# Patterns and Inductive Reasoning ```Algebra 2 Curriculum &amp; Pacing Guide
Pacing Guide
1st Marking Period
2nd Marking Period
I. Pretest
I. Matrices (2 Weeks)
II. Fundamentals of Algebra (2 Weeks)
III. Linear Functions (3 Weeks)
III. 2nd Quarterly Exam
IV. Systems (3 Weeks)
V. 1st Quarterly Exam
3rd Marking Period
4th Marking Period
I. Exponential &amp; Logarithmic Functions (5 Weeks)
I. Complete Rational Functions &amp; Polynomials (Last 3 of 6 Weeks)
II. Begin Rational Functions &amp; Polynomials (First 3 of 6 Weeks)
III. 3rd Quarterly Exam
III. Probability &amp; Data Analysis – Optional (2 Weeks)
IV. 4th Quarterly (Final) Exam
Fundamentals of Algebra (2 weeks)
Why are functions and relations represented in multiple ways?
How are functions and relations useful?
How are patterns of change represented in functions?
Students should be
able to…
Evaluate expressions using
the Order of Operations
Algebra 2 Coll: 1.1, 1.2
Solving equations &amp;
inequalities
Algebra 2 Coll: 1.3, 1.6
Identify domain &amp; range,
dependent &amp; independent
variables
Algebra 2 Coll: 2.1
Apply the vertical line test
Algebra 2 Coll: 2.1
Apply this discussion to real
world problems
Middletown Public Schools
Instructional Strategies and
Activities
SAT Correlation or Real
World Applications
2.2.a.1 Recognize vectors and matrices as
systems that have some, but not all,
of the properties of real numbers.
1.3.a.1 Model and solve problems with
equations and linear inequalities.
1.1.a.3 Identify the characteristics of
functions and relations, including
domain and range.
Scientific Method
1.1.a.3 Identify the characteristics of
functions and relations, including
domain and range.
1.1.a.2 Make and justify predictions based on
patterns.
3.1.a.2 Test the validity of logical arguments.
August 2010
2
Linear Functions (3 weeks)
What makes a relationship linear?
Why are linear functions useful?
What are the different ways that rate-of-change (slope) can be used to represent various concepts?
How do I generate a line of best fit from a given set of data?
What different information is obtained from equivalent forms of algebraic equations?
Students should be
able to…
Graph Equations &amp;
Inequalities
Algebra 2 Adv: 1-7, 2-1, 22, 3-1, 3-2
Algebra 2 Coll: 2.2, 2.3, 2.6
Write the equation of a line
given information
Algebra 2 Coll: 2.4
1.2.a.1 Represent functions and relations on
the coordinate plane.
1.2.a.2 Recognize the effect of changes in
parameters on the graphs of
functions or relations.
1.1.a.2 Make and justify predictions based on
patterns.
Fit a trend line to a data set
Algebra 2 Coll: 2.5
1.1.a.2 Make and justify predictions based on
patterns.
Apply linear functions to
real world problems
1.1.a.2 Make and justify predictions based on
patterns.
3.1.a.2 Test the validity of logical arguments.
Middletown Public Schools
Instructional Strategies and
Activities
Linear Functions Mini-Poster
http://www.teachforever.com/2008/1
2/project-idea-linear-functionsmini.html
August 2010
SAT Correlation or Real
World Applications
Interpolation,
Extrapolation,
Predictions,
Simple Interest,
Fixed/Variable Cost,
Stock Market
3
*Advanced Algebra 2 will teach the Systems Unit and Matrices Unit simultaneously.*
Systems (3 weeks)
How are systems of equations and inequalities useful?
How does the solution to a system of inequalities relate to the solution to a system of equations?
Which problem-solving strategy is most appropriate in each situation?
Students should be
able to…
Instructional Strategies and
Activities
SAT Correlation or Real
World Applications
Solve a system of equations
1.3.a.3 Use logarithms, vectors and matrices
Algebra 2 Adv: 4-1, 4-2, 4-6
to solve problems.
