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Intermediate Algebra 1 Alignment to Common Core HS Algebra II
(Bridging Document)
Semester: 1 Quarter: 1
Essential Questions
(DRAFT)
1. What situation will produce a function versus a relation?
2. What is the purpose of writing a function in multiple forms? What information can I gain from the various forms?
3. What are the characteristics of a graph? How do I use a graph to identify characteristics of a function and translate the information to the
function notation? (common characteristics and making connections among all function types – do you want the functions listed here?)
4. How does a function's domain and range provide vital information regarding the context of the problem and its solutions?
5. What does a solution look like? (this is an appropriate place to start the conversation about the connections between domain and discrete
and continuous, and range to determine an extraneous solution.)
California Common Core High School Algebra II (2013)
Functions: Building Functions - Build new functions from existing functions
3. Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for
specific values of k (both positive and negative); find the value of k given the graphs.
Experiment with cases and illustrate an explanation of the effects on the graph using
technology. Include recognizing even and odd functions from their graphs and algebraic
expressions for them.
Functions: Interpreting Functions - Analyze functions using different
representations
7. Graph functions expressed symbolically and show key features of the graph, by hand in
simple cases and using technology for more complicated cases.
a. Graph linear and quadratic functions and show intercepts, maxima, and minima.
b. Graph square root, cube root, and piecewise-defined functions, including step functions
and absolute value functions.
8. Write a function defined by an expression in different but equivalent forms to reveal and
explain different properties of the function.
a. Use the process of factoring and completing the square in a quadratic function to show
zeros, extreme values, and symmetry of the graph, and interpret these in terms of a
context.
California Content Standard (2006)
24.0 Students solve problems involving functional concepts, such as
composition, defining the inverse function and performing arithmetic
operations on functions
9.0 Students demonstrate and explain the effect that changing a
coefficient has on the graph of quadratic functions; that is, students can
determine how the graph of a parabola changes as a, b, and c vary in
the equation y = a(x-b)2 + c.
1.0 Students solve equations and inequalities involving absolute
value.
Notes Unit 1 Foundations for Functions connects with the Common Core Conceptual Category: Functions: Building Functions (F-BF) and Interpreting Functions (F-IF)
The Unit titles come from the current Sweetwater pacing guide for Intermediate Algebra. They somewhat align with the units described in Appendix A:
Designing High School Mathematics Based on the Common Core Standards:
Unit 1: Polynomial, Rational and Radical Relationships
Unit 3: Modeling with Functions
Reminder, whether following the Integrated or Traditional Pathway the connections made here are not perfectly aligned with how Intermediate
Algebra has been taught in our district over the last few years. The units from Appendix A referenced above are the closest match and indicate what our
students will eventually need to master. Additionally, Appendix A is not a pacing guide, but a suggested organization of concepts. It is hoped that with
this in mind, adjustments to instruction can be made to facilitate the transition to the common Core Standards.
Intermediate Algebra 1 Alignment to Common Core HS Algebra II (DRAFT)
Semester: 1 Quarter: 1 (Bridging Document) 5/31/2013
5/3/2017
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Essential Questions (pending revision)
Given the context of the problem, how do I make decisions about what solution(s) methods to use?
What reasoning do I need in order to interpret the viability of the solution(s) (i.e. solution(s), no solution and infinite; real or complex numbers) for
functions, including inequalities?
How do I construct a viable argument to justify a solution(s) and solution method?
California Common Core High School Algebra II (2013)
Algebra: Reasoning with Equations and Inequalities - Represent
and solve equations and inequalities graphically
12. Graph the solutions to a linear inequality in two variables as a halfplane (excluding the boundary in the case of a strict inequality), and
graph the solution set to a system of linear inequalities in two variables
as the intersection of the corresponding half-planes
Solve systems of equations
5. Prove that, given a system of two equations in two variables,
replacing one equation by the sum of that equation and a multiple of the
other produces a system with the same solutions.
6. Solve systems of linear equations exactly and approximately (e.g.,
with graphs), focusing on pairs of linear equations in two variables
8. (+) Represent a system of linear equations as a single matrix
equation in a vector variable.
9. (+) Find the inverse of a matrix if it exists and use it to solve systems
of linear equations (using technology for matrices of dimension 3 × 3 or
greater).
California Content Standard (2006)
2.0 Students solve systems of linear equations and inequalities (in
two or three variables) by substitution, with graphs, or with
matrices.
