East St. Louis High School
Algebra 1, Geometry and Algebra 2
Curriculum Guides
September, 2012 Discussion Drafts
A High School Math Curriculum Plan for use during the transition
to PARCC (replacing PSAE) in 2015 and new textbooks by 2014.
Algebra 1
Unit/(Weeks)
1. Patterns and expressions (3)
2. Equations (4)
3. Creating linear functions (4)
4. Representing and applying
linear functions (5)
5. Direct and indirect variation
(3)
6. Data (4)
7. Systems of equations (3)
8. Exponential functions (3)
9. Linear inequalities and
linear programming (3)
Topics
(see unit objectives below)
Variables, exponents,
expressions, graphs
Solving linear equations
Resources
Common Core Standards
Textbook 1-1 – 1-4, 5-7
A-SSE 1-3
Textbook 3-1, 3-2, 3-3
A-CED 1-2, A-REI 1, 3, 4, 5,
10, 11, 12
F-IF 1-6, 7a,b, 8b, 9
F-BF 1a,b, 3
F-LE 1, 2, 3, 5
Graphs, tables, equations
Graphs, parent functions, slope,
intercept, predicting
Proportions, inverse variation
5-1 – 5-4
6-1 – 6-6
Scatterplots, central tendency,
standard deviation, lines of best
fit, correlation vs. causation
Systems of linear equations,
conditions for 0, 1 and infinite
number of solutions
Multiplicative change,
exponential models, geometric
series
Inequalities, systems of
inequalities, applications
6-7, 1-5, 1-6
S-ID 1-9
7-1 – 7-4
A-REI 6
8-6, 8-7. 8-8
F-LE 2, 4
Textbook 4-1 – 4-4, 7-5. 7-6
Baker’s Choice unit
Need to add problems,
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A-REI 4, 11
Textbook 3-4 and 3-7, 5-5, 5-6
Modeling
The “big ideas” of an Algebra 1 course:
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The procedures or steps used to solve algebraic equations and generate equivalent (including simplified) expressions can be
justified on the basis of a distinct set of properties, including commutative, associative, and distributive properties; addition
and multiplication properties of equality; inverse and identity properties for addition and multiplication; and properties of
exponents and roots.
Linear relationships, including arithmetic sequences, represent additive change and have a constant slope or rate of change;
alternatively, exponential relationships, including geometric sequences, represent multiplicative change and have increasing
or decreasing slopes or rates of change.
Proportional relationships are linear functions, in the form y = mx where m is the rate of change that when graphed, form
lines that pass through the origin.
An algebraic function is a rule that assigns one number (a unique output) to the given input and is used to generalize
patterns or relationships and predict an output for an given input or an input for any given output.
Different, but equivalent, forms of linear functions, including y = mx + b; ax + by = c; and (y – y1) = a (x – x1), reveal
different aspects of the function.
Functional situations involving two related variable quantities can be represented with words, tables, graphs, and symbolic
equations among which given functions can be translated.
A unique linear relationship can be created from two data points or from a single data point and a rate of change; when
graphed, every linear relationship can be expressed as a translation (slide) and a rotation of the y = x line or parent function.
The key processes of an Algebra 1 course:
Instruction and assessment should be conducted in ways that ensure that:
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Students explain their reasoning and justify their answers.
Students use multiple representations of mathematical ideas.
Students make connections between and among related mathematical ideas.
Students recognize and apply mathematical skills and concepts in real-world situations.
UNIT OBJECTIVES
Unit 1: Patterns – introduces many of the big ideas, sets instructional routines, uses tile patterns to display patterns
graphically
 The student will represent a given tile pattern with words, in a table, with a graph, or with an equation and identity how they
are equivalent.
 The student will model algebraic expressions in a variety of ways (for example, using algebra tiles, sketches/diagrams, bar
models).
 The student will use real number properties (identity, inverse, commutative, associative, distributive) to simplify and evaluate
algebraic expressions and to write equivalent expressions.
 The student will create and differentiate iterative and explicit rules for patterns.
 The student will recognize, describe, and extend arithmetic sequences; determine a specific term of a sequence when given an
explicit formula; write an explicit rule for the nth term of an arithmetic sequence; and write a recursive rule for the nth term of
an arithmetic sequence.
Reach-Back Standards
6.EE.A - Apply and extend previous understandings of arithmetic to algebraic expressions.
