMULA FROM THE PATTERN
(continued)
3. The rectangular prisms below have their volumes written below
them.
Y
X
W
6 ft.
4 ft.
2 ft.
2 ft.
2 ft.
V = 8 ft3
2 ft.
3 ft.
V = 24 ft3
Length
Width
4 ft.
2 ft.
V = 48 ft3
Height
Volume
W
X
Y
What pattern do you see for finding the volume?
Based on the pattern, write a formula for finding the volume of a
rectangular prism.
_______________________________
Draw and label another rectangular prism to show that the formula
works.
Grade 5 – Develop Formulas for Area,
Perimeter, and Volume
© 2004 Evans Newton Incorporated
6
Last printed 9/7/04
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The Back Page
Talk About It
Parent —
Ask your son or daughter the following question:
9How do you use patterns to find formulas?
Student —
Answer the above question in a complete sentence on the
reverse side of this page.
OR
Do the following activity on the reverse side of this page:
9Use a ruler to draw four different rectangles. Make a
table to list the length, width, and area. Write a
formula from the pattern you find in the table.
__________________________ __________________________
Student’s Name
Parent or Guardian’s Signature
Grade 5 – Develop Formulas for Area,
Perimeter, and Volume
© 2004 Evans Newton Incorporated
7
Last printed 9/7/04