Mathematics Curriculum Guide
HS Algebra 1 SDC Modified
2016-17
Page 1 of 12
Paramount Unified School District
Educational Services
HS Algebra 1 SDC Modified – Topic 3
Stage One – Desired Results
Topic 3: Inequalities (Chapter 3)
In this unit students connect and extend the skills for solving multi-step equations learned in the last unit with solving inequalities in this unit.
Students will learn to graph solutions of simple and compound inequalities on a number line with an arrow that points left or right from an open or
closed circle, and understand the significance of the arrow and the circle. Students will also learn the properties of inequalities for addition,
subtraction, multiplication, and division. They will apply all of these skills to real-world situations and problems to find and analyze solutions.
Common Misconceptions and/or Errors:
 Graphing Equalities: Graphing compound inequalities requires that students remember that and means intersection and or means union.
And implies that both inequalities are true, so the solutions must satisfy both inequalities. Or implies that either of the inequalities can be
true, so all solutions are included in the set.
 Equivalent Inequalities: Multiplying and dividing an inequality by a negative number requires students to remember to reverse the inequality
symbol. Students make two common errors with regards to this rule.
o They simply forget to change the symbol.
o They change the symbol when there is a negative number in the problem, even though the problem may not require multiplying or
dividing by a negative.
Page 2 of 12
HS Algebra 1 SDC Modified – Topic 3
Stage One – Desired Results
Paramount Unified School District
Educational Services
Topic 3: Inequalities (Chapter 3)
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-CED 1. Create
equations and
inequalities in
one variable
including ones
with absolute
value and use
them to solve
problems.
A-REI 3. Solve
linear
equations and
inequalities in
one variable,
including
equations with
coefficients
represented by
letters.
Timeframe: 3.5 weeks/17 days
Start Date: October 13, 2016
Assessment Dates: Nov. 3-4, 2016
Meaning-Making
Understandings
Students will understand that…
 An inequality is a mathematical sentence that uses an inequality symbol to compare the values of two expressions.
 Inequalities can be represented with symbols.
 The solution of an inequality can be represented on a number line.
 Properties of numbers and equality can transform an equation into equivalent simpler equations. This process is
used to find solutions.
 In the same way equations are solved using properties of equality, inequalities are solved using properties of
inequality.
 The Addition and Subtraction Properties of Inequality can be used to solve inequalities.
 When multiplying or dividing a negative number, it is necessary to reverse the inequality sign.
 Equivalent inequalities are inequalities that have the same solutions.
 The solution of a multi-step inequality can be found using the properties of inequality and inverse operations to
form a series of simpler inequality
 The properties of inequality can be used repeatedly to isolate the variable.
Essential Questions
Students will keep considering…
 How can inequalities that appear to be
different be equivalent?
 How can you create an inequality that
will model a real-life situation?
 What do the solutions of inequalities
represent?
Acquisition
Knowledge
Students will know…
Vocabulary: inequalities, at least, at most, is greater than, is less than, inequality
sign, variable, equivalent inequalities, properties of inequality (addition and
subtraction), isolate, inverse operations, coefficients, constants
Procedures for:
 Steps in solving simple equations using inverse properties
 Steps in solving simple inequalities using inverse properties
 The relationship between the inequality symbol and the shading on the number
line.
 The difference between an open circle and a closed circle in relation to the
inequalities.
Skills
Students will be skilled at and able to do the following…
 Construct a viable argument to justify a solution method.
 Graph the solution of an inequality.
 Explain each step in solving and simplifying simple inequalities
(verbally and in writing).
 Create a linear inequality that represents a real-life situation.
Page 3 of 12
Paramount Unified School District
HS Algebra 1 SDC Modified – Topic 3
Stage Two – Evidence of Learning
Educational Services
Topic 3: Inequalities (Chapter 3)
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?
Opportunities





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




Unit assessments
Teacher-created quizzes and/or mid-unit assessments
Illustrative Mathematics tasks (https://www.illustrativemathematics.org/)
Performance tasks
Page 4 of 12
Paramount Unified School District
Educational Services
HS Algebra 1 SDC Modified – Topic 3
Stage Two – Evidence of Learning
Topic 3: Inequalities (Chapter 3)
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
SBAC Targets (DOK)
Standards
 Construct a viable
argument to
justify a solution
method.
Create equations
that describe
numbers or
relationships. (1,2)
 Graph the
solution of an
inequality.
Solve equations
and inequalities in
one and two
variables. (1,2)
A-CED 1. Create
equations and
inequalities in one
variable including
ones with
absolute value
and use them to
solve problems.
 Explain each step
in solving and
simplifying simple
inequalities
(verbally and in
writing).

Create a linear
inequality that
represents a reallife situation.
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)
Examples
A-REI 3. Solve linear
equations and
inequalities in one
variable, including
equations with
coefficients
represented by
letters.
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HS Algebra 1 SDC Modified – Topic 3
Stage Three –Learning Experiences & Instruction
Paramount Unified School District
Educational Services
Topic 3: Inequalities (Chapter 3)
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.
