Download CH0 Performance Indicators-Algebra of Calculus Prerequisites

College Algebra
Unit 0 – Algebra of Calculus
Scoring Criteria
U1.PI 1
Interpret rational and irrational
numbers and use properties of
rational and irrational numbers.
“1” – Emerging
I have demonstrated the most
basic knowledge/skills relevant
to this standard.
CCSS Domain(s): Number and Quantity ; Algebra
“2” – Developing
I have demonstrated relevant
knowledge/skills, but have not
yet demonstrated convincing
evidence of fully meeting the
standard.
“3” – Achieving
I have demonstrated that I
have the knowledge/skills
defined in the standard.
Level 1
I can identify rational
numbers and I know that
numbers that are not rational
are irrational.
L2: Level 1, plus…
I can perform basic Algebraic
operations involving rational
and irrational numbers.
L3: Level 2, plus…
I can explain informally that
every number has a decimal
expansion ; for rational
numbers show that decimal
expansion repeats eventually
into a rational number.
I can apply basic properties of
integer exponents to generate
equivalent numerical
expressions.
I can use radical symbols to
represent solutions to power
equations.
I can explain the properties of
rational exponents and apply
these properties to simplify
polynomial expressions.
“4” – Excelling
I have demonstrated the
knowledge/skills defined by
the standard with a high level
of understanding/ability as
defined by the discipline.
L4: Level 3, plus…
I can use rational
approximation of irrational
number to compare the size of
irrational numbers without the
use of a calculator.
Performance Indicators
CCSS: N-RN 3
U1.PI 2
Extend the properties of
exponents to rational exponents
I can apply the properties of
rational exponents to rewrite
more complex rational
expressions in their simplified
equivalent form.
CCSS: N-RN 1, N-RN 2
U1.PI 3
Interpret Structure of Expressions
and use the structure of an
expression to rewrite it.
I can interpret parts of an
expression, such as terms,
factors, and coefficients.
I can use the structure of an
expression to identify ways to
re-write it. For example, I
recognize that the difference
of the squares can be use to
rewrite
I can rewrite a simple rational
expression involving
polynomials in different forms
and add, subtract, multiply, and
divide rational expressions.
x 4  y 4  ( x 2 )2  ( y 2 )2 
CCSS: A-SSE 2, A-APR 6, A-APR 7
I can explain that rational
expressions form a system
analogous to the rational
numbers, closed under
addition, subtraction,
multiplication, and division by
a nonzero rational expression.
( x 2  y 2 )( x 2  y 2 )
U1.PI 4
Perform Arithmetic Operations
with Complex Numbers.
CCSS: N-CN1, N-CN 2, N-CN 3
I can identify a complex
number i such that i²=-1, and
I know that every complex
number has the form a+bi
with a and b real.
I can convert complex
numbers from their radical
form into standard a+bi form.
I can use the relationship
i²=-1 and the commutative,
associative, and distributive
properties to add, subtract, and
multiply complex numbers.
I can find a conjugate of a
complex number; and use
complex conjugates to find
products and quotients of
complex numbers.