Name:
Teacher:
Class/ Block:
Date:
Polynomial Farm
Please answer each question, given the farm is in a rectangular shape. Cleary identify your
final answer!! (2 points each)
No work or explanation = No Credit
2𝑥 − 1
Corn
Beans
Pumpkins
6𝑥 + 1
Potatoes
𝑥2 − 9
𝑥+6
5𝑥 − 2
Squash
6𝑥
3𝑥 + 2
4𝑥
𝑥
𝑥 2 + 6𝑥 − 7
1. a. Write an expression that represents the length of the west side of the field.
b. Simplify the polynomial expression that represents the west side of the field.
2. a. Write an expression that represents the length of the east side of the field.
b. Simplify the polynomial expression that represents the east side of the field.
3. a. What do you know about the dimensions of the East and West sides of the field?
b. Use this information to solve for x.
Adapted from Polynomial Farm by Emily O’Rourke, Northside High School, Roanoke, Virginia
Name:
Teacher:
Class/ Block:
Date:
4. a. Write a polynomial expression that represents the perimeter of the pumpkin field.
b. Simplify the polynomial expression that represents the perimeter of the pumpkin
field. State one reason why the perimeter would be useful to Farmer Bob.
5. a. Write a polynomial expression that represents the area of the potato field.
b. Simplify the polynomial expression that represents the area of the potato field.
State one reason why the calculated area would be useful to Farmer Bob.
6. a. The farmer would like his bean plants to grow to a height of (x + 3). Write a
polynomial expression to find the volume of the bean plants if they reach a height of
(x + 3).
b. Simplify the polynomial expression that represents the volume of the bean plants
if they reach a height of (x + 3).
7. a. Farmer Bob realized he forgot to include a zucchini field into his field layout. He
plans to use half the length and half the width of the squash field in order to plant
zucchini. Write a polynomial expression that represents the area of the new zucchini
field.
b. Simplify the polynomial expression that represents the area of the newly added
zucchini field.
8. Extra Credit: Write and simplify polynomial expressions that represent the perimeter
and area of the cornfield.
Adapted from Polynomial Farm by Emily O’Rourke, Northside High School, Roanoke, Virginia
Name:
Teacher:
Class/ Block:
Date:
Self-Assessing Form
#
1a.
1b.
2a.
2b.
3a.
3b.
4a.
4b.
4b+.
5a.
5b.
5b+.
6a.
6b.
7a.
7b.
Bonus
Element
The expression that represents the length of the East
side of the field is provided.
The East side of the field polynomial expression is
simplified.
The expression that represents the length of the West
side of the field is provided.
The West side of the field polynomial expression is
simplified.
W vs. e
Solve for x
The polynomial expression that represents the
perimeter of the pumpkin field is provided.
The polynomial expression that represents the
perimeter of the pumpkin field is simplified.
The usefulness of the perimeter in terms of Farmer Bob’s
fields is provided.
The polynomial expression that represents the area of
the potato field is provided.
The polynomial expression that represents the area of
the potato field is simplified.
The usefulness of the area in terms of Farmer Bob’s
fields is provided.
The polynomial expression to find the volume of the
bean plants if they reach a height of (x+3) is provided.
The polynomial expression to find the volume of the
bean plants if they reach a height of (x+3) is
calculated.
A polynomial expression that represents the area of
the new zucchini field is written.
A polynomial expression that represents the area of
the new zucchini field is simplified.
The “Polynomial Farm” worksheet is completed on
time.
The student actively and respectfully participated in
the reflective discussion.
All written work is legible.
The mathematical responses are well organized.
Self-assessment is completed on time.
The expression that represents the length of the south
side of the field is provided.
The south side of the field polynomial expression is
simplified.
Total
Points
Value
Self
Teacher
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
6
52
Adapted from Polynomial Farm by Emily O’Rourke, Northside High School, Roanoke, Virginia
Name:
Teacher:
Class/ Block:
Date:
#
1a.
1b.
2a.
2b.
3a.
3b.
4a.
4b.
4b+.
5a.
5b.
5b+.
6a.
Element
The expression that
represents the length of the
East side of the field is
provided.
The East side of the field
polynomial expression is
simplified.
The expression that
represents the length of the
West side of the field is
provided.
The West side of the field
polynomial expression is
simplified.
The explanation of the
relationship of West and
East sides of the field
Using the above
relationship solve for x.
The polynomial expression
that represents the
perimeter of the pumpkin
field is provided.
The polynomial expression
that represents the
perimeter of the pumpkin
field is simplified.
The usefulness of the
perimeter in terms of
Farmer Bob’s fields is
provided.
The polynomial expression
that represents the area of
the potato field is provided.
The polynomial expression
that represents the area of
the potato field is
simplified.
The usefulness of the area
in terms of Farmer Bob’s
fields is provided.
The polynomial expression
to find the volume of the
Self-Assessing Rubric
0
1
2
No length provided
Length is
incomplete
Length is provide
Not simplified
Simplification
incomplete
Simplification
provided
No length provided
Length is
incomplete
Length is provide
Not simplified
Simplification
incomplete
Simplification
provided
Incorrect or no
equation
generated
Explanation
incomplete or
incorrect
Equation
generated but not
solved correctly
No perimeter
provided
Perimeter is
incomplete
Perimeter is provide
Not simplified
Simplification
incomplete
Simplification
provided
Perimeter
usefulness not
provided
Perimeter
usefulness
incomplete
Perimeter
usefulness
provided
No area provided
Area is incomplete
Area is provided
Not simplified
Simplification
incomplete
Simplification
provided
Area usefulness not
provided
Area usefulness
incomplete
Area usefulness
provided
No volume
provided
Volume is
incomplete
Volume is provided
Explanation not
given
Explanation given
and correct
Equation
generated and
solved correctly
Adapted from Polynomial Farm by Emily O’Rourke, Northside High School, Roanoke, Virginia
Name:
Teacher:
Class/ Block:
Date:
6b.
7a.
7b.
bean plants if they reach a
height of (x+3) is provided.
The polynomial expression
to find the volume of the
bean plants if they reach a
height of (x+3) is
calculated.
A polynomial expression
that represents the area of
the new zucchini field is
written.
A polynomial expression
that represents the area of
the new zucchini field is
simplified.
The “Polynomial Farm”
worksheet is completed on
time.
The student actively and
respectfully participated in
the reflective discussion.
Volume
incomplete
Volume
calculation
provided
No area provided
Area is incomplete
Area is provided
Not simplified
Simplification
incomplete
Simplification
provided
No worksheet
Worksheet is
incomplete or not
provided on time.
Worksheet
completed on time
Does not actively
or respectfully
participate
Written work
illegible
All written work is legible.
The mathematical
responses are well
organized.
Self-assessment is
completed on time.
Bonus
Volume not
calculated
Written work
partially legible
Actively and
respectfully
participates
Written work
legible
No evidence of
organization
Not fully organized
Well organized
No self-assessment
Self-assessment is
incomplete or not
provided on time
Self-assessment
provided on time
Does not fully
participate
The expression that
represents the length of the
south side of the field is
provided.
The south side of the field
polynomial expression is
simplified.
Adapted from Polynomial Farm by Emily O’Rourke, Northside High School, Roanoke, Virginia