Algebra 2 Coll:3.1, 3.2
Graph a systems of
inequalities
Algebra 2 Coll: 3.3
Apply solving systems of
equations and graphing
inequalities for Linear
Programming
Algebra 2 Coll: 3.4
Apply systems of equations
and inequalities to real
world problems
Algebra 2 Coll:
Middletown Public Schools
1.3.a.1 Determine equivalent representations
of an algebraic equation or
inequality to simplify and solve
problems.
Optimization,
Profit Maximization,
Resource Allocation,
Statisticians,
Accounting
1.1.a.6 Understand and use optimization
strategies, including linear
programming.
1.1.a.2 Make and justify predictions based on
patterns.
3.1.a.2 Test the validity of logical arguments.
Mixture Problems
August 2010
4
Matrices (2 weeks)
How can matrices help organize information and how do I manipulate them?
Why are matrices useful in displaying data and solving problems?
Students should be
able to…
Instructional Strategies and
Activities
2.2.a.1 Select and use appropriate methods
for computing to solve problems in a
variety of contexts.
2.2.a.2 Solve problems involving scientific
notation and absolute value.
Use the determinant to solve 2.2.a.1 Select and use appropriate methods
a system of equations
for computing to solve problems in a
(Cramer’s Rule)
variety of contexts.
2.2.a.2 Solve problems involving scientific
Algebra 2 Coll: 4.3
notation and absolute value.
Solve systems with 32.2.a.1 Select and use appropriate methods
Variables using Inverse
for computing to solve problems in a
Matrices
variety of contexts.
2.2.a.2 Solve problems involving scientific
Algebra 2 Coll: 4.4
notation and absolute value.
Apply systems of equations
and matrices to real world 1.1.a.2 Make and justify predictions based on
problems
patterns.
3.1.a.2 Test the validity of logical arguments.
Algebra 2 Coll: 4.5
SAT Correlation or Real
World Applications
Perform matrix operations
Algebra 2 Coll: 4.1, 4.2
Middletown Public Schools
Data Entry,
Computer Programming,
Engineers,
Astronomers,
Marketing,
Announcers,
Statisticians
August 2010
5
Quadratics &amp; Complex Numbers (5 weeks)
Which problem-solving strategy is most appropriate in each situation?
How do quadratic relations model real-world problems and their solutions?
Why are complex numbers important?
How are real, imaginary, and complex numbers related?
How can graphical and analytic methods be used to support each other in the solution of a problem?
Students should be
able to…
Algebra 2 Coll: 5.1
Algebra 2 Coll: 5.1
by factoring, by graphing,
and by completing the
square
Algebra 2 Coll: 5.2, 5.3, 5.5
with imaginary solutions
10-3
Algebra 2 Coll: 5.4, 5.6
Middletown Public Schools
1.1.a.1 Identify, describe, create and
generalize numeric, geometric and
statistical patterns with tables,
graphs, words and symbolic rules.
1.1.a.1 Identify, describe, create and
generalize numeric, geometric and
statistical patterns with tables,
graphs, words and symbolic rules.
1.2.a.1 Represent functions and relations on
the coordinate plane.
1.2.a.2 Recognize the effect of changes in
parameters on the graphs of
functions or relations.
2.1.a.2 Select and use an appropriate form of
number (integer, fraction, decimal,
ratio, percent, exponential, scientific
notation, irrational) to solve practical
problems involving order,
magnitude, measures, labels,
locations and scales.
2.1. a.1 Compare, locate, label and order real
numbers on number lines, scales,
coordinate grids and measurement
tools.
2.2.a.2 Perform operations with complex
Instructional Strategies and
Activities
http://www.teachforever.com/2009/04/b
August 2010
SAT Correlation or
Real World
Applications
Projectile Trajectories,
Stopping Distance,
Economics,
Finance,
Architecture
6
numbers, matrices, determinants and
logarithms.
expression
Algebra 2 Coll: 5.1
and functions to real world
problems
Algebra 2 Coll: 5.8
Middletown Public Schools
1.3.a.1 Determine equivalent representations
of an algebraic equation or
inequality to simplify and solve
problems.