6.EE.A.2 - Write, read, and evaluate expressions in which letters stand for numbers.
a. Write expressions that record operations with numbers and with letters standing for numbers.
b. Identify parts of an expression, using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts
of an expression as a single entity.
c. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world
problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there
are no parentheses to specify a particular order (Order of Operations).
6.EE.A.3 - Apply the properties of operations to generate equivalent expressions.
6.EE.A.4 - Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which
value is substituted into them).
6.EE.B - Reason about and solve one-variable equations and inequalities.
6.EE.B.6 - Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand
that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
7.EE.A - Use properties of operations to generate equivalent expressions.
7.EE.A.1 - Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational
coefficients.
7.EE.A.2 - Understand that rewriting an expression in different forms in a problem context can shed light on the problem of how the
quantities in it are related.
8.F.A - Define, evaluate, and compare functions.
8.F.A.2 - Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or
by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an
algebraic expression, determine which function has the greater rate of change.
Unit 2: Equations
 The student will model algebraic equations in a variety of ways (for example, using algebra tiles, sketches/diagrams, bar
models) and will identify and create equivalent equations. (much of this done in grades 6-8)
 Given a mathematical or real-world situation, the student will define a variable, write an equation or an inequality, solve the
equation or inequality, and interpret the solution. (much of this done in grades 6-8)
 The student will graph the solutions of equations and inequalities on a number line.
 The student will use real number properties (identity, inverse, commutative, associative, distributive) to justify steps in solving
equations and inequalities.
Reach Back Standards:
6.EE.B - Reason about and solve one-variable equations and inequalities.
6.EE.B.6 - Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if
any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation
or inequality true.
6.EE.B. 6 - Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand
that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
6.EE.B.7 - Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in
which p, q and x are all nonnegative rational numbers.
6.EE.B.8 - Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical
problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities
on number line diagrams.
7.EE.B - Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
7.EE.B.4 - Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and
inequalities to solve problems by reasoning about the quantities.
a. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers.
Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the
operations used in each approach.
b. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers.
Graph the solution set of the inequality and interpret it in the context of the problem.
8.EE.C - Analyze and solve linear equations and pairs of simultaneous linear equations.
8.EE.C.7 - Solve linear equations in one variable.
a. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of
these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the
form x = a, a = a, or a = b results (where a and b are different numbers).
b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using
the distributive property and collecting like terms.
Unit 3: Linear functional situations – introduces the concept of function through activities that relate two variables
 The student will recognize and apply real-world functions in a variety of representations and translate among verbal, tabular,
graphic, and algebraic representations of functions.
 The student will recognize an example of a function; identify the role of independent and dependent variables in a function;
determine the domain and range of a linear function; find the slope and intercepts of a linear function; and use function notation
to evaluate a function for a specified value.
Reach Back Standards:
6.EE.C - Represent and analyze quantitative relationships between dependent and independent variables.
6.EE.C.9 - Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an
equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent
variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the
equation.
8.EE.B - Understand the connections between proportional relationships, lines, and linear equations.
8.EE.B.5 - Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional
relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine
which of two moving objects has greater speed.
8.EE.B.6 - Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the
coordinate plane; derive the equation for a line through the origin and the equation for a line intercepting the vertical axis at b.
8.F.A - Define, evaluate, and compare functions.
8.F.A.1 - Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered
pairs consisting of an input and the corresponding output.
8.F.A.2 - Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or
by verbal descriptions).
8.F.A.3 - Interpret the equation as defining a linear function, whose graph is a straight line; give examples of functions that are not
linear
8.F.B - Use functions to model relationships between quantities
8.F.B.4 - Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of
the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph.
Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table
of values.
8.F.B.5 - Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is
increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described
verbally.
Unit 4: Representing function situations
 The student will recognize functions in a variety of representations and a variety of contexts and translate among verbal,
tabular, graphic, and algebraic representations of functions (including the use of function notation, f(n)).
 The student will describe how the aspects of the function such as the dependent and independent variables and slope and yintercept are reflected in the different representations.
 The student will explain how the change in one variable affects the change in another variable.
 The student will understand that the slope of a line represents a constant rate of change.
 The student will show how changes in parameters affect the graph of the function.
Reach Back Standards:
6.EE.C Represent and analyze quantitative relationships between dependent and independent variables.
