Mathematics Curriculum Guide
High School Algebra 1
2016-17
Page 1 of 8
High School Algebra 1 – Topic 5
Stage One – Desired Results
Paramount Unified School District
Educational Services
Topic 5: Linear Systems (Part 1)
Transfer Goals
1) Demonstrate perseverance by making sense of a never-before-seen problem, developing a plan, and evaluating a strategy and solution.
2) Effectively communicate orally, in writing, and using models (e.g., concrete, representational, abstract) for a given purpose and audience.
3) Construct viable arguments and critique the reasoning of others using precise mathematical language.
Standards
A-REI 11. 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.
★
A-REI 5. 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.
A-REI 6. Solve systems of linear equations
exactly and approximately (e.g., with
graphs), focusing on pairs of linear
equations in two variables.
Timeframe: 3 weeks/14 days
Start Date: November 10, 2016
Assessment Dates: December 6-7, 2016
Meaning-Making
Understandings
Students will understand that…
Essential Questions
Students will keep considering…
 Systems of linear equations can be used to model problems.
 Systems of equations can be solved by graphing, substitution, or
eliminating a variable.
 When a system has at least one equation that can be solved quickly
for a variable, the system can be solved efficiently using
substitution.
 Systems written in standard form may be solved using elimination.
 Some problems can be modeled by systems of linear equations.
 What is a system of linear equations?
 How can systems of linear equations model realworld situations?
Acquisition
Knowledge
Students will know…
Vocabulary: system of linear equations, solution of a
system of linear equations, consistent, dependent,
independent, inconsistent, substitution method,
elimination method
Procedures for solving:
 Systems of equations by graphing.
 Systems of equations by substitution.
 Systems of equations by elimination.
Skills
Students will be skilled at and able to do the following…
 Construct a viable argument to justify a solution method.
 Explain each step in solving a system of linear equations
(verbally and in writing).
 Construct an argument that explains the types of conditions
that may identify the most appropriate method to use in
solving a system of linear equations.
 Solve systems of equations by graphing, substitution, and
elimination.
 Model real-life situations using systems of linear equations.
Page 2 of 8
Paramount Unified School District
Educational Services
High School Algebra 1 – Topic 5
Stage Two – Evidence of Learning
Topic 5: Linear Systems (Part 1)
Transfer is a student’s ability to independently apply understanding in a novel or unfamiliar situation. In mathematics, this requires that students use reasoning
and strategy, not merely plug in numbers in a familiar-looking exercise, via a memorized algorithm.
Transfer goals highlight the effective uses of understanding, knowledge, and skills we seek in the long run – that is, what we want students to be able to do
when they confront new challenges, both in and outside school, beyond the current lessons and unit. These goals were developed so all students can apply their
learning to mathematical or real-world problems while simultaneously engaging in the Standards for Mathematical Practices. In the mathematics classroom,
assessment opportunities should reflect student progress towards meeting the transfer goals.
With this in mind, the revised PUSD transfer goals are:
1) Demonstrate perseverance by making sense of a never-before-seen problem, developing a plan, and evaluating a strategy and solution.
2) Effectively communicate orally, in writing, and by using models (e.g., concrete, representational, abstract) for a given purpose and audience.
3) Construct viable arguments and critique the reasoning of others using precise mathematical language.
Multiple measures will be used to evaluate student acquisition, meaning-making and transfer. Formative and summative assessments play an important role in
determining the extent to which students achieve the desired results in stage one.
Formative Assessment
Summative Assessment
Aligning Assessment to Stage One
 What constitutes evidence of understanding for this lesson?
 What evidence must be collected and assessed, given the desired results
defined in stage one?
 Through what other evidence during the lesson (e.g. response to questions,
observations, journals, etc.) will students demonstrate achievement of the
 What is evidence of understanding (as opposed to recall)?
desired results?
 Through what task(s) will students demonstrate the desired understandings?
 How will students reflect upon, self-assess, and set goals for their future
learning?





Discussions and student presentations
Checking for understanding (using response boards)
Ticket out the door, Cornell note summary, and error analysis
Performance Tasks within a Unit
Teacher-created assessments/quizzes
Opportunities
 Unit assessments
 Teacher-created quizzes and/or mid-unit assessments
 Illustrative Mathematics tasks (https://www.illustrativemathematics.org/)
 Performance tasks
Page 3 of 8
Paramount Unified School District
Educational Services
High School Algebra 1 – Topic 5
Stage Two – Evidence of Learning
Topic 5: Linear Systems (Part 1)
The following pages address how a given skill may be assessed. Assessment guidelines, examples and possible question types have been provided to assist
teachers in developing formative and summative assessments that reflect the rigor of the standards. These exact examples cannot be used for instruction or
assessment, but can be modified by teachers.