Essential Questions:
Standards: A-CED 1, A-REI 3
 How can inequalities that appear to be different be equivalent?
 How can you create an inequality that will model a real-life situation?
 What do the solutions of inequalities represent?
Time
2 Days
(Oct.
13-14)
Lesson/
Activity
Focus Questions for
Lessons
Topic Opener
SMP: 2,4
(pg. 163)
Focus Questions:
 What strategy could you try in
order to solve the problem?
 What information is given in
the problem?
 What math drawing or
diagram could you make and
label to represent the
problem?
 How can you be sure you
wrote a correct inequality for
a real-world situation?
Opener will be
revisited in
Lessons 3-2 and
3-4
Understandings
Timeframe: 3.5 weeks/17 days
Start Date: October 13, 2016
Assessment Dates: November 3-4, 2016
Knowledge
Skills
Resources
 There are multiple ways to
represent the problem/
situation to include but not
limited to inequalities.
 The relationship between the
quantities of the
problem/situation specifically
between the number of
empty boxes needed and the
number of empty boxes
available.
Vocabulary: no more than,
least number
 Model the situation by
representing the number
of empty boxes needed by
the variable.
 Write an inequality that
relates the variable to the
known quantities.
 Manipulate the symbols
to solve an inequality.
 Contextualize the
solution.
Note: Opener will be
revisited in Lessons 3-2
and 3-4.
 An inequality is a
mathematical sentence that
uses an inequality symbol to
compare the values of two
expressions.
 Inequalities can be
represented with symbols.
 The solution of an inequality
can be represented on a
number line.
Vocabulary: inequalities,
solution of an inequality
 Represent situations with
inequalities.
 Determine the validity of a
solution in terms of the
situation.
 Graph the solution of an
inequality.
Common Core
Problems: # 5, 6, 7, 40,
41, 42, 57, 58, 59
Inquiry Question:
p. 163
2 Days
(Oct.
17-18)
Lesson 3-1:
Inequalities
and Their
Graphs
SMP:1,2,3,4,6
(pp. 164-170)
A-REI 3
Focus Question:
 How do you represent
quantities with a simple line
graph?
Inquiry Question Options
p. 177 Problem 75
Students will know…
 A solution to an inequality is
any number that makes the
inequality true.
 The relationship between the
inequality symbol and the
shading on the number line.
 The difference between an
open circle and a closed circle
in relation to the inequalities.
Additional Vocabulary
Support (3-1)
Page 6 of 12
Time
2 Days
(Oct.
19-20)
Lesson/
Activity
Focus Questions
for Lessons
Understandings
Knowledge
Lesson 3-2:
Solving
Inequalities
Using
Addition or
Subtraction
SMP:1,2,3,4
(pp. 171-177)
Focus Questions:
 How can you solve
inequalities?
 Which properties of inequality
would you use to solve an
inequality?
 What is a general rule for
properties of inequalities?
 In the same way equations
are solved using properties of
equality, inequalities are
solved using properties of
inequality.
 The Addition and Subtraction
Properties of Inequality can
be used to solve inequalities.
Vocabulary: inequalities, at
least, at most, is greater than, is
less than, inequality sign,
variable, equivalent inequalities,
properties of inequality
(addition and subtraction),
isolate, inverse operations,
coefficients, constants
A-REI 3
A-CED 1
2 Days
(Oct.
21, 24)
Lesson 3-3:
Solving
Inequalities
Using
Multiplication
or Division
SMP:
1,2,3,4,7
(pp. 178-183)
A-REI 3
A-CED 1
Concepts:
 Steps in solving simple
inequalities using inverse
properties
Inquiry Question:
p. 177 Problem 75
Focus Questions:
 How can you solve
inequalities?
 Which properties of inequality
would you use to solve an
inequality?
 What is a general rule for
properties of inequalities?
 When should you reverse the
direction of the inequality
symbol?
 In the same way
multiplication and division are
used to solve equations,
multiplication and division can
be used to solve inequalities.
 When multiplying or dividing
a negative number, it is
necessary to reverse the
inequality sign.
Vocabulary: inequalities, at
least, at most, is greater than, is
less than, inequality sign,
variable, equivalent inequalities,
properties of inequality
(addition and subtraction),
isolate, inverse operations,
coefficients, constants
Concepts:
 Steps in solving simple
inequalities using inverse
properties
Inquiry Question Options
p. 185 problem 59
Skills
Additional
Resources
 Construct a viable
argument to justify a
solution method
 Explain each step in
solving and simplifying
simple inequalities
(verbally and in writing).
 Create a linear inequality
that represents a real-life
situation
Note: Review Unit 2
Assessment concepts
(1/2 day)
 Solve one-step
inequalities using
multiplication and
division.
 Construct a viable
argument to justify a
solution method
 Explain each step in
solving and simplifying
simple inequalities
(verbally and in writing).
