ALGEBRA 1: NJDOE MODEL CURRICULUM
Course:
Algebra I
CONTENT AREA: Mathematics
STUDENT
LEARNING
OBJECTIVES
#
1
CCSS/
NJCCCS
Solve systems of linear
equations in two
variables graphically
and algebraically.
Include solutions that
have been found by
UNIT #: 2
UNIT NAME: Linear Relationships
Instructional Strategies, Resources, Projects,
integration of technology
1. Good tutorial on the multiple ways of solving systems:
http://www.regentsprep.org/Regents/math/ALGEBRA/AE3/indexAE3.htm
A.REI.5
A.REI.6
2. Potential lesson plan on understanding the possible number of solutions to a system:
http://www.learner.org/workshops/algebra/workshop3/lessonplan1.html
replacing one equation
by the sum of that
equation and a multiple
of the other.
2
3
Find approximate
solutions of linear
equations by making a
table of values, using
technology to graph
and successive
approximations.
Graph equations,
inequalities, and
systems of inequalities
Page 1 of 6
1. Online tutorial on how to solve a linear system using the TI:
http://www.tncurriculumcenter.org/learning_expectation/2751
A.REI.11
2. Have students plug values in by hand and then use calculator/excel to show the increased
precision.
A.REI.10
1. Understanding systems of Linear Inequalities:
http://www.purplemath.com/modules/syslneq.htm
A.REI.11
Curriculum: Algebra 1-Unit 2: LINEAR RELATIONSHIPS
KK, EE July 2013
ALGEBRA 1: NJDOE MODEL CURRICULUM
CONTENT AREA: Mathematics
4
in two variables and
explain that the
A.REI.12
solution to an
equation is all points
along the curve, the
solution to a system of
linear functions is the
point of intersection,
and the solution to a
system of inequalities
is the intersection of
the corresponding
half-planes. ★
Explain and interpret
the definition of
functions including
domain and range and
how they are related;
F.IF.1
correctly use function
F.IF.2
notation in a context
and evaluate functions
for inputs and their
corresponding
outputs.
Page 2 of 6
Course:
Algebra I
UNIT #: 2
UNIT NAME: Linear Relationships
2. Be sure to bridge gap between old method of solving for something like x > 3 on a number
line to the new way of representing on the Cartesian plane. (relate the shaded regions)
3. Compare and contrast the three options for answers of solving systems of equations and
what they look like to the possible options of solutions when solving systems of inequalities.
1. Understanding domain and range in relation to function notation
http://www.coolmath.com/algebra/15-functions/05-domain-range-01.htm
2. Pinterest ideas for all things function/function notation related:
http://pinterest.com/andi_cath/algebra-functions/
Curriculum: Algebra 1-Unit 2: LINEAR RELATIONSHIPS
KK, EE July 2013
ALGEBRA 1: NJDOE MODEL CURRICULUM
Course:
Algebra I
CONTENT AREA: Mathematics
5
Write a function for a
geometric sequence
defined recursively,
whose domain is a
subset of the integers.
UNIT #: 2
UNIT NAME: Linear Relationships
1. Understanding arithmetic vs. Geometric sequences:
http://www.purplemath.com/modules/series3.htm
F.IF.3
2. Geometric sequences:
http://www.regentsprep.org/Regents/math/algtrig/ATP2/GeoSeq.htm
3. Geometric sequences example problems:
http://www.kutasoftware.com/FreeWorksheets/Alg2Worksheets/Geometric%20Sequences.pdf
7
8
Graph functions by
hand (in simple cases)
and with technology
(in complex cases) to
describe linear
relationships between
two quantities and
identify, describe, and
compare domain and
other key features in
one or multiple
representations. ★
Compare properties of
two functions each
represented in a
different way
Page 3 of 6
F.IF.5
F.IF.7
1. Give grouped students a word problem that can be described using a linear equation. Have
students graph this linear equation and identify the important components in context (domain,
range, slope, y-intercept). Then have students compare their graph with others encouraging
discussion about why their graphs differ from other groups and what within their word
problems indicated such a difference.
F.IF.9,
A.REI.11
F.IF.9
1. Who shares my function? (Give students different representations of one function and have them
find the other people in the class that share their same function)
https://wikis.uit.tufts.edu/confluence/pages/viewpage.action?pageId=32413608
Curriculum: Algebra 1-Unit 2: LINEAR RELATIONSHIPS
KK, EE July 2013
ALGEBRA 1: NJDOE MODEL CURRICULUM
CONTENT AREA: Mathematics
(algebraically,
graphically, numerically
in tables, or by verbal
descriptions).
Course:
Algebra I
UNIT #: 2
UNIT NAME: Linear Relationships
2. Multiple representations video: http://projectsharetexas.org/resource/connecting-multiplerepresentations-linear-functions
3. Good opportunity for a jigsaw activity creating groups for each representation
Major Supporting Additional (identified by PARCC Model Content Frameworks)
Bold Type indicates grade level fluency requirements. (Identified by PARCC Model Content Frameworks).
Selected Opportunities for Connections to Mathematical Practices
1. Make sense of problems and persevere in solving them. *
2. Reason abstractly and quantitatively.
SLO 4 Determine the relationship between domain and range of a function and explain the connection to the inputs and outputs.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics. *
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
SLO 5 Describing the regularity in the way terms cancel can lead to a general formula for a geometric sequence.
*MP.1 and MP.4 are overarching practices relevant to Algebra 1. (PARCC Model Content Frameworks)
All of the content presented in this course has connections to the standards for mathematical practices.
Bold type identifies possible starting points for connections to the SLOs in this unit.
Page 4 of 6
Curriculum: Algebra 1-Unit 2: LINEAR RELATIONSHIPS
KK, EE July 2013
ALGEBRA 1: NJDOE MODEL CURRICULUM
CONTENT AREA: Mathematics
Code #
A.REI.5
A.REI.6
A.REI.10
A.REI.11
A.REI.12
F.IF.1
F.IF.2
F.IF.3
F.IF.5
Page 5 of 6
Course:
Algebra I
UNIT #: 2
UNIT NAME: Linear Relationships
Common Core State Standards
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.
Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two
variables.
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.
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.
Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For
example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1.
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.★
Curriculum: Algebra 1-Unit 2: LINEAR RELATIONSHIPS
KK, EE July 2013
ALGEBRA 1: NJDOE MODEL CURRICULUM
CONTENT AREA: Mathematics
Course:
Algebra I
UNIT #: 2
UNIT NAME: Linear Relationships
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 functions.
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or
F.IF.9
by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say
which has the larger maximum.
Major Supporting Additional (identified by PARCC Model Content Frameworks)
Bold Type indicates grade level fluency requirements. (Identified by PARCC Model Content Frameworks).
F.IF.7
Page 6 of 6
Curriculum: Algebra 1-Unit 2: LINEAR RELATIONSHIPS
KK, EE July 2013