1.1.a.2 Make and justify predictions based on
patterns.
3.1.a.2 Test the validity of logical arguments.
August 2010
7
Exponential Functions &amp; Logarithmic Functions (5 weeks)
How do exponential functions model real-world problems and their solutions?
How are the properties of exponential and logarithmic functions used to evaluate functions and solve problems?
Students should be
able to …
Simplify and apply the
exponential properties
6-10
Algebra 2 Coll: 6.1
Instructional Strategies and
Activities
1.1.a.1 Describe and compare properties and
classes of functions, including
exponential, polynomial, rational,
logarithmic and trigonometric.
2.1.a.2 Select and use an appropriate form of
number (integer, fraction, decimal,
ratio, percent, exponential, scientific
notation, irrational, complex) to
solve practical problems involving
order, magnitude, measures, labels,
locations and scales.
Compound Interest,
Population Growth,
Exponential Decay,
Richter Scale,
Measuring pH,
Measuring Sound (dB)
1.2.a.1 Relate the graphical representation of
Graph exponential functions
a function to its function family and
find equations, intercepts, maximum
Algebra 2 Coll: 8.1, 8.2, 8.3
or minimum values, asymptotes and
line of symmetry for that function.
Evaluate an exponential
2.1.a.4 Judge the effects of computations
expression
with powers and roots on the
magnitude of results
Algebra 2 Coll: 8.1, 8.2, 8.3
Simplify and apply the
1.1.a.1 Describe and compare properties and
logarithmic properties
classes of functions, including
exponential, polynomial, rational,
Algebra 2 Coll: 8.4, 8.5
logarithmic and trigonometric.
Middletown Public Schools
SAT Correlation or
Real World
Applications
August 2010
8
Graph logarithmic functions
Algebra 2 Coll: 8.4
Solve exponential equations
using logarithms
Algebra 2 Coll: 8.6
Simplify logarithmic
expressions
Algebra 2 Coll: 8.5
1.2.a.1 Relate the graphical representation of
a function to its function family and
find equations, intercepts, maximum
or minimum values, asymptotes and
line of symmetry for that function.
1.1.a.4 Solve problems involving financial
applications including compound
interest, amortization of loans, and
investments.
1.3.a.3 Use logarithms, vectors and matrices
to solve problems.
2.2.a.2 Perform operations with complex
numbers, matrices, determinants and
logarithms.
2.2.a.2 Perform operations with complex
numbers, matrices, determinants and
logarithms.
1.1.a..2 Analyze essential relations in a
Apply exponential and
problem to determine possible
logarithmic equations to
functions that could model the
solve real world applications
situation
3.1.a.2 Test the validity of logical arguments.
Algebra 2 Coll: 8.7
Middletown Public Schools
Census Project
August 2010
9
Rational Functions &amp; Polynomials (6 weeks)
How do polynomial functions model real-world problems and their solutions?
How can the properties of fractions be extended to algebraic rational expressions?
When do we solve for a variable and when do we leave it factored form?
How are the zeros of the polynomial function, the factors of the polynomial, and the solution to the polynomial related?
Students should be
able to…
Graph functions including
asymptotes, discontinuities,
and complex solutions
10-3, 10-4
Algebra 2 Coll: 6.2, 9.2
1.1.a.7 Apply the concepts of limits to
sequences and asymptotic behavior
of functions.
1.2.a.1 Relate the graphical representation of
a function to its function family and
find equations, intercepts, maximum
or minimum values, asymptotes and
line of symmetry for that function.
Factor polynomials
Algebra 2 Coll: 6.4, 6.5
2.2.a.2 Perform operations with complex
numbers, matrices, determinants and
logarithms.