6.EE.C.9 Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an
equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent
variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the
equation.
8.F.A Define, evaluate, and compare functions.
8.F.A.1 Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered
pairs consisting of an input and the corresponding output.
8.F.A.2 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or
by verbal descriptions).
8.F.A.3 Interpret the equation as defining a linear function, whose graph is a straight line; give examples of functions that are not
linear.
8.F.B Use functions to model relationships between quantities
8.F.B.4 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of
the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph.
Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table
of values.
8.F.B.5 Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is
increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been
described verbally.
8.EE.B Understand the connections between proportional relationships, lines, and linear equations.
8.EE.B.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional
relationships represented in different ways.
8.EE.B.6 Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the
coordinate plane; derive the equation for a line through the origin and the equation for a line intercepting the vertical axis at b.
Unit 5: Direct and indirect variation
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The student will recognize that when the ratio between two varying quantities is invariant, the two quantities are said to be
directly proportional; when the product of two varying quantities is invariant, the two quantities are said to be inversely
proportional.
The student will use proportional relationships and proportional reasoning to solve real-world problems.
The student will distinguish directly proportional relationships (y/x = k or y = kx) from other relationships, including inverse
proportionality (xy = k or y = k/x).
The student will recognize that y = kx represents a proportional relationship and that when b ≠ 0, y = kx + b does not represent
a proportional relationship.
The student will recognize that the graph of a proportional relationship is a line that passes through the point (0, 0).
The student will translate among verbal, tabular, graphical, and algebraic representations of direct and inverse variation.
The student will apply direct and inverse variation to solve real-world and mathematical problems.
Reach Back Standards:
7.RP.A - Analyze proportional relationships and use them to solve real-world and mathematical problems.
7.RP.A.2 - Recognize and represent proportional relationships between quantities.
a. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a
coordinate plane and observing whether the graph is a straight line through the origin.
b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional
relationships.
c. Represent proportional relationships by equations.
d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the
points (0, 0) and (1, r) where r is the unit rate.
8.EE.B - Understand the connections between proportional relationships, lines, and linear equations.
8.EE.B.5 - Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional
relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine
which of two moving objects has greater speed.
8.EE.B.6 - Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the
coordinate plane; derive the equation for a line through the origin and the equation for a line intercepting the vertical axis at b.
Unit 6: Data (scatter plots, correlation, lines of best fit)
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 The basic modeling cycle is summarized in the diagram. It involves (1) identifying variables in the situation and selecting
those that represent essential features, (2) formulating a model by creating and selecting geometric, graphical, tabular,
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algebraic, or statistical representations that describe relationships between the variables, (3) analyzing and performing
operations on these relationships to draw conclusions, (4) interpreting the results of the mathematics in terms of the original
situation, (5) validating the conclusions by comparing them with the situation, and then either improving the model or, if it is
acceptable, (6) reporting on the conclusions and the reasoning behind them.
The student will construct, interpret and draw and justify conclusions from scatter plots.
The student will describe the advantages and disadvantages of using scatter plots to represent data.
The student will describe relationships in data represented in scatter plots (linear, nonlinear, positive correlation, negative
correlation, no correlation).
 The student will find an equation that represents linear trend, when it is appropriate, for real-world data and use the equation,
table, or graph to make predictions and solve real-world problems.
Reach-Back Standards:
8.SP.A Investigate patterns of association in bivariate data.
8.SP.A.1 Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two
quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear
association.
8.SP.A.2 Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots
that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of
the data points to the line.
8.SP.A.3 Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the
slope and intercept.
8.SP.A.4 Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and
relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables
collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association
between the two variables.
Unit 7: Systems of equations
 The student will understand that a system of simultaneous linear equations in two unknowns contains two distinct linear
equations with two unknowns and the solution to the system is the point (x, y) that makes both equations true.
 Given a mathematical or real-world situation, the student will define the variables and write an appropriate system of linear
equations.
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The student will use tables and graphs to find and interpret solutions to systems of equations in mathematical and real-world
contexts.
The student will describe the characteristics of the slopes of parallel and perpendicular lines in terms of slope.
Reach Back Standards:
8.EE.C - Analyze and solve linear equations and pairs of simultaneous linear equations.
