Mathematics Curriculum Guide
Algebra 1 SDC Modified
2016-17
Page 1 of 10
Algebra 1 SDC Modified – Topic 4
Stage One – Desired Results
Paramount Unified School District
Educational Services
Topic 4: Linear Functions
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
N-Q 2
A-CED 2
F-IF 1
F-IF 2
F-LE 1b
F-IF 6
Timeframe: 5 weeks/23 days
Start Date: November 7, 2016
Assessment Dates: December 14-15, 2016
Meaning-Making
Understandings
Essential Questions
Students will keep considering…
Students will understand that…










Equations can be used to solve a solution of given real-world problems.
A function is a special type of relation where each value in the domain is paired with one value in the range.
A vertical line test shows whether a relation is a function.
Ratios may be used to show a relationship between changing quantities.
The slope of a line is consistent from point to point.
Vertical lines have an undefined slope. Horizontal lines have a slope of 0.
The slope and y-intercept of a line can be used to graph the equation of a line.
The slope of a line will determine whether the line is increasing or decreasing.
The equation of a line can be written in slope-intercept form, standard form, and point-slope form.
Any two equations for the same line are equivalent.








How can you represent and describe functions?
Can function describe real-world situations?
How are functions different from relations?
How are the domain and range related? What can the
domain and range tell you about the relation or function?
How can you determine if a function is linear or not?
What information does the equation of a line give?
What does the slope of a line indicate about the line?
Which forms of equation (slope-intercept form, point-slope
form, and standard form) would be more appropriate to a
given situation?
F-IF 7
Acquisition
F-LE 2
G-GPE 5
Knowledge
Students will know…
Vocabulary: function rule, function, modeling, independent variable,
dependent variable, discrete, continuous, relation, domain, range, vertical line
test, rate of change, slope, slope formula, horizontal line, vertical line, positive,
negative, zero, undefined, increasing line, decreasing line, slope-intercept
form, slope, y-intercept, rise over run, increasing, decreasing, point-slope form,
standard form Ax + By = C, x-intercept, y-intercept
Skills
Students will be skilled at and able to do the following…












Identify and justify what the independent and dependent variables are.
Identify and justify if a function is continuous or discrete.
Determine if a relation is a function, and find the domain and range of a function.
Use function notation to define a function rule.
Determine the slope of a line given two points, a table, or its graph.*
Given a point and the slope of a line, students will be able to find a missing coordinate of
another point on the line.
Create a graph of the given linear function using the slope-intercept form.
Graph a linear function using its equation.
Write a linear equation given the slope and y-intercept.
Students will be able to write the equation of a line in point-slope form.
Students will be able to change from point-slope form to slope-intercept form.
Change equations from standard from to slope intercept form.
Page 2 of 10
Paramount Unified School District
Educational Services
Algebra 1 SDC Modified – Topic 4
Stage Two – Evidence of Learning
Topic 4: Linear Functions
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 10
Paramount Unified School District
Educational Services
Algebra 1 SDC Modified – Topic 4
Stage Two – Evidence of Learning
Topic 4: Linear Functions
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)
 Identify and justify what the
independent and dependent
variables are.
 Identify and justify if a
function is continuous or
discrete.
 Determine if a relation is a
function, and find the domain
and range of a function.
 Use function notation to
define a function rule.
 Determine the slope of a line
given two points, a table, or
its graph.*
 Given a point and the slope of
a line, students will be able to
find a missing coordinate of
another point on the line.
 Create a graph of the given
linear function using the
slope-intercept form.
 Graph a linear function using
its equation.
 Write a linear equation given
the slope and y-intercept.
 Students will be able to write
the equation of a line in pointslope form.
 Students will be able to
change from point-slope form
to slope-intercept form.
 Change equations from
standard from to slope
intercept form.
Create equations
that describe
numbers or
relationships. (1,2)
Solve equations
and inequalities in
one and two
variables. (1,2)
Standards
N-Q 2
Examples
A-CED 2
F-IF 1
F-IF 2
F-LE 1b
F-IF 6
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)
F-IF 7
F-LE 2
G-GPE 5
Page 4 of 10
Paramount Unified School District
Educational Services
Algebra 1 SDC Modified – Topic 4
Stage Three –Learning Experiences & Instruction
Topic 4: Linear Functions
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: N-Q 2, A-CED 2, F-IF 1, F-IF 2,








F-LE 1b, F-IF 6, F-IF 7, F-LE 2, G-GPE 5
How can you represent and describe functions?
Can function describe real-world situations?
How are functions different from relations?
How are the domain and range related? What can the domain and range tell you about the relation or function?
How can you determine if a function is linear or not?
What information does the equation of a line give?
What does the slope of a line indicate about the line?
Which forms of equation (slope-intercept form, point-slope form, and standard form) would be more appropriate to a given situation?
Time
2 Days
(Nov.
7-8)
*Note:
Review
coordinate
plane
and
graphing
ordered
pairs.