Unit Skills
 Construct a viable
argument to justify a
solution method.
 Explain each step in
solving a system of
linear equations
(verbally and in writing).
 Construct an argument
that explains the types
of conditions that may
identify the most
appropriate method to
use in solving a system
of linear equations.
 Solve systems of
equations by graphing,
substitution, and
elimination.
 Model real-life
situations using systems
of linear equations.
SBAC Targets (DOK)
Create equations
that describe
numbers or
relationships. (1,2)
Solve equations
and inequalities in
one and two
variables. (1,2)
Interpret results in
the context of a
situation. (2)
Identify important
quantities in a
practical situation
and map their
relationships (e.g.,
using diagrams,
graphs, etc.)
(1,2,3)
Standards
Examples
A-REI 11. 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. ★
A-REI 5. 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.
A-REI 6. Solve systems of
linear equations exactly and
approximately (e.g., with
graphs), focusing on pairs of
linear equations in two
variables.
Page 4 of 8
High School Algebra 1 – Topic 5
Stage Three –Learning Experiences & Instruction
Paramount Unified School District
Educational Services
Topic 5: Linear Systems (Part 1)
Transfer Goals
1)
2)
3)
Demonstrate perseverance by making sense of a never-before-seen problem, developing a plan, and evaluating a strategy and solution.
Effectively communicate orally, in writing, and using models (e.g., concrete, representational, abstract) for a given purpose and audience.
Construct viable arguments and critique the reasoning of others using precise mathematical language.
Essential Questions:


Standards: A-REI 11, A-REI 5, A-REI 6
What is a system of linear equations?
How can systems of linear equations model real-world situations?
Time
2 days
(Nov.
10 & 14)
Lesson/
Activity
Lesson 6-0:
Solve Systems
by Tables
SMP 5
A-REI 11
2 days
(Nov.
15-16)
Lesson 6-1:
Solve Systems
by Graphing
SMP 1, 2, 4
(pp. 364-369)
A-REI 6
Focus Questions for
Lessons
Understandings
Timeframe: 3 weeks/14 days
Start Date: November 10, 2016
Assessment Dates: December 6-7, 2016
Knowledge
 What is a system of
linear equations?
 What does a system of
equations represent?
 How can you use tables
to solve a system of
equations?
 When is it useful to use
tables?
 A system of linear
equations shows the
relationship between
two or more variables.
 A system consists of
two or more
equations.
 A system of linear
equations can be
solved using tables.
 A point on both tables
represents a solution.
 Know the limits of
solving systems by
tables.
Vocabulary: system of equations, tables,
estimation, solution, ordered pair
Focus Question(s):
 How does graphing
each equation help you
find the solution?
 When is graphing an
efficient method for
solving a system of
equations?
 Is it possible for two
lines to have more than
one point in common?
Explain.
Inquiry Question(s):
 P. 364 Solve it!
 A system of linear
equations and
inequalities can be
solved graphically to
find a point of
intersection.
 Systems of linear
equations can be used
to model problems.
 Systems of equations
can be solved in more
than one way.
Vocabulary: system of linear equations,
solution of a system of linear equations,
consistent, independent, dependent,
inconsistent.
Students will know…
 How to use the table of values to
determine the solution to a system of
linear equations.
 That an ordered pair that appears on
both tables of a system of linear
equations is the solution of that system.
 That using a table of values is a strategic
mathematical tool to approximating a
solution to a system of linear equations.
Students will know…
 How to graph linear equations (Prerequisite knowledge).
 That intersecting lines has one solution.
 That coinciding lines has infinitely many
solutions.
 That parallel lines has no solution.
Skills
Resources
 Use a table to represent
a relationship between
the domain and range
of a linear equation.
 Be able to use tables to
model a system.
 Be able to describe
when you can use a
table, and when you
cannot use a table to
solve a system.
 Choose increments
strategically and be able
to approximate
solutions.