8.EE.C.8 - Analyze and solve pairs of simultaneous linear equations.
a. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs,
because points of intersection satisfy both equations simultaneously.
b. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve
simple cases by inspection. For example, and have no solutions because cannot simultaneously be 5 and 6.
c. Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for
two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.
Unit 8: Exponential Functions (multiplicative change vs. additive change)
 The student will compare and contrast linear and exponential models.
 The student will identify key features of an exponential curve.
 The student will describe how rates of change may be used to identify members of the exponential function family.
 The student will describe the role of the parameters in context
 The student will write and use models for exponential growth and decay
 The student will identify simple transformations of the exponential parent function.
Reach Back Standards:
8.F.A - Define, evaluate, and compare functions.
8.F.A.2 - Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or
by verbal descriptions).
8.F.A.3 - Interpret the equation as defining a linear function, whose graph is a straight line; give examples of functions that are not
linear.
8.F.B - Use functions to model relationships between quantities
8.F.B.5 - Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is
increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described
verbally.
Unit 9: Linear Inequalities and Linear Programming
 The student will solve realistic optimization problems using the tools of linear programming
Reach Back Standards:
6.EE.B Reason about and solve one-variable equations and inequalities.
6.EE.B.5 Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the
equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.
6.EE.B.8 Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize
that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
7.EE.B Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
7.EE.B.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve
problems by reasoning about the quantities.
b. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the
solution set of the inequality and interpret it in the context of the problem.
Geometry
Unit/(Weeks)
1. Geometric tools and terms
(3)
2. Parallel and perpendicular
lines (3)
3. Triangles and quadrilaterals
(3)
4. Congruence (4)
5. Similarity (5)
6. Circles (4)
7. Surface area and volume (4)
8. Probability (4)
Topics
Segments, Angles,
Constructions, Dimension
Angle/line relationships
Resources
Textbook Chapter 1
Classifying triangles and
quadrilaterals, properties
Congruence theorems
Similarity, scale, right
triangles, right triangle trig
Area, chords, angles, tangents
Textbook Chapters 5 and 6
Common Core Standards
Textbook Chapter 3
Textbook Chapter 4
Textbook Chapters 7 and 8
G-CO 1-13 G-GPE4, 6, 7
G-SRT-1-8
Textbook Chapter 12
Textbook Chapter 11
G-C 1, 2, 3, 5
G-GMD 1-4
S-CP 1-7
Independent and conditional
probability, sample space
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supplemental materials.
Get copies of Discovering
Geometry for supplementing
Key objective is making conjectures and justifying them. Justification or proof should be based on concrete materials,
Euclidean theorems and postulates, constructions, real world examples, and coordinate geometry as appropriate.
Algebra 2
Unit/Weeks
1. Linear functions and
equations (9)
Topics
(see unit key skills and
concepts below)
Tables, graphs, verbal and
symbolic representations and
their relationships
Slope and intercept and their
interpretations
Creating linear functions
Solving problems involving
linear equations and
inequalities
Resources
Common Core Standards
Textbook Chapters 1, 2 and 3
A-SSE 1-4
A-CED 1-2
A-REI 1, 2, 4, 7, 11
F-IF 3, 4, 6, 7, 8a, 9
F-BF 1, 2, 3, 4a
2. Quadratic equations and
functions (6)
Textbook Chapter 5
A-CED 3-4
A-REI 1, 2, 4, 7, 11
F-IF 3, 4, 6, 7, 8a, 9
F-BF 1, 2, 3, 4a
3. Exponential equations and
functions (6)
4. Polynomial and rational
functions (6)
5. Statistics (5)
Textbook Chapter 8
F-LE 2, 4
Textbook Chapters 6 and 7 and
9
Textbook Chapter 12
A-APR 1, 2, 3, 4, 6
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Modeling
Making inferences, justifying
conclusions, simulations,
sampling,
S-IC 1-6
Assumptions
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With approximately 1000 pages and 14 chapters in a typical Algebra II textbook, it is essentially impossible for teachers, and probably
inappropriate for most students, to attempt to cover all of the topics in a typical textbook.
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Topics such as matrices, series and sequences, trigonometry and conic sections have all been covered or considered for coverage in Algebra
II courses. While important, none of these topics is deemed more important than the skills and concepts listed below and all can be
effectively addressed in a Pre-calculus course that follows Algebra II.