2 Days
(Nov.
9-10)
Lesson/ Activity
Topic Opener
SMP 1, 2, 3, 4, 6
Lesson: How Much Does a
100x100 In-N-Out
Cheeseburger Cost?
The main idea of the lesson
opener is to spark student
interest in the problem. Students
may try to figure out how much a
3x3 burger would cost. This
lesson may be revisited so that
students write a function rule in
which they will be able to find the
cost of an NxN burger.
Lesson 4-5: Writing a
Function Rule
SMP 1, 2, 3, 4
(pp. 262-267)
N-Q 2, A-CED 2
Timeframe: 5 weeks/23 days
Start Date: November 7, 2016
Assessment Dates: December 14-15, 2016
Focus Questions for Lessons
Understandings
Knowledge
Skills
Resources
 How is this problem similar to or
different from problems that we
have encountered in the past?
 What methods can we use to
solve this problem?
 How many variables are there in
this problem, what are they, and
how are they related?
 Solutions may be
expressed using a graph,
an input-output table, or
a written explanation, or
an equation
 The cost of a
cheeseburger at In-N-Out
will be dependent on the
number of meat &
cheese layers.
 There is only one layer of
lettuce and tomato per
burger.
Vocabulary: In-N-Out
cheeseburger, hamburger, and
3x3 burger.
 Construct a viable
argument to justify a
solution method
 Working towards: Create a
linear equation that
represents a real-life
situation
PDF Lesson: How
Much Does a
100x100 In-N-Out
Cheeseburger
Cost? on the L
Drive in Algebra
2014-2015 Folder
 Can you write an equation that
represents the real-world
situation?
 How can a model help you write
an equation? How can drawing a
diagram help you write a rule?
 How can you determine which
variable is dependent and
independent?
 How can you determine if a
function is discrete or
continuous?
 Many real-world
situations can be
represented by
equations. Once you see
a pattern in a
relationship, you can
write a rule.
 Equations can be used to
solve a solution of given
real-world problems.
 A function can represent a
real-life situation.
 There can only be one price
for a cheeseburger with a set
number of cheese and
patties.
Vocabulary: function rule,
function, modeling,
independent variable,
dependent variable, discrete,
continuous
 Discrete functions have
variable that can be
counted.
 Continuous functions have
variables that can be
measured.
http://robertkapli
nsky.com/work/i
n-n-out-100-x100/
 To create a linear function
that represents a given
real-world situation.
 Identify and justify what
the independent and
dependent variables are.
 Identify and justify if a
function is continuous or
discrete.
Common Core
Problems:
5, 6, 22, 23, 26,
30
Learn Zillion:
8TNWK9F
Page 5 of 10
Time
2 days
(Nov.
14-15)
Lesson/ Activity
Lesson 4-6:
Formalizing Relations
and Functions
SMP 1, 2, 3, 4, 6
(pp. 268-273)
Focus Questions
for Lessons
Understandings
 How are functions and relations
related?
 How can you determine if a
relation is a function or not?
 A function is a special
type of relation where
each value in the domain
is paired with one value
in the range.
 A vertical line test shows
whether a relation is a
function.
Vocabulary: relation, domain,
range, vertical line test
 What does the slope tell you
about the relations between
two quantities?
 Why does the rate of change
need to be constant for a
relation to be linear?
 How is the slope formula and
finding the slope of the line from
a graph representative of the
same process?
 Ratios may be used to
show a relationship
between changing
quantities.
 The slope of a line is
consistent from point to
point.
 Vertical lines have an
undefined slope.
Horizontal lines have a
slope of 0.
 How can you use the slope & yintercept of a line to create a
graph?
 How do you know the direction
of the line and the position of
the line?
 What must you know to write
the equation of a line in slopeintercept form?
 The slope and y-intercept
of a line can be used to
graph the equation of a
line.
 The slope of a line will
determine whether the
line is increasing or
decreasing.
 One form for writing the
equation of a line is the
slope-intercept
F-IF 1, F-IF 2
2 days
(Nov.
16-17)
Lesson 5-1: Rate of
Change and Slope
SMP 1, 2, 3, 4
(pp. 294-300)
F-LE 1b, F-IF 6
3 Days
(Nov. 18,
28, 29)
Lesson 5-3: Intercept
Form
SMP 1, 2, 3, & 4
(pp. 308-314)
F-IF 7
Knowledge
Skills
Additional
Resources
 Determine if a relation is a
function
 Find the domain and
range of a function
 Use function notation to
define a function rule.
Common Core
Problems:
5-7, 26-28, 30, 35
Vocabulary: rate of change,
slope, slope formula,
horizontal line, vertical line,
positive, negative, zero,
undefined, increasing line,
decreasing line.
 Find the slope of a line
through two given points.
 Find the slope of a line from
the graph of the line.
 Determine the slope of a
line given two points, a
table, or its graph.*
 Given a point and the
slope of a line, students
will be able to find a
missing coordinate of
another point on the line.