 Create a linear inequality
that represents a real-life
situation
Common Core
Problems: #6, 49, 60,
62
Common Core
Problems: # 6, 7, 8, 68,
70, 73
Thinking Map: Create
a Tree Map that will
span lessons 3.2-3.3
and will show the
Addition, Subtraction,
Multiplication, &
Division Properties of
Inequality.
3-3 Think about a plan
worksheet
Thinking Map: Add to
the Tree Map that was
created in lesson 3-2
that will show the
Addition, Subtraction,
Multiplication, &
Division Properties of
Inequality.
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 12
Time
Lesson/
Activity
Focus Questions for
Lessons
Understandings
Knowledge
Skills
3 Days
(Oct.
25-27)
Lesson 3-4:
Solving MultiStep Inequalities
SMP: 1,2,3,4
(pp. 186-192)
Focus Questions:
 How can you be sure that you
solved an inequality correctly?
 Why is the Addition Property
of Inequality used before the
Multiplication Property of
Inequality to isolate the
variable?
 What is the difference and
similarity between solving a
multi-step inequality and
solving a multi-step equation?
 What are the solutions of an
inequality where the variable
terms cancel?
 In the same way
multiplication and division are
used to solve equations,
multiplication and division can
be used to solve inequalities.
 The properties of inequality
are used to transform the
original inequality into a
series of simpler, equivalent
inequalities.
 The solution of an inequality
can be found using the
properties of inequality and
inverse operations to form a
series of simpler inequalities.
Vocabulary: Solve
inequalities, at least, at
most, is greater than, is less
than, inequality sign,
variable, equivalent
inequalities, properties of
inequality (addition,
subtraction, multiplication,
and division), isolate, inverse
operations, coefficients,
constants
 Solve multi-step inequalities.
 Use previous established
results of identity equations
and equations with no
solution to understand
inequalities with special
solutions.
 Construct a viable argument
to justify a solution method
 Explain each step in solving
and simplifying simple
inequalities (verbally and in
writing).
 Create a linear inequality
that represents a real-life
situation.
A-REI 3
A-CED 1
Inquiry Question Options
p. 187 Problem 2
1 Day
(Oct.
28)
Concepts:
 Steps in solving simple
inequalities using inverse
properties
Lessons 3.1-3.4 Common Quiz
Teacher Generated Quiz
Use this day to assess student learning.
1 Day
(Oct.
31)
Topic 3 Performance Task
See attached “Performance Task” Options for details
2 Days
(Nov.
1-2)
Review Topic 3 Concepts & Skills
Use Textbook Resources and/or Teacher Created Items
2 Days
(Nov.
3-4)
Topic 3 Assessment
(Created and provided by PUSD)
Additional
Resources
Common Core
problems: #6, 7, 8,
44, 46, 48, 50, 52,
53, 54
Additional
Vocabulary Support
Worksheet (Use
with Flow Map)
Form G Practice
page 2 (word
problems)
Note: Provide a
review before
administering the
common quiz.
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 8 of 12
Paramount Unified School District
Educational Services
Algebra Topic 3 Performance Task (Option 1)
Name:
AlgebraName:_________________________
Task:
Bernardo and Silvia play the following game. An integer between 0 and 999,
inclusive, is selected and given to Bernardo. Whenever Bernardo receives a
number, he doubles it and passes the result to Silvia. Whenever Silvia receives a
number, she adds 50 to it and passes the result to Bernardo. The winner is the last
person who produces a number less than 1000. What is the smallest initial number
that results in a win for Bernardo?
Method 1:
Method 2:
Page 9 of 12
Using the RACE method, explain how you solve the problem.
R
A
C
E
Observations: Listen to and record the strategies that you saw others present. Which
strategies were the most efficient?
Reflection: Reflect on what strategies you used or saw others use in their presentation.
What did you/they do well? What do you/they need to work on?
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
Taken from: https://www.illustrativemathematics.org/contentstandards/HSA/CED/A/1/tasks/1010
Page 10 of 12
Paramount Unified School District
Educational Services
Algebra Topic 3 Performance Task (Option 2)
Name:
AlgebraName:_________________________
Situation:
Chase and his brother like to play basketball. About a month ago they decided to keep track of
how many games they have each won. As of today, Chase has won 18 out of the 30 games against his brother.
Part 1: How many games would Chase have to win Part 2: How many games would Chase have to win in
a row in order to have a 90% winning record?
in a row in order to have a 75% wining record?
Part 3: Is Chase able to reach a 100% winning
Part 4: Suppose that after reaching a winning record
record? Explain why or why not.
of 90% in part (2), Chase had a losing streak. How
many games in a row would Chase have to lose in
order to drop down to a winning record below 55%
again?
Page 11 of 12
Using the RACE method, explain how you solved Part 4 and Justify why your answer is reasonable.
R
A
C
E
Observations: Listen to and record the strategies that you saw others present. Which
strategies were the most efficient?
Reflection: Reflect on what strategies you used or saw others use in their presentation.
What did you/they do well? What do you/they need to work on?
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
Taken from: https://www.illustrativemathematics.org/contentstandards/HSA/CED/A/1/tasks/702
Page 12 of 12