For many Algebra II courses, the first half of the year consists of a review of nearly all of the topics already taught, but rarely mastered or
understood, in Algebra I. We acknowledge the need for review of Algebra I topics, but assume that a well taught and well designed Algebra
I course that focuses primarily on linear equations, inequalities and functions will require less review and enable Algebra II to move for
quickly to quadratic and polynomial functions.

Given the focus on functions and the connections between symbolic, tabular and graphical representations, we assume that a graphics
calculator will be available to every student and effectively used to enhance the learning of the mathematical content of Algebra II and to
better apply the skills and concepts of the course.

The fundamental purpose of Algebra II is to continue to develop and deepen students’ understanding of functions and their applications.
As such, Algebra II builds on and reinforces the skills and concepts of Algebra I, prepares students for the skills and concepts of preCalculus and Calculus, prepares students for the mathematics required by a statistics course, and prepares students to successfully take the
SAT and ACT college admissions examinations.
The “big ideas” of an Algebra II course:
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Functions are mathematical rules for taking input (independent variables) and producing output (dependent variables).
Algebraic properties allow for the generation of equivalent forms of most expressions and equations.
Linear functions are additive (that is, the dependent variable increases additively), exponential functions are multiplicative
(that is, the dependent variable increases multiplicatively).
There is a direct relationship, for any function, among a point on a graph of the function, an ordered pair in a table of the
function, and a solution to the symbolic form of the function.
The graphs of functions can be visualized and predicted based on transformations of a parent function (that is, all linear
functions are transformations of the parent function or line y = x, and all quadratic functions are transformations of the parent
function y = x2).
The graph of the inverse of a function is its reflection across the line y = x.

Just as subtraction undoes or is the inverse of addition, the square root is the inverse of squaring and square root functions are
the inverse of quadratic functions, and finding a log is the inverse of raising to a power and logarithmic functions are the
inverse of exponential functions.
The key processes of an Algebra II course:
Instruction and assessment should be conducted in ways that ensure that:




Students explain their reasoning and justify their answers.
Students make and use multiple representations of mathematical ideas.
Students make connections between and among related mathematical ideas.
Students recognize and apply mathematical skills and concepts in real-world situations.
Unit 1: Review and reinforce big ideas and key skills of linear equations and functions
Key skills
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Use algebraic properties and laws to develop and identify
equivalent expressions
Evaluate algebraic expressions, including those with
exponents and absolute value
Solve 1-variable linear equations and inequalities
Graph linear functions
Solve systems of linear equations
Perform operations on rational expressions
Model situations with linear functions and apply these
functions to real-world situations
Determine whether a scatterplot appears to show a linear
trend, and if so, draw a trend line, write an equation for that
line, and use the equation to make predictions
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Key concepts
Differentiate among rational, irrational and real numbers
Understand and justify the laws of exponents
Represent and understand the equivalence of symbolic,
tabular and graphical representations of a linear function
Use algebraic properties to justify the steps used in solving
equations and inequalities
Understand slope as a rate of change
Translate among equivalent forms of linear functions [e.g., y
= mx+b, Ax +By = C,
(y-Y) = a (x – X) + k].
Describe the solution to a system of equations and relate the
solutions to the problem’s original context.
Unit 2: Quadratic functions
Key skills
 Solve quadratic equations and inequalities
 Graph quadratic equations and inequalities
 Solve systems of quadratic equations and quadratic and linear
equations
 Model situations with quadratic functions and apply these
functions to real-world situations
 Identify and interpret graphs and tables of quadratic functions
 Use the parent function (y = ax2) to describe and predict the
effects of parameter changes on the graphs of quadratic
functions
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Key concepts
Represent and understand the equivalence of symbolic,
tabular and graphical representations of quadratic functions
Use completing the square to derive the quadratic formula
Analyze and explain the reasoning used to solve a system of
equations
Understand that quadratic functions have equal second
differences
Translate among equivalent forms of quadratic functions
[e.g., ax2 + bx + c and a(x-h)2 + k]
Understand the relationship between factors and roots
Understand and use the relationship between the values of a, b
and c in a quadratic equation and the nature of the roots
Unit 3: Polynomials and polynomial functions- Consider adding some Transformational work here
Key skills
Key concepts
 Simplify and perform operations on polynomials
 Represent and understand the equivalence of symbolic,
tabular and graphical representations of polynomial functions
 Solve polynomial equations
 Relate the degree of a polynomial to its general shape and
 Identify and interpret graphs and tables of polynomial
number of roots
functions
 Understand the key characteristics of polynomial functions,
 Model situations with polynomial functions and apply these
including domain, range, intercepts, asymptotes, and shape
functions to real-world situations
n
 Use the parent function (y = ax ) to describe and predict the
effects of parameter changes on the graphs of polynomial
functions
Unit 4: Patterns, series and recursion
Key skills
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Extend patterns based on arithmetic and geometric
sequences, given specified initial terms and patterns of
change.
