Oley Valley School District
Algebra 1
Unit 2: Functions
Subject
Mathematics
Grade /
Course
9th / Algebra I
Unit of
Study
Pacing
II.
Functions (major
work)
Topics Within Unit: Relations, Functions, Function Notation, Domain & Range,
Discrete vs Continuous, Linear vs Nonlinear Functions, Rate of Change, Linear Function
Applications, Scatterplots, Correlation
Weeks: 15
Current Priority State Standards and/or Common Core Standards
List the priority standards that will be taught during this unit of study.
CC.2.2.HS.C.1
Use the concept and notation of functions to interpret and apply them in terms of their context.
CC.2.2.HS.C.2
Graph and analyze functions and use their properties to make connections between the different representations.
CC.2.2.HS.C.3
Write functions or sequences that model relationships between two quantities.
CC.2.2.HS.C.4
Interpret the effects transformations have on functions and find the inverses of functions.
CC.2.2.HS.C.5
Construct and compare linear, quadratic, and exponential models to solve problems.
CC.2.2.HS.C.6
Interpret functions in terms of the situations they model.
CC.2.1.HS.F.3
Apply quantitative reasoning to choose and interpret units and scales in formulas, graphs, and data displays.
CC.2.1.HS.F.4
Use units as a way to understand problems and to guide the solution of multi-step problems.
Current Supporting State Standards and/or Common Core Standards
List the supporting standards that will be taught during this unit of study. Supporting standards should not be unwrapped.
CC.2.4.HS.B.1
Summarize, represent, and interpret data on a single count or measurement variable.
CC.2.4.HS.B.2
Summarize, represent, and interpret data on two categorical and quantitative variables.
CC.2.4.HS.B.3
Analyze linear models to make interpretations based on the data.
CC.SMP.1 Make sense of problems and persevere in solving them.
CC.SMP.2 Reason abstractly and quantitatively.
CC.SMP.3 Construct viable arguments and critique the reasoning of others.
CC.SMP.4 Model with mathematics.
CC.SMP.5 Use appropriate tools strategically.
CC.SMP.6 Attend to precision.
CC.SMP.7 Look for and make use of structure.
CC.SMP.8 Look for and express regularity in repeated reasoning.
Priority Standards
CC.2.2.HS.C.1
Use the concept and notation of functions
to interpret and apply them in terms of
their context.
“Unwrapped” Concepts
“Unwrapped” Skills
(Students need to know)
(Students need to be able to do)
{PA CORE Anchor Descriptor}
{PA CORE Eligible Content Anchors}
A1.2.1.1 Analyze and/or use patterns
or relations.
A1.2.2.1 Describe, compute, and/or
use the rate of change (slope) of a
line
Webb’s Depth
of Knowledge
(Level 1, 2, 3, 4)
A1.2.1.1.1 Analyze a set of data for the
existence of a pattern and represent the pattern
algebraically and/or graphically.
1 - Identify
A1.2.1.1.2 Determine whether a relation is a
function, given a set of points or a graph.
2 - Graph
1 - Represent
2 - Distinguish
A1.2.1.1.3 Identify the domain or range of a
relation (may be presented as ordered pairs, a
graph, or a table).
2 - Determine
A1.2.2.1.1 Identify, describe, and/or use
constant rates of change.
4 - Analyze
A1.2.2.1.2 Apply the concept of linear rate of
change (slope) to solve problems.
A1.2.2.1.3 Write {construct} or identify a
3 - Construct
4 - Apply Concepts
linear equation when given:
A1.2.2.1.3.a the graph of the line.
A1.2.2.1.3.b two points on the line.
A1.2.2.1.3.c the slope and a point on
the line.
A1.2.2.1.4 Determine the slope and/or yintercept represented by a linear equation or
graph.
CC.2.2.HS.C.2
Graph and analyze functions and use their
properties to make connections between
the different representations.
A1.2.1.1 Analyze and/or use patterns
or relations.
A1.2.1.2 Interpret and/or use linear
functions and their equations, tables,
or graphs.
A1.2.2.1 Describe, compute, and/or
use the rate of change (slope) of a
line.
A1.2.1.1.1 Analyze a set of data for the
existence of a pattern and represent the pattern
algebraically and/or graphically.
1 - Identify
A1.2.1.1.2 Determine whether a relation is a
function, given a set of points or a graph.
2 - Graph
1 - Represent
2 - Distinguish
A1.2.1.1.3 Identify the domain or range of a
relation (may be presented as ordered pairs, a
graph, or a table).
2 - Determine
A1.2.1.2.1 Create, interpret, and/or use the
equation, graph, or table of a linear function.
4 - Analyze
A1.2.1.2.2 Translate from one representation of
a linear function to another (i.e., graph, table,
and equation).
A1.2.2.1.1 Identify, describe, and/or use
constant rates of change.
2 - Interpret
4 - Create
CC.2.2.HS.C.3
Write functions or sequences that model
relationships between two quantities.
A1.1.2.1 Write, solve, and/or graph
linear equations using various
methods
A1.2.1.1 Analyze and/or use patterns
or relations.
A1.2.1.2 Interpret and/or use linear
functions and their equations, tables,
or graphs.
A1.2.2.1 Describe, compute, and/or
use the rate of change (slope) of a
line.
A1.1.2.1.1 Write, solve, and/or apply a linear
equation (including problem situations).
1 - Identify
1 - Represent
A1.1.2.1.2 Use and/or identify an algebraic
property to justify any step in an equationsolving process.
2 - Graph
A1.1.2.1.3 Interpret solutions to problems in the
context of the problem situation.
2 - Determine
2 - Distinguish
A1.2.1.1.1 Analyze a set of data for the
existence of a pattern and represent the pattern
algebraically and/or graphically.
2 - Interpret
A1.2.1.1.2 Determine whether a relation is a
function, given a set of points or a graph.
4 - Analyze
A1.2.1.1.3 Identify the domain or range of a
relation (may be presented as ordered pairs, a
graph, or a table).
A1.2.1.2.1 Create, interpret, and/or use the
equation, graph, or table of a linear function.
A1.2.1.2.2 Translate from one representation of
a linear function to another (i.e., graph, table,
and equation).
A1.2.2.1.3 Write {construct} or identify a
linear equation when given:
A1.2.2.1.3.a the graph of the line.
A1.2.2.1.3.b two points on the line.
3 - Construct
4 - Create
A1.2.2.1.3.c the slope and a point on
the line.
A1.2.2.1.4 Determine the slope and/or yintercept represented by a linear equation or
graph.
CC.2.2.HS.C.4
Determine the effects transformations
have on functions and find the inverses of
functions.
CC.2.2.HS.C.5
Construct and compare linear, quadratic,
and exponential models to solve
problems.
A1.2.1.2 Interpret and/or use linear
functions and their equations, tables,
or graphs.
A1.2.1.2.1 Create, interpret, and/or use the
equation, graph, or table of a linear function.
2 - Interpret
4 - Create
A1.2.1.2.2 Translate from one representation of
a linear function to another (i.e., graph, table,
and equation).
A1.2.2.1 Describe, compute, and/or
use the rate of change (slope) of a
line.
A1.2.2.1.1 Identify, describe, and/or use
constant rates of change.
1 - Identify
