Download 2015-2016 Algebra 2nd Quarter Mathematics Scope and Sequence

2015-2016 Algebra 2nd Quarter Mathematics Scope and Sequence
Unifying Concept: Functions and Systems
Mathematics Content Focus:
Mathematical Practice Focus
(Both Book Chapters 3, 4, 5)
Mathematically Proficient Students…
Students will:
1. Make sense of problems and persevere in solving
them.
 Reasoning with Equations
2. Reason abstractly and quantitatively.
 Interpreting Functions
3. Construct viable arguments and critique the reasoning
 Building Functions
of others.
 Linear Equations
4. Model with mathematics.
- Graph
- Write
5. Use appropriate tools strategically.
- Solve
- Model Real World
6. Attend to precision.
 Linear Inequalities
7. Look for and make use of structure.
- Write
Model Real World
8. Look for and express regularity in repeated reasoning.
- Graph
Solve and justify
 Piecewise linear Functions Graph
 Systems of Linear Equations and Inequalities
- Graph
- Write
- Solve
- Model Real World
A-REI.B.3
A-REI.D.10
A-REI.D.11
A-REI.D.12
A-CED.A.1
A-CED.A.2
A-CED.A.3
F-IF.A.1
F-IF.A.2
F-IF.B.4
Target Standards
Solve linear equations and inequalities in one variable, including equations with coefficients
represented by letters.
Understand that the graph of an equation in two variables is the set of all its solutions plotted in the
coordinate plane, often forming a curve (which could be a line).
Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x)
intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using
technology to graph the functions, make tables of values, or find successive approximations.
Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential,
and logarithmic functions. ★
Graph the solutions to a linear inequality in two variables as a half-plane (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.
Create equations and inequalities in one variable and use them to solve problems. Include
equations arising from linear and quadratic functions, and simple rational and exponential
functions.
Create equations in two or more variables to represent relationships between quantities; graph
equations on coordinate axes with labels and scales.
Represent constraints by equations or inequalities, and by systems of equations and/or
inequalities, and interpret solutions as viable or nonviable options in a modeling context. For
example, represent inequalities describing nutritional and cost constraints on combinations of
different foods.
Understand that a function from one set (called the domain) to another set (called the range)
assigns to each element of the domain exactly one element of the range. If f is a function and x is
an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph
of f is the graph of the equation y = f(x).
Use function notation, evaluate functions for inputs in their domains, and interpret statements that
use function notation in terms of a context.
For a function that models a relationship between two quantities, interpret key features of graphs
and tables in terms of the quantities, and sketch graphs showing key features given a verbal
description of the relationship. Key features include: intercepts; intervals where the function is
increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end
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2015-2016 Algebra 2nd Quarter Mathematics Scope and Sequence
behavior; and periodicity. ★
F-IF.B.5
F-IF.B.6
Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it
describes. For example, if the function h(n) gives the number of person-hours it takes to assemble
n engines in a factory, then the positive integers would be an appropriate domain for the function.
★
Calculate and interpret the average rate of change of a function (presented symbolically or as a
table) over a specified interval. Estimate the rate of change from a graph. ★
Quarter Major Clusters
Arizona considers Major Clusters as groups of related standards that require greater emphasis than some of the
others due to the depth of the ideas and the time it takes to master these groups of related standards.
A-REI.B Solve equations and inequalities in one variable
Essential Concepts
Essential Questions
 Equations and inequalities are solved using properties
 What do you use to justify your steps when
of operations, equality, and inequality, which can
solving linear and non-linear equations and
justify each step of the process.
inequalities?
 A solution to an equation can be checked, by
 How do you determine and justify whether a
substituting in that value for the variable and
solution to an equation or inequality is correct?
simplifying to see if the equation or inequality holds
 How do operations performed on real numbers
true.
affect the relationship between the quantities in
an inequality?
A-REI.D Represent and solve equations and inequalities graphically
Essential Concepts:
Essential Questions:
 The graph of an equation in two variables is the set of
 How do you determine if a given ordered pair is
all its solutions plotted in the coordinate plane.
a solution to an equation?
 Solving a system of equations algebraically yields an
 Why are the x-coordinates of the points where
exact solution; solving by graphing or by comparing
the graphs of the equations y = f(x) and y = g(x)
tables of values yields an approximate solution.
intersect equal to the solutions of the equation
f(x) = g(x)?
 The solutions (solution set) of a linear inequality in two
variables are represented graphically as a half-plane.
 When graphing a linear inequality, how do you
determine which half-plane to shade in order to
 The solution set of a system of linear inequalities in
represent the solution set?
two variables is the intersection of the corresponding
half-planes.
 How do you represent the solution set of a
system of linear inequalities on a graph?
A-CED.A Create equations that describe numbers or relationships
Essential Concepts
Essential Questions
 Equations and inequalities can be created to represent  How do you translate real-world situations into
and solve real-world and mathematical problems.
mathematical equations and inequalities?
 Relationships between two quantities can be
 How do you determine if a situation is best
represented through the creation of equations in two
represented by an equation, an inequality, a
variables and graphed on coordinate axes with labels
system of equations or a system of inequalities?
and scales.
 Why would you want to create an equation or
 Solutions are viable or not in different situations
inequality to represent a real-world problem?
depending upon the constraints of the given context.
 How are graphs of equations and inequalities
similar and different?
 How do you determine if a given point is a viable
solution to a system of equations or inequalities,
both on a graph and using the equations?
F-IF.A Understand the concept of a function and use function notation
Essential Concepts:
Essential Questions:
 A function is a rule that assigns each input exactly one
 Given a table or graph, how do you determine if
output.
it represents a function?
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2015-2016 Algebra 2nd Quarter Mathematics Scope and Sequence
 In function notation, f(x) denotes that f is a function of
 How is a graph related to its algebraic function?
x.
 How could you use function notation to
 The set of all inputs (x) for a function is called the
represent a specific output of a function?
domain; the set of all outputs (f(x)) for a function is
called the range.
 The domain and range of a function can be expressed
as a set of numbers using set notation, an inequality,
or as a graphed solution.
 The graph of a function f is the graph of the equation y
= f(x).
 Algebraic equations, written in function notation, can
be used to evaluate functions for a given input.
 For a function f(x), f(a) represents the value of the
function when x = a.
F-IF.B Interpret functions that arise in applications in terms of the context
Essential Concepts:
Essential Questions:
 Key features of a graph or table may include
 How can you describe the shape of a graph?
intercepts, intervals in which the function is increasing,
 How can you relate the shape of a graph to the
decreasing or constant, intervals in which the function
meaning of the relationship it represents?
is positive, negative or zero, symmetry, maxima,
 How would you determine the appropriate
minima, and end behavior.
domain for a function describing a real-life
 Given a verbal description of a relationship that can be
situation?
modeled by a function, a table or graph can be
 Given a function that describes a real-life
constructed and used to interpret key features of that
situation, what can the average rate of change of
function.
the function tell you?
 The meaning of the key features of a graph or table,
 How do the parts of a graph of a function relate
such as domain, range, rate of change and intercepts,
to its real world context?
can be interpreted in the context of a problem.
 The intervals over which a function is increasing,
decreasing or constant, positive, negative or zero are
subsets of the function’s domain.
 The appropriate domain for a function describing a
real-life situation may be smaller than the largest
possible domain.
 The average rate of change of a function y = f(x) over
an interval [a,b] is
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Dy f (b) - f (a)
.
=
Dx
b-a
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