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Find the value of any term in a sequence.
 Develop the general term for arithmetic and geometric
sequences, and develop methods for calculating sums of
terms for finite arithmetic and geometric sequences and the
sum of a convergent infinite geometric series.
 Express a given well defined sequence with an initial term
as a recursive relationship.
 Develop the closed form representation for a linear
recursive relationship.
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Key concepts
Understand that sequences expressed recursively can be
expressed explicitly or in closed form and vise versa
Unit 5: Exponential and logarithmic functions
Key skills
 Simplify and perform operations on exponential and
logarithmic expressions
 Solve exponential and logarithmic equations
 Identify and interpret graphs and tables of exponential and
logarithmic functions
 Model situations with exponential and logarithmic functions
and apply these functions to real-world situations
 Use the parent functions (y = ax and y = log x) to describe and
predict the effects of parameter changes on the graphs of
exponential and logarithmic functions
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Unit 6: Rational and Radical Functions
Key skills
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Simplify and perform operations on rational and radical
expressions
Solve rational and radical equations
Model situations with rational and radical functions and
apply these functions to real-world situations
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Key concepts
Represent and understand the equivalence of symbolic,
tabular and graphical representations of exponential and
logarithmic functions
Understand the key characteristics of exponential and
logarithmic functions, including domain, range, intercepts,
asymptotes, and shape
Understand the inverse nature of exponential and logarithmic
functions
Key concepts
Understand nth roots and exponents as inverse operations
Represent and understand the equivalence of symbolic,
tabular and graphical representations of a rational and radical
functions
Unit 7: Probability and statistics- Consider: Two-way tables and conditional probabilities are an important component here
Key skills
Key concepts
 Summarize and compare sets of data using a variety of
 Understand correlation as a measure of the strength of a linear
statistics, including means and standard deviations
relationship
 Find and use least squares lines as a model for data that
 Relate the expansion of (x + y)n with the possible outcomes of
suggest a linear trend
a binominal experiment and the nth row of Pascal’s triangle.
 Use permutations, combinations and other systematic
 Understand and interpret measures of central tendency and
counting methods to determine the number of ways events can
measures of spread
occur.
 Understand the key characteristics of the normal distribution
 Compare theoretical and empirical probability
and use them to estimate probabilities.
 Compute and graph cumulative frequencies.
 Calculate expected value for simple experiments
High Leverage Instructional Practices that Need to Be Observed in ALL Instruction
1. Effective teachers of mathematics respond to most student answers with “why?”, “how do you know that?”, or “can you explain your
thinking?”
2. Effective teachers of mathematics conduct daily cumulative review of critical and prerequisite skills and concepts at the beginning of
every lesson.
3. Effective teachers of mathematics elicit, value, and celebrate alternative approaches to solving mathematics problems so that students
are taught that mathematics is a sense-making process for understanding why and not memorizing the right procedure to get the one
right answer.
4. Effective teachers of mathematics provide multiple representations – for example, models, diagrams, number lines, tables and graphs,
as well as symbols – of all mathematical work to support the visualization of skills and concepts.
5. Effective teachers of mathematics create language-rich classrooms that emphasize terminology, vocabulary, explanations and
solutions.
6. Effective teachers of mathematics take every opportunity to develop number sense by asking for, and justifying, estimates, mental
calculations and equivalent forms of numbers.
7. Effective teachers of mathematics embed the mathematical content they are teaching in contexts to connect the mathematics to the
real world.
8. Effective teachers of mathematics devote the last five minutes of every lesson to some form of formative assessments, for example,
an exit slip, to assess the degree to which the lesson’s objective was accomplished.
9. Effective teachers of mathematics demonstrate through the coherence of their instruction that their lessons – the tasks, the activities,
the questions and the assessments – were carefully planned.