Practice &
Problem Solving
Workbook:
 5-1 Think
About a Plan
 5-1 Practice p.
139
Vocabulary: slope-intercept
form, slope, y-intercept, rise
over run, increasing,
decreasing.
 Create a graph of the
given linear function using
the slope-intercept form.
 Create a linear equation
that represents a real-life
situation.*
 Graph a linear function
using its equation.
 Write a linear equation
given the slope and yintercept.
 Students know that if a
relation is a function for
each value in the domain
there is only value for
range.
 Students know what a
vertical line test is.
 The equation of a line, and
its graph represent the same
line.
 All points that make the
equation true; are points on
the line.
TEST PREP:
5-1 Standardized
Test Prep p. 141
Problems 3 & 5
Practice &
Problem Solving
Workbook:
 5-3 Practice p.
147
TEST PREP:
5-3 Standardized
Test Prep p. 149
Problems 1-4
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 6 of 10
Time
2 Days
(Nov.
30 &
Dec. 1)
2 Days
(Dec.
2 & 5)
Lesson/
Activity
Understandings
Knowledge
Skills
Additional
Resources
Lessons 4.5, 4.6, 5.1, 5.3 Common Quiz
Teacher Generated Quiz
Use this day to assess student learning.
Lesson 5-4: PointSlope Form
SMP 1, 3, and 4
(pp. 315-320)
F-LE 2
2 Days
(Dec.
6-7)
Focus Questions for
Lessons
Lesson 5-5:
Standard From
SMP 1, 2, 3, and 4
(pp. 322-328)
G-GPE 5
 Given the equation of a line in
point-slope form, how can you
determine the slope and
another point that lies on the
line?
 Describe the situation in which
using the point-slope form is
appropriate.
 Point-slope form is a form for
writing the equation of a line.
 Any two equations for the
same line are equivalent.
 The slope and any point on
the line can be used to write
an equation of the line.
 How do you graph an equation
written in standard form?
 How can you write an equation
is slope intercept form given it
in standard form? How can you
write an equation in standard
form
 The standard form of a linear
equation makes it possible to
find intercepts and draw
graphs quickly.
Vocabulary: point-slope
form
 Write a linear equation
using point-slope form.
 Know the steps to change
a point-slope form to
slope-intercept form.
Vocabulary: standard form
Ax + By = C, x-intercept, yintercept.
 Write a linear equation in
standard form.
 Understand that the
same line can be written
in slope-intercept form,
point-slope form, or
standard form.
2 Days
(Dec.
8-9)
Topic 4 Performance Task
See attached “Performance Task” for details
2 Days
(Dec.
12-13)
Review Topic 4 Concepts & Skills
Use Textbook Resources and/or Teacher Created Items
2 Days
(Dec.
14-15)
Topic 4 Assessment
(Created and provided by PUSD)
 Construct a viable argument
to justify a solution method.
 Students will be able to write
the equation of a line in
point-slope form.
 Students will be able to
change from point-slope
form to slope-intercept
form.
 Create a linear equation that
represents a real-life
situation.*
 Change equations from
standard from to slope
intercept form.
Practice & Problem
Solving Workbook:
5-4 Practice p. 151
Problems 1-4, 15,
17-20.
TEST PREP:
5-4 Standardized
Test Prep p. 153
Problems 1-4
Practice & Problem
Solving Workbook:
5-5 Practice p. 155
Problems 1-12
TEST PREP:
5-5 Standardized
Test Prep p. 157
Problems 3, 4, & 5
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 10
Paramount Unified School District
Educational Services
Algebra Topic 4 Performance Task
Name:
AlgebraName:_________________________
Problem
Solving Task:
Have you noticed that dropping objects into a glass
of water raises the water level? The diagram and
table below show what happens to the height (y)
of the water in a certain glass when different
numbers of identical marbles(x) are dropped into it.
Write an equation that represents the situation.
Use the race method to describe how you found the
equation. Then answer the questions on the back.
Strategy 1:
Equation:
Strategy 2:
Equation:
Page 8 of 10
Explanation:
R
A
C
E
______________________________________
______________________________________
______________________________________
______________________________________
______________________________________
______________________________________
______________________________________
______________________________________
______________________________________
______________________________________
______________________________________
______________________________________
______________________________________
______________________________________
Page 9 of 10
Is the relation a function? ___________________ Why or Why not?_____________________
_____________________________________________________________________________
_____________________________________________________________________________
Is the relation linear? ___________________ Why or Why not?_________________________
_____________________________________________________________________________
_____________________________________________________________________________
What is the independent variable? ___________________________ What is the dependent
variable? ____________________________________________________________________
Is the relation discrete or continuous? How do you know?
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
What is the domain?___________________________________________________________
What is the range?____________________________________________________________
What is the lowest water level the glass could have?
_____________________________________________________________________________
_____________________________________________________________________________
How many marbles can be dropped into the glass before the water overflows?_____________
Explain how you determined this.
_____________________________________________________________________________
_____________________________________________________________________________
_____________________________________________________________________________
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?
Page 10 of 10