Download algebra curriculum

Course Title:
Algebra
Levels:
2, 3, 4
Grade:
9
Length of Course:
One Year
Credits:
5.0
Prerequisites:
Description:
Prealgebra, Discovering Algebra or Grade 8 Math
Over a three-year sequence, students build a foundation and develop the concepts and skills of Algebra. This
ninth grade curriculum continues to emphasize an intuitive approach as it transitions to abstraction, and completes
the development of Algebra I. As it did in the preceding grades, mathematical development is focused on big
ideas, such as equivalence, operational reasoning, and linearity. Grade 9 Algebra adds to the big ideas with a
focus on rate of change. Algebraic activities include representational and transformational tasks, as well as
generalizing and justifying activities. Throughout the course, concepts and skills are initially presented through real
and familiar situations, followed by activities that enable students to determine, develop and articulate structural
distinctions.
This course is designed to provide students with an appropriate balance between the development of key concepts
and the mastery of skills. Technology is integrated, wherever appropriate, in the form of graphing calculators and
computer programs.
Evaluation:
Student performance will be measured using a variety of assessments, such as class work, writing tasks, homework,
teacher-generated tests and quizzes, and a common departmental Quarterly Assessments, Midterm and Final Exam.
Assessments will emphasize how well key concepts have been understood as well as the extent to which required skills
have been mastered.
Text: Algebra (Mc Dougal) 2011
Adoption Date: July 2012
Page 1
COLUMBIA HIGH SCHOOL
ALGEBRA CURRICULUM
Learning Objectives
The student will …
Content Outline
1. Approach solving
equations as a process
of reasoning and
explaining the
reasoning.
1. Represent real world situations with linear
equations.
Solve single-variable
linear equations with
rational coefficients.
Construct viable
arguments to justify
solution methods.
4. Compare and contrast solution methods; make
decisions as to which is preferable for given types
of problems.
Recognize, express
and solve problems
that can be modeled
using single-variable
linear equation
2. Explain solutions in the context of the problem.
3. Solve simple linear equations.
5. Know that the solution(s) is the value(s) that
make the equation true.
6. Solve equations using combining like terms and
the distributive property.
7. Solve equations with rational coefficients.
8. Solve equations with variables on both sides,
including those with no and infinite solutions.
NJCCSS:
N-Q-1,2,3; A-SSE-1,2
A-CED-1,2,3; A-REI-1,3
Adoption Date: July 2012
Instructional
Materials
Printed Materials:
Larson Algebra
Ch 3.1-3.4
Technology: TI83+
Supplies: graph
paper
Notes
NJCCSS Practice
Standards are
identified in the
Appendix A. They
identify essential
processes and
practices that need to
be enacted in the
development of this
and all subsequent
learning (content)
objective identified in
this curriculum.
See pacing chart
(Appendix B) to
determine the
approximate time
required this and all
subsequent
objectives.
Page 2
COLUMBIA HIGH SCHOOL
ALGEBRA CURRICULUM
Learning Objectives
The student will …
Content Outline
2. Recognize and solve 1. Represent, apply and explain methods for solve
real world problems
problems involving rates and ratios, proportions
involving proportional
and percents.
reasoning and rational
2. Apply proportions to similar figures
numbers, including
percent problems.
NJCCSS: N-Q 1
3. Reason
quantitatively and use
units to solve
problems.
Solve equations
involving several
variables for one
variable in terms of the
others.
NJCCSS:
N-Q-1,2,3
A-CED-4
1. Transform equations
a. define appropriate quantities for the purpose of
descriptive modeling
2. Work with formulas
a. Use units as a way to understand problems and
to guide the solution of multi-step problems
b. choose and interpret units consistently in a
formula
c. Choose a level of accuracy appropriate to the
limitations on measurement when reporting
quantities.