Notes Unit 2 Linear Systems connects with the Common Core Conceptual Category : Algebra: Reasoning with Equations and Inequalities (A-REI)
The Unit titles come from the current Sweetwater pacing guide for Intermediate Algebra. They somewhat align with the units described in Appendix A:
Designing High School Mathematics Based on the Common Core Standards:
Unit 1: Polynomial, Rational and Radical Relationships
Unit 3: Modeling with Functions
Reminder, whether following the Integrated or Traditional Pathway the connections made here are not perfectly aligned with how Intermediate
Algebra has been taught in our district over the last few years. The units from Appendix A referenced above are the closest match and indicate what our
students will eventually need to master. Additionally, Appendix A is not a pacing guide, but a suggested organization of concepts. It is hoped that with
this in mind, adjustments to instruction can be made to facilitate the transition to the common Core Standards.
Intermediate Algebra 1 Alignment to Common Core HS Algebra II (DRAFT)
Semester: 1 Quarter: 1 (Bridging Document) 5/31/2013
5/3/2017
Essential Questions(pending revision)
What information can I gain about a quadratic function from its various forms (standard form, vertex form, factored form, etc.) and how are the forms related?
What are the key features of a graph? How do I use the graph of a parabola to identify key features of a quadratic function and translate the information to the
function notation?
Given the context of the problem what information provided by a graph and/or solution(s) is extraneous and what information is vital (i.e. range and domain,
continuous vs. discrete)?
What are the similarities that exist in performing arithmetic operations among complex and rational numbers?
California Common Core High School Algebra II (2013)
Functions: Interpreting Functions - Analyze functions using different
California Content Standard (2006)
representations
7. Graph functions expressed symbolically and show key features of the graph, by hand in
simple cases and using technology for more complicated cases.
a. Graph linear and quadratic functions and show intercepts, maxima, and minima.
8. Write a function defined by an expression in different but equivalent forms to reveal and
explain different properties of the function.
a. Use the process of factoring and completing the square in a quadratic function to show
zeros, extreme values, and symmetry of the graph, and interpret these in terms of a
context.
Algebra: Seeing Structure in Expressions - Write expressions in equivalent forms
to solve problems
3. Choose and produce an equivalent form of an expression to reveal and explain
properties of the quantity represented by the expression.
a. Factor a quadratic expression to reveal the zeros of the function it defines.
b. Complete the square in a quadratic expression to reveal the maximum or minimum
value of the function it defines.
Algebra: Reasoning with Equations and Inequalities - Solve equations and
inequalities in one variable
4. Solve quadratic equations in one variable.
a. Use the method of completing the square to transform any quadratic equation in x into
an equation of the form (x – p)2 = q that has the same solutions. Derive the quadratic
formula from this form.
b. Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots,
completing the square, the quadratic formula and factoring, as appropriate to the initial
form of the equation. Recognize when the quadratic formula gives complex solutions and
write them as a ± bi for real numbers a and b.
Number and Quantity: The Complex Number System - Perform arithmetic
operations with complex numbers.
2. Use the relation i2 = –1 and the commutative, associative, and distributive properties to
add, subtract, and multiply complex numbers.
3. (+) Find the conjugate of a complex number; use conjugates to find moduli and
quotients of complex numbers.
9.0 Students demonstrate and explain the effect that changing a
coefficient has on the graph of quadratic functions; that is, students can
determine how the graph of a parabola changes as a, b, and c vary in
the equation y = a(x-b)2 + c.
10.0 Students graph quadratic functions and determine the maxima,
minima, and zeros of the function.
8.0 Students solve and graph quadratic equations by factoring,
completing the square, or using the quadratic formula. Students apply
these techniques in solving word problems. They also solve quadratic
equations in the complex number system
6.0 Students add, subtract, multiply, and divide complex numbers.
Notes Unit 3 Quadratic Functions connects with the Common Core Conceptual Categories: : Functions: Interpreting Functions (F-IF) Algebra:
Reasoning with Equations and Inequalities (A-REI) and Seeing Structure in Expressions (A-SSE) Number and Quantity: The Complex Number System
(N-CN)
Also see explanation about units found in Appendix A in the previous Notes boxes
Intermediate Algebra 1 Alignment to Common Core HS Algebra II (DRAFT)
Semester: 1 Quarter: 1 (Bridging Document) 5/31/2013
5/3/2017
Intermediate Algebra 1 Alignment to Common Core HS Algebra II (DRAFT)
Semester: 1 Quarter: 1 (Bridging Document) 5/31/2013
5/3/2017