LearnZillion Lesson code:
7689 (see problem at
the end of this
document)
 Solve systems of
equations by graphing
 Analyze special systems
 Construct a viable
argument to justify a
solution method.*
 Explain each step in
solving a system of
linear equations by
graphing (verbally and
in writing).*
Common Core Problems:
#6,7,8,9,31,32,33,40,41,42
6-1 Practice Form G
Emphasize ‘Reasoning’
Problems 10, 11, 15
6-1 Standardized Test Prep
p. 173 Problems 2,3,4
LearnZillion Lesson code:
6743
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Time
2 days
(Nov.
17-18)
Lesson/
Activity
Focus Questions
for Lessons
Lesson 6-2:
Solving
Systems Using
Substitution
SMP 1, 2, 3, 4
(pp. 372-377)
Focus Question(s):
 What is a good situation
for using the
substitution method?
Inquiry Question(s):
 p. 372 Solve it!
A-REI 6
Understandings
 When a system has
at least one
equation that can be
solved quickly for a
variable, the system
can be solved
efficiently using
substitution.
Knowledge
Vocabulary: substitution method
Students will know…
 That substitution depends on
substituting an equal value into an
equation.
 The difference between systems
with infinitely many solutions and no
solution when using the substitution
method.
Skills
 Explain each step in
solving a system of
linear equations
(verbally and in
writing).
 Recognize when a
solution of a system
has infinitely many
solutions or no
solution algebraically.
Additional
Resources
Common Core Problems:
#6,33,35,37,38,40,41
6-2 Practice Form G
Problems #1-9, 22-33
Emphasize ‘Writing’ &
‘Reasoning’ Probs. 13, 14
6-1 Standardized Test Prep
p. 173 Problems #2,3,4
LearnZillion Lesson code:
7834
3 days
(Nov.
28-30)
Lesson 6-3:
Solving
Systems Using
Elimination
SMP 1, 2, 3, 4,
6
(pp. 378-384)
A-REI 5
Focus Question(s):
 What kind of
coefficients of x or y
are needed to solve a
system using
elimination?
 What criteria is
necessary before you
can solve a linear
system using
elimination?
 Create a system that
can be solved using
the elimination
method. Solve the
system.
 There is more than
one way to solve a
system of equations.
 Systems that are
written in standard
form make it easier
to eliminate a
variable.
Inquiry Question(s):
 p. 378 Solve it!
Vocabulary: elimination method,
standard form
Students will know…
 How to write a linear equation in
standard form (Pre-requisite
knowledge).
 That the least common multiple is
used to determine by what number
each equation needs to be
multiplied.
 That adding like terms is used when
the linear equations are combined
using addition or subtraction.
 That one-step equations are solved
after one of the variables has been
eliminated.
 That substitution is used after the
first variable has been solved for to
find the value of the second variable.
 Explain each step in
solving a system of
linear equations
(verbally and in
writing).
 Identify
correspondences
between elimination
and substitution
approaches.
Common Core Problems:
#4,5,6,27,28,29,31,38,44
6-3 Practice Form G
Problems #1-9, 19-30
Emphasize ‘Writing’ &
‘Reasoning’ Probs. 10 &
13
6-3 Standardized Test
Prep p. 181 Problem 1
LearnZillion Lesson code:
7835
Common Core Practices
 Instruction in the Standards for Mathematical Practices
 Use of Talk Moves
 Note-taking
 Use of Manipulatives
 Use of Technology
 Use of Real-world Scenarios
 Project-based Learning
 Thinking Maps
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Time
Lesson/
Activity
Focus Questions for
Lessons
Understandings
1 Day
(Dec. 1)
Knowledge
Skills
Additional
Resources
Lessons 6.0-6.3 Common Quiz
Teacher Generated Quiz
Use this day to assess student learning.
2 Days
(Dec.
2 & 5)
Review Topic 5 Concepts & Skills
Use Textbook Resources and/or Teacher Created Items
2 Days
(Dec.
6-7)
Topic 5 Assessment
(Created and provided by PUSD)
Common Core Practices
 Instruction in the Standards for Mathematical Practices
 Use of Talk Moves
 Note-taking
 Use of Manipulatives
 Use of Technology
 Use of Real-world Scenarios
 Project-based Learning
 Thinking Maps
Page 7 of 8
Lesson 6-0: Solve Systems by Tables
Use this lesson with LearnZillion Lesson code: 7689
https://learnzillion.com/lesson_plans/7689-find-the-solution-to-a-pair-of-linearequations-by-using-tables
Inquiry Question:
Setting it up:
Solution with a Table:
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