Adoption Date: July 2012
Instructional
Materials
Notes
Printed Materials:
Larson Algebra
Ch3.5, 3.6, 3.6
extention, 3.7
Technology: TI83+
Supplies: graph
paper
Printed Materials:
Larson Algebra Ch
3.8
Technology:TI-83+
Supplies: graph
paper
Page 3
COLUMBIA HIGH SCHOOL
ALGEBRA CURRICULUM
Learning Objectives
The student will …
4. (A) Model and
explain the concept of
a function using
situations, graphs,
tables, and functional
notation.
(B) Interpret functions
that arise in
applications in terms of
the context.
(C) Analyze functions
using different
representations.
Graph linear functions
given an equation or
table and interpret the
graph in the context of
the problem.
Recognize slope as
rate of change and use
the slope and
intercepts to answer
questions about a
problem with or without
context.
NJCCSS: F-IF-1 to 6,9
A-REI-10
Content Outline
A. 1. Demonstrate understanding/apply and explain the concept of a
function (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.)
2. Use function notation to…
a. evaluate functions for inputs in their domains
b. interpret statements that use function notation in terms of a context
c. Recognize that sequences are functions, sometimes defined
recursively, whose domain is a subset of the integers.
B 1. Interpret, connect and analyze different representations for
functions.
a. Graph linear functions using a table.
b. Write and graph functions for horizontal and vertical lines.
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 it describes. Key features include:a. intercepts; b.
intervals where the function is increasing/decreasing, positive/
negative; c. slope
2. Relate the domain of a function to its graph and, where possible,
to the quantitative relationship it describes.
Represent situations using standard form or slope-intercept form of
an equation. Find pairs of values for the linear relationship 4.
Interpret x and y intercept in the context of the problem. Use these
values to graph equations in standard form.
1. Find and interpret constant rate of change (slope) with or without
context.
2. Graph equations w/ the slope and y-intercept.
3. 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).
Adoption Date: July 2012
Instructional
Materials
Notes
Printed
Materials:
2c example
Larson Algebra The Fibonacci
Ch 4.1-4.5
sequence is
defined
Technology:
recursively by
TI-83+
f(0)=f(1)=1,
Supplies:
f(n+1) = f(n) + f(ngraph paper
1) for n> 1.
Page 4
COLUMBIA HIGH SCHOOL
ALGEBRA CURRICULUM
Learning Objectives
The student will …
Content Outline
5. Recognize, describe A. Write linear equations in slope-intercept form,
and represent linear
point-slope form (level 4 only) and standard
relationships using
form, and use these equations to solve
words, tables, numerical
problems.
patterns, graphs, and
equations. Translate
B. Write equations for parallel and perpendicular
among these
lines, interpret in context.
representations.
Describe, analyze and
use key characteristics
of linear functions and
their graphs
Interpret and compare
linear models for data
that exhibit a linear
trend including
contextual problems.
NJCCSS : S-ID-6, 8
G-GEPE-5
Instructional
Materials
Notes
Printed Materials:
Larson Algebra
Ch. 5.1-5.7
Technology: TI-83+
Supplies: graph
paper
C. Prove the slope criteria for parallel and
perpendicular lines and use them to solve
geometric problems (e.g., find the equation of
a line parallel or perpendicular to a given line
that passes through a given point)
D. Scatterplots
1. Plot bivariate data with a scatterplot and
describe the nature of any possible linear trends:
positive or negative, weak or strong.
2. Approximate a trend line by drawing on the
scatterplot through the cloud of points. Give the
equation for this line.
3. Use these trend lines to predict values.
4. Compute (using technology) and interpret the
correlation coefficient of a linear fit.
Adoption Date: July 2012
Page 5
COLUMBIA HIGH SCHOOL
ALGEBRA CURRICULUM
Learning Objectives
The student will …
6. Solve inequalities
and graph solutions on
a number line.
Model real world
situations with
inequalities and
explain solutions in the
context of the problem.
NJCCSS A-CED-1,
3 A-REI-3
7. Solve equations
involving the absolute
value of a linear
expression.
NJCCSS
Content Outline
1. Represent real world situations with linear
inequalities
2. Explain solutions in the context of the problem.
3. Solve simple linear inequalities
6. Solve inequalities using combining like terms
and distributive law.