1 - Represent
A1.2.2.1.2 Apply the concept of linear rate of
change (slope) to solve problems.
A1.2.2.1.3 Write {construct} or identify a
linear equation when given:
A1.2.2.1.3.a the graph of the line.
A1.2.2.1.3.b two points on the line.
A1.2.2.1.3.c the slope and a point on
the line.
2 - Graph
2 - Determine
2 - Interpret
3 - Construct
4 - Apply Concepts
A1.2.2.1.4 Determine the slope and/or yintercept represented by a linear equation or
graph.
CC.2.2.HS.C.6
Interpret functions in terms of the
situations they model.
A1.2.1.2 Interpret and/or use linear
functions and their equations, tables,
or graphs.
A1.2.1.2.1 Create, interpret, and/or use the
equation, graph, or table of a linear function.
1 - Compute
A1.2.2.1.2 Apply the concept of linear rate of
change (slope) to solve problems.
A1.2.2.1 Describe, compute, and/or
use the rate of change (slope) of a
line.
A1.2.2.1.3 Write {construct} or identify a
linear equation when given:
A1.2.2.1.3.a the graph of the line.
A1.2.2.2. Analyze and/or interpret
data on a scatterplot.
1 - Identify
A1.2.2.1.3.b two points on the line.
1 - Use
2 - Interpret
2 - Describe
3 - Construct
4 - Apply Concepts
A1.2.2.1.3.c the slope and a point on
the line.
A1.2.2.2.1 Draw, identify, find, and/or write an
equation for a line of best fit for a scatterplot.
CC.2.1.HS.F.3
Apply quantitative reasoning to choose
and interpret units and scales in formulas,
graphs, and data displays.
A1.1.2.1 Write, solve, and/or graph
linear equations using various
methods.
A1.2.1.2 Interpret and/or use linear
functions and their equations, tables,
A1.1.2.1.1 Write, solve, and/or apply a linear
equation (including problem situations).
1 - Solve
2 - Identify
A1.1.2.1.2 Use and/or identify an algebraic
property to justify any step in an equationsolving process.
2 - Interpret
A1.1.2.1.3 Interpret solutions to problems in the
context of the problem situation.
4 - Create
3 - Justify
A1.2.1.2.1 Create, interpret, and/or use the
equation, graph, or table of a linear function.
or graphs.
4 - Apply Concepts
A1.2.2.1.2 Apply the concept of linear rate of
change (slope) to solve problems.
CC.2.1.HS.F.4
Use units as a way to understand
problems and to guide the solution of
multi-step problems.
A1.1.2.1 Write, solve, and/or graph
linear equations using various
methods.
A1.2.1.2 Interpret and/or use linear
functions and their equations, tables,
or graphs.
A1.1.2.1.1 Write, solve, and/or apply a linear
equation (including problem situations).
1 - Solve
2 - Identify
A1.1.2.1.2 Use and/or identify an algebraic
property to justify any step in an equationsolving process.
2 - Interpret
A1.1.2.1.3 Interpret solutions to problems in the
context of the problem situation.
4 - Create
3 - Justify
A1.2.1.2.1 Create, interpret, and/or use the
equation, graph, or table of a linear function.
A1.2.2.1.2 Apply the concept of linear rate of
change (slope) to solve problems.
Essential Questions
Essential Questions are engaging, open-ended questions that
educators use to spark initial student interest in learning the
content of the unit about to commence.
Corresponding Big Ideas
Big ideas are what you want your students to discover on their own as a result of instruction and
learning activities.
Identify the Big Ideas for each corresponding essential question.
Identify the Essential Questions that will be used throughout
this unit to focus your instruction and assessment. For
consideration, ask yourself the following about each essential
question:
The goal is for students to effectively be able to respond to the teacher’s essential questions
with the big ideas, stated in their
1.
2.
Is this question written in student friendly language?
Can this question be answered with one of the Big
Ideas?
3. Does the question lead the students to discovery of
the Big Ideas?
4. Does the question go beyond who, what, where,
when and ask the students to explain how and why?
1. What is a relation?
1. A relation exists when there are two quantities that are measured together.
2. When is a relation also a function?
2. A function is a particular type of relation such that each element of the domain is paired with
exactly one element of the range.
3. What is the domain of a relation?
3. The domain of a relation is the set of all possible inputs.
4. What is the range of a function?
4. The range of a relation is the set of all possible outputs.
5. How can the independent and dependent variables be
identified?
5. The independent variable is associated with the domain of a relation, whereas the dependent
variable is associated with the range.
6. What is the “vertical line test”?
6. The vertical line test can be used to determine whether a given relation represents a function.
If any vertical line that can be drawn intersects with the graph of the relation more than one
time, then the relation is not a function, since this represents an element of the domain being
paired with more than one unique element of the range.
7. What are mapping diagrams used for?
7. Mapping diagrams are used to map domain elements to range elements, creating an alternate
way to identify functions vs nonfunctional relations.
8. What does it mean for a function to be discrete or
continuous?
8. Discrete functions consist of finite points, whereas continuous functions contain intervals
over which there are infinitely many possible domain and range values.
9. What’s the difference between linear and nonlinear
functions?
9. Linear functions are functions for which constant changes in the domain lead to
corresponding constant changes in the range. The graph of a linear function is a straight line.
Nonlinear functions possess neither of these characteristics.
10. What does rate of change tell us about the nature of a
linear relationship?
10. Rate of change (aka “slope”) visually represents the ratio between vertical change and
horizontal change for the graph of a linear function. It simultaneously represents the ratio
between changes to the dependent variable (y) and corresponding changes to the independent
variable (x).
11. What does initial value mean?
11. Initial value (aka “y-intercept”) is visually represent the value on the y-axis where the graph
of a linear function intersects it. It simultaneously represents the value of the dependent variable
(y) when the corresponding independent variable (x) is equal to zero.
12. How can we use a linear function model to make
predictions?
12. Once a linear model has been constructed, it is rather simple to identify other ordered pairs
that are on the line (and therefore fit the model).
13. How can linear functions be used to represent real world
problems?
13. Many real-world problems can be represented and solved by linear function models.
Plan for Instruction
Make connections between learning experiences and teaching strategies.
Engaging Learning Experiences
Performance Tasks)

Styrofoam cups: http://goo.gl/KTzW8J

Super stairs: http://goo.gl/BovUqs

(Authentic
Researched-based Effective Teaching
Strategies

Three Act Math

Inquiry Learning
Penny circle: http://goo.gl/ey1WLy

Cooperative Learning

Fry’s bank: http://goo.gl/t48u4x


Lines & Linear Equations: http://goo.gl/HWyGnB
Daily Formative Assessment using
Plickers, 3M, etc.
Assessments
Identify Formative Assessments - short, ungraded “checks for student understanding” for the educator to administer throughout the unit of study that are
directly aligned to the Project-based Assessment and that coincide with learning progressions—the “building block chunks” of instruction.
Formative (daily check-in to assess learning – used to drive future instruction) Assessments:
Project-based Assessments:
Unit Vocabulary
Tier 2
Tier 3
(Non-Content Specific Words that may cause confusion or
difficulty)
(Content Specific Words that may cause confusion or
difficulty)

Function

Slope (Rate of Change)

Relation

Y-Intercept

Domain

Initial Value


Range
Scatterplot

Line of Best Fit

Correlation

Linear

Model

Transformation

Nonlinear

Quadratic

Exponentional
Instructional Resources and Materials
Program / Text

Technology

www.teacher.desmos.com

www.101qs.com

www.visualpatterns.org

www.graphingstories.com

www.yummymath.org


https://www.illustrativemathematics.org/





Learnzillion:
https://goo.gl/7YKLVG
Mathshell:
http://map.mathshell.org/
101qs - sample lesson:
http://goo.gl/KTzW8J
Teacher
Created
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