Divide polynomials using
synthetic division
Algebra 2 Coll: 6.5
Factor higher degree
polynomials (factor
theorem)
Algebra 2 Coll: 6.4, 6.5
Find products and quotients
of polynomials
Algebra 2 Coll: 6.3
Middletown Public Schools
Instructional Strategies and
Activities
SAT Correlation or
Real World
Applications
http://www.parkridge.k12.nj.us/dcaine/T
he%20Birthday%20Polynomial%20Proj
ect.pdf
Unit Conversions,
Potential Energy,
Cryptography,
Robotics,
Forestry
2.2.a.2 Perform operations with complex
numbers, matrices, determinants and
logarithms.
2.2.a.2 Perform operations with complex
numbers, matrices, determinants and
logarithms.
1.3.a.2 Combine, compose and invert
functions
2.2.a.2 Perform operations with complex
numbers, matrices, determinants and
logarithms.
August 2010
10
Find the sums and
Differences of polynomials
Algebra 2 Coll: 6.3
1.3.a.2 Combine, compose and invert
functions
2.2.a.2 Perform operations with complex
numbers, matrices, determinants and
logarithms.
Solve fractional equations
(identify domain and
extraneous solutions)
Algebra 2 Coll: 9.6
1.1.a.5 Solve problems involving direct and
inverse variation
Apply polynomial and
fractional equations to solve
real world applications
Algebra 2 Coll: 6.9
Middletown Public Schools
1.1.a.2 Analyze essential relations in a
problem to determine possible
functions that could model the
situation.
3.1.a.2 Analyze essential relations in a
problem to determine possible
functions that could model the
situation.
August 2010
11
How do radical functions model real-world problems and their solutions?
Students should be
able to…
Algebra 2 Coll: 7.5
Instructional Strategies and
Activities
1.2.a.2 Relate the graphical representation of
a function to its function family and
find equations, intercepts, maximum
or minimum values, asymptotes and
line of symmetry for that function.
Simplify radical expressions 2.1.a.4 Judge the effects of computations
with powers and roots on the
Algebra 2 Coll: 7.1, 7.2, 7.3
magnitude of results
Algebra 2 Coll: 7.4, 7.6
solve real world applications
Algebra 2 Coll:
Middletown Public Schools
SAT Correlation or
Real World
Applications
Astronomy,
Engineering,
Meteorology,
Genetics,
2.1.a.4 Judge the effects of computations
with powers and roots on the
magnitude of results
1.1.a.2 Analyze essential relations in a
problem to determine possible
functions that could model the
situation.
3.1.a.2 Test the validity of logical arguments.
August 2010
12
Probability &amp; Data Analysis (2 Weeks) – Optional, if time allows.
How can probability be used to make wise decisions in life?
Students should be
able to…
Define probability
Algebra 2 Coll: 12.1, 12.3
Apply combinations and
permutations
Algebra 2 Coll: 12.1, 12.2
Apply the fundamental
counting principles
Algebra 2 Coll: 12.1
Apply Conditional
probability
Algebra 2 Coll: 12.5
Be able to find the
probability of unions and
intersections
Algebra 2 Coll: 12.4
Apply Probability to solve
real-world problems.
Algebra 2 Coll:
Middletown Public Schools
Instructional Strategies and
Activities
SAT Correlation or
Real World
Applications
4.2.a.1 Determine statistical measures to
describe univariate data.
4.2.a.1 Determine statistical measures to
describe univariate data.
4.3.a.1 Understand and use permutations,
combinations, recursion and
mathematical induction to solve
problems.
Predictions,
Expected Value,
Decision Making,
Gambling
4.2.a.1 Determine statistical measures to
describe univariate data.
4.2.a.1 Determine statistical measures to
describe univariate data.
4.2.a.1 Determine statistical measures to
describe univariate data.
4.2.a.1 Determine statistical measures to
describe univariate data.
August 2010
13
Middletown Public Schools
August 2010
14
```