7. Solve inequalities with rational coefficients.
8. Solve inequalities with variables on both sides,
including those with no and infinite solutions.
Solve compound inequalities (Level 4 only:
Algebra II leaders would like us to do this)
1. Solve equations with absolute value
expressions.
Instructional
Materials
Notes
Printed Materials:
Larson Algebra
Ch 6.1-6.4
Technology: TI-83+
Supplies: graph
paper
Printed Materials:
Larson Algebra Ch 6.5
Technology: TI-83+
Supplies: graph paper
A-REI-1;
F-IF-1
Adoption Date: July 2012
Page 6
COLUMBIA HIGH SCHOOL
ALGEBRA CURRICULUM
Learning Objectives
The student will …
8. Graph and analyze
the graph of the
solution set of a twovariable linear
inequality.
NJCCSS F-IF-1,5
9. Solve systems of
linear equations in two
variables using
algebraic and graphic
procedures.
Recognize, express
and solve problems
that can be modeled
using one or twovariable inequalities; or
two variable systems
of linear equations.
Interpret their solutions
in terms of the context
of the problem.
Content Outline
1. Explain how any point in the shaded region satisfies
the equation.
2. Model a real world situation with a two-variable linear
inequality and explain the solution set in the context of
the problem.
3. Graph a linear equality with correct shading and
dotted/dashed lines.
1. Explain that the solution to a system of linear
equations is the ordered pair that satisfies both
equations.
2. Use tables to confirm the solution to a system.
3. Solve systems graphically by finding the point of
intersection, both with technology and by hand.
Instructional
Materials
Notes
Printed Materials:
Larson Algebra
Ch6.7
Technology: TI83+
Supplies: graph
paper
Printed Materials:
Larson Algebra Ch 7
Technology: TI-83+
Supplies: graph
paper
4. Confirm that a solution satisfies both equations
algebraically.
5. Solve systems using algebraic techniques.
6. Decide which method is best to solve a given system.
7. Given an algebraic representation, represent the
solution set to a system of linear inequalities graphically.
8. Model real world situations using systems of linear
equations and inequalities.
NJCCSS A-REI-6
Adoption Date: July 2012
Page 7
COLUMBIA HIGH SCHOOL
ALGEBRA CURRICULUM
Learning Objectives
The student will …
Content Outline
Instructional
Materials
Notes
10. Summarize,
1. Represent data with plots on the real number
represent, and interpret
line (dot plots, histograms, and box plots).
data on a single count or
2. Use statistics appropriate to the shape of the
measurement variable(1-4),
data distribution to compare center (median,
or on 2categorical and
mean) and spread (interquartile range,
quantitative variables(5-6).
standard deviation) of two or more different
data sets.
Interpret linear models(7-9)
3. Interpret differences in shape, center, and
spread in the context of the data sets,
CCSS S-ID-1-5, 7, 9
accounting for possible effects of extreme
data points (outliers).
4. Use the mean and standard deviation of a
data set to fit it to a normal distribution and to
estimate population percentages. Recognize
that there are data sets for which such a
procedure is not appropriate. Use calculators,
spreadsheets, and tables to estimate areas
under the normal curve.
5. Summarize categorical data for two categories
in two-way frequency tables. Interpret relative
frequencies in the context of the data
(including joint, marginal, and conditional
relative frequencies). Recognize possible
associations and trends in the data.
9. Distinguish between correlation and causation.
Adoption Date: July 2012
Page 8
COLUMBIA HIGH SCHOOL
ALGEBRA CURRICULUM
Learning Objectives
The student will …
11. Determine and
evaluate random
processes underlying
statistical
experiments(1-2).
Content Outline
1. Understand statistics as a process for making
inferences about population parameters based on
a random sample from that population.
Instructional
Materials
Preliminary/review:
Technology: TI-83+
Supplies: graph paper
Supplementary
materials
2. Decide if a specified model is consistent with
results from a given data-generating process, e.g.,
Make inferences and
District constructed
using simulation.
justify conclusions from
tasks
sample surveys,
3. Recognize the purposes of and differences
experiments and
among sample surveys, experiments, and
observational
observational studies; explain how randomization
studies(3-6).
relates to each.
