Download ACCESS HS ALGEBRA 1B UNIT 5: INTERPRETING FUNCTIONS

ACCESS HS ALGEBRA 1B UNIT 5: INTERPRETING FUNCTIONS
As a district-wide commitment to achieve a viable curriculum for all students, this curriculum organizer was developed to assist
teacher in prioritizing standards, time, effort, and resources to maximize student learning. Please note the recommended pacing is 89 weeks per unit and should take the needs of students into consideration. Standards for language, speaking and listening will be
embedded throughout the year due to their critical role in the ongoing development of literacy skills for effective communication and
comprehension.
Unit Focus &
Pacing
Unit 5
8-9 Weeks
Understand the
Concept of a
Function and
Use Function
Notation
Interpret
Functions that
Arise in
Applications in
Terms of the
Context
Overview
Students will understand that a function is comprised of a
domain and a range and the function models a relationship
between two quantities. Students will understand the domain
of a function to its graph and how to calculate and interpret
the average rate of change of a function. Students will be
able to graph functions and compare the properties of two
functions represented in a different way.
Focus
MAFS.912.F-IF.1.AP.1a
MAFS.912.F-IF.1.AP.1b
MAFS.912.F-IF.1.AP.2a
MAFS.912.F-IF.1.AP.3a
MAFS.912.F-IF.2.AP.4a
MAFS.912.F-IF.2.AP.4b
MAFS.912.F-IF.2.AP.5a
MAFS.912.F-IF.2.AP.6a
MAFS.912.F-IF.2.AP.6b
MAFS.912.F-IF.2.AP.6c
MAFS.912.F-IF.3.AP.7a
MAFS.912.F-IF.3.AP.7b
MAFS.912.F-IF.3.AP.8a
MAFS.912.F-IF.3.AP.8b
MAFS.912.F-IF.3.AP.9a
Access Points
Embedded
Ongoing
ELD.K12.ELL.MA.1
ELD.K12.ELL.SI.1
LAFS.910.SL.1.1
LAFS.910.SL.1.2
LAFS.910.SL.1.3
LAFS.910.SL.2.4
LAFS.910.RST.1.3
LAFS.910.RST.2.4
LAFS.910.RST.3.7
LAFS.910.WHST.1.1
LAFS.910.WHST.2.4
LAFS.910.WHST.3.9
Analyze
Functions Using
Different
Representations
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ACCESS HS ALGEBRA 1B UNIT 5: INTERPRETING FUNCTIONS
Unit Scale (Multidimensional) (MDS)
The multidimensional, unit scale is a curricular organizer for the unit and provides preliminary unpacking of the focus standards. The
MDS should prompt PLCs to further explore questions #1, “What do we expect all students to learn?”
4.0
3.0
The student is able to utilize the 3.0 standards independently through choice and real-life application.
UNDERSTAND THE CONCEPT OF A FUNCTION AND USE FUNCTION NOTATION
MAFS.912.F-IF.1.AP.1a: Demonstrate that to be 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.
MAFS.912.F-IF.1.AP.1b: Map elements of the domain sets to the corresponding range sets of functions and determine the rules in the
relationship.
MAFS.912.F-IF.1.AP.2a: Match the correct function notation to a function or a model of a function (e.g., x f(x) y).
MAFS.912.F-IF.1.AP.3a: Recognize that the domain of a sequence is a subset of the integers.
INTERPRET FUNCