Saskatchewan Common Mathematics Assessments
Pre Assessment
Outcome: P9.4 Demonstrate understanding of polynomials (limited to polynomials of
degree less than or equal to 2) including:





Modeling
generalizing strategies for addition, subtraction, multiplication, and division
analyzing
relating to context
comparing for equivalency
1. Define polynomial:
Level
1
2. Label each expression as a monomial, binomial or a trinomial. (indicator f) (1mk each)
a. 5x² - 2x
_________
b. 4x³
_________
c. 4 – 6x³ + 5x
_________
d. 3x² - 8x
_________
3. Label which are expressions and which are equations. (1mk each)
a. 2x² + 3x – 6
_________
b. 2x + 2 = 10
_________
c. 4xy – 6
_________
d. 2p³ - 7 = 44
_________
4. A large white square represents an x² tile, a black rectangle represents a –x tile, and a small
white represents a 1 tile. (Indicator b/c). (2mks)
What polynomial does this collection represent?
5. Identify the degree of each polynomial? (Indicator d). (1mk each).
a. 7t + 4
_________
b. 4
_________
c. 4p² -7 +6
_________
d. 13v
_________
6. Add or subtract the following as needed.
a. 3x + 1 + 4x – 2
b. -y² + 7y – 5 - (2y² + 7y – 4)
(Indicator J). (1mk each)
Level
2
7. Multiply or divide the following. (Indicator M). (1mk each)
a. 5x · 3y =
b. 6x ( x + 1 ) =
c.
6x
=
3
d. 25xy ÷ 5xy =
8. Keith does not understand how the terms 2𝑘 𝑎𝑛𝑑 𝑘 2 are different. Use algebra tiles to
model these terms and explain the difference.
9. The polynomial 54𝑠 2 represents the surface area of a cube. Determine a polynomial that
represents the area of one face.
Level
3
10. Use your answer from question 8. Determine the length of an edge of the cube.
11. Martin is placing square ceramic tiles on his rectangular kitchen floor. He uses a total of 180 square tiles.
The length is 8 tiles longer than the width. If the floor is x tiles wide, which equation would represent the
area of Martin’s kitchen?
a.
b.
c.
d.
x2 + 8x −180 = 0
x2 + 8x +180 = 0
8x2 −180 = 0
8x2 +180 = 0
Draw a diagram to help you explain how you got this answer.
Level
4
Teacher Section
Answer Key
1
2a
2b
2c
2d
3a
3b
3c
3d
4
5a
5b
5c
5d
6a
6b
7a
7b
7c
7d
8
9
10
11
F
F
F
F
D
D
D
D
J
J
m
m
m
m
Answer
Level
Indicator
Question
Teacher Notes: Students should be provided with manipulatives to assist them in creating
models while working with polynomials.
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
3
3
3
4
One term or the sum of terms whose variables have whole number exponents.
Binomial
Monomial
Trinomial
Binomial
Expression
Equation
Expression
Equation
3𝑥 2 − 3𝑥 + 5
1
0
2
1
7x-1
−3𝑦 2 − 1
15xy
6𝑥 2 + 6𝑥
2x
5
Answers will vary
9𝑠 2
3s
x2 +8x -180 = 0 (a)
Outcome: P9.4 Demonstrate understanding of polynomials (limited to polynomials of degree less than or equal to 2) including:





Modeling
generalizing strategies for addition, subtraction, multiplication, and division
analyzing
relating to context
comparing for equivalency
Description
of Levels:
(based on
Marzano,
2007)
Indicators
and
Learning
Targets for
each Level:
up to Level 1
There is a partial
understanding of
some of the
simpler details and
processes.
Prior knowledge is
understood.
up to Level 2
No major errors or
omissions regarding the
simpler details or
processes, but major
errors or omissions
regarding the complex
processes may be present.
up to Level 3
No major errors or omissions
regarding any of the
information and/or processes
that were explicitly taught.
This is the target level for
proficiency.
up to Level 4
In addition to level
3 performance, indepth inferences
and applications
go beyond what
was explicitly
taught.
Demonstrate an
understanding of
equations and
expressions by:
 Distinguishing
between
equations and
expressions
 Evaluating
expressions
 Verifying
solutions to
equations
b. Represent polynomials
concretely or pictorially
and describe how the
concrete or pictorial
model reflects the
symbolic form.
a.Model (concretely or
pictorially) and describe the
relationship between x and x2.
In addition to level
3 performance, indepth inferences
and applications
go beyond what
was explicitly
taught.
d. Identify the variables,
degree, number of terms
and coefficients,
including the constant
term, of a given
simplified polynomial
expression and explain
the role or significance of
each.
f.Sort a set of
polynomials into
monomials, binomials,
and trinomials.
Studentfriendly
descriptions
of learning
targets.
i.Explain why terms with
different variable
exponents cannot be
added or subtracted.
(b).I can use models/tiles
to represent symbolic
polynomial expressions
(d).I can identify parts of
a polynomial expression
and explain their purpose
(f)I can sort polynomials
into monomials,
binomials, and trinomials.
(i) I can explain why
terms with different
variable exponents cannot
be added or subtracted.
c.Write a polynomial for a
given concrete or pictorial
representation.
h.Write equivalent forms of a
polynomial expression by
interchanging terms or by
decomposing terms, and
justify the equivalence.
k.Verify whether or not the
simplification of the addition
or subtraction of two
polynomials is correct and
explain.
o.Verify whether or not the
simplification of the
multiplication or division of a
polynomial by a monomial is
correct.
(a) I can show with
models/diagrams the
relationship of squared values.
(c)I can write a polynomial
expression from
models/algebra tiles
(h)I can simplify/manipulate
polynomials and show their
equivalence.
(k) I can check/explain if the
simplification of the addition
or subtraction of two
polynomials is correct
(o) I can check whether or not
I can create, solve
and share a
problem with one
or more operations
involving
polynomials.
the multiplication or division
of a polynomial by a
monomial is correct.