NJCCSS S-IC-1-6
4. Use data from a sample survey to estimate a
population mean or proportion; develop a margin of
error through the use of simulation models for
random sampling.
5. Use data from a randomized experiment to
compare two treatments; use simulations to decide
if differences between parameters are significant.
6. Evaluate reports based on data.
Adoption Date: July 2012
Notes
Use measures of
center and spread to
compare and analyze
data sets.
1. Find the mean,
median, and mode of
a data set.
2. Decide and justify
which measure best
represents the data.
3. Determine how
measures of center
and spread are
effected by adding
a number to a data
set (in context)
4. Construct data sets
with given
measures of center
and spread
Page 9
COLUMBIA HIGH SCHOOL
ALGEBRA CURRICULUM
Learning
Objectives
The student will …
Content Outline
1. Find the probability of a single event or compound event occurring
12. Apply
with or without replacement.
probability
1. Describe events as subsets of a sample space (the set of
concepts to
outcomes) using characteristics (or categories) of the outcomes, or
determine the
likelihood an event as unions, intersections, or complements of other events (“or,”
“and,” “not”).
will occur in
2. Understand that two events A and B are independent if the
practical
probability of A and B occurring together is the product of their
situations.
probabilities, and use this characterization to determine if they are
NJCCSS S-CP-1-7 independent.
3. Understand the conditional probability of A given B as P(A and
B)/P(B), and interpret independence of A and B as saying that the
conditional probability of A given B is the same as the probability of
A, and the conditional probability of B given A is the same as the
probability of B.
4. Construct and interpret two-way frequency tables of data when
two categories are associated with each object being classified.
Use the two-way table as a sample space to decide if events are
independent and to approximate conditional probabilities.
5. Recognize and explain the concepts of conditional probability
and independence in everyday language and everyday situations.
6. Find the conditional probability of A given B as the fraction of B’s
outcomes that also belong to A, and interpret the answer in terms
of the model.
7. Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B),
and interpret the answer in terms of the model.
Adoption Date: July 2012
Instructional
Materials
Notes
Printed Materials:
Larson Algebra
Ch 13
Technology: TI83+
Supplies: graph
paper
Page 10
COLUMBIA HIGH SCHOOL
ALGEBRA CURRICULUM
Learning Objectives
The student will …
13. Use counting
principles to determine
the number of ways an
event can occur.
Interpret and justify
solutions.
Content Outline
1. Find the number of possible outcomes for
single or compound events.
2. Distinguish between a combination and
permutation and use these to solve problems
3. Use permutations and combinations to compute
probabilities of compound events and solve
problems.
1. Use product and quotient properties to rewrite
14. Apply the laws of
exponential expressions
exponents to numerical
2. Rewrite expressions so that all exponents are
and algebraic
positive (Equivalent forms)
expressions with
3. Solve problems using exponents
integral exponents to
4. Convert between standard form and scientific
rewrite them in
different but equivalent notation
forms or to solve
problems. NJCCSS NRN-2
Instructional
Materials
Notes
Printed Materials:
Larson Algebra Ch 13
Technology: TI-83+
Supplies: graph paper
NJCCSS S-CP-9
Adoption Date: July 2012
Printed Materials:
Larson Algebra
Ch 8 8.5-8.6
Technology: TI-83+
Supplies: graph paper
Page 11
COLUMBIA HIGH SCHOOL
ALGEBRA CURRICULUM
Learning Objectives
The student will …
15. Model and solve
problems involving
exponential growth and
decay.
NJCCSS A-SSE-1,2,3
Content Outline
1. Model exponential function form y = abx
2. Analyze y-intercept and constant multiple to
write a function rule
3. Graph exponential functions as continuous
and positive
4. Model and/or solve real world problems
16. Add, subtract and
1. Classify, add, subtract, & multiply polynomials
multiply polynomial
2. Use polynomials to represent real world
expressions with or without a
situations; solve problems using polynomials
context.
3 Understand that polynomials form a system analogous to
NJCCSS A-APR-1,2
17. Factor simple
polynomial expressions with
or without context.
Solve factored polynomial
equations with or without
context.
NJCCSS A-APR-3
Adoption Date: July 2012
the integers, namely, they are closed under the
operations of addition, subtraction, and multiplication.
1. Identify and factor out the GCF.
2. Factor trinomials. Use products of binomials to
represent area.
3. Identify and factor the difference of squares.
4. Use the zero-product property to solve
quadratic equations.
Instructional
Materials
Notes
Printed Materials:
Larson Algebra
Ch 8 8.5-8.6
Technology: TI-83+
Supplies: graph paper
Printed Materials:
Larson Algebra
Ch 9 9.1-9.2
Technology: TI-83+
Printed Materials:
Larson Algebra Ch 9
Technology: TI-83+
Supplies: graph paper
Page 12
COLUMBIA HIGH SCHOOL
ALGEBRA CURRICULUM
Learning Objectives
The student will …
18. Recognize, describe,
represent and analyze a
quadratic function using
words, tables, graphs and
equations.
Analyze a table, numerical
pattern, graph, equation or
context to determine whether
a linear or quadratic
relationship could be
represented.
Recognize and solve
problems that can be
modeled using a quadratic
function. Interpret the solution
in terms of the context of the
original problem.
NJCCSS A-SSE-3,A-REI-4,7
19. Solve quadratic
equations.
NJCCSS A-SSE-3, A-REI-4,7
Adoption Date: July 2012
Content Outline
1. Find the value of the vertex from a table (noting the
symmetry).
2. Determine positive or negative value of a based on
the graph. Determine the value of c from the graph.
3. Compare and contrast different graphs of quadratic
functions, noting differences in width and how this
will relate to their relative equations.
4. Identify equations whose graphs will be symmetric
to the y-axis (b=0).
5. Model real world situations with a quadratic
equation, including vertical motion and area.
6. Find the vertex from the equation of a parabola.
7. Use the quadratic model of a given context to
answer contextual questions.
8. Distinguish between functions with a maximum and
minimum value, and this may relate to a given
context.
1. Solve using inverse operations when b=0.
2. Solve using the quadratic formula for all
quadratic equations.
3. Solve a binomial square by taking the square
root of both sides. (level 4 only)
4. Solve graphically, by hand (approximation) and
with technology.
5. Interpret solution in the context of the problem.
Instructional
Materials
Notes
Printed
Materials:
Larson Algebra
Ch 10 10.1-10.3
Technology: TI83+
Supplies: graph
paper
Printed Materials:
Larson Algebra
Ch 10 10.4-10.6
Technology: TI83+
Supplies: graph
paper
Page 13
COLUMBIA HIGH SCHOOL
ALGEBRA CURRICULUM
Learning Objectives
The student will …
20. Analyze a table, numerical
pattern, graph, equation or
context to determine whether a
linear, quadratic or exponential
relationship could be
represented. Or, given the type
of relationship, determine the
elements of the table, numerical
pattern or graph.
Content Outline
1. Use the shape of the graph to distinguish
between functions.
Printed Materials:
2. Analyze the change in the y-values to
distinguish between functions.
Ch 10 10.8
3. Complete a table given the type of
function.
Technology: TI-83+
4. Find other points given the type of
function.
NJCCSS A-REI-11 F-IF-4-7,9
5. Solve real world problems.
21. Use the properties of
radicals to rewrite numerical and
algebraic expressions containing
square roots in different but
equivalent forms or to solve
problems. NJCCSS N-RN-1,2;
1.
2.
3.
4.
A-APR-6; A-REI-2
Adoption Date: July 2012
Instructional
Materials
Write square root radicals in simplest form
Find products and quotients of radicals
Rationalize the denominator
Add, subtract and multiply radical
expressions
5. Solve real world problems
Notes
Larson Algebra
Supplies: graph paper
Printed Materials:
Larson Algebra Ch
11.2
Technology: TI-83+
Supplies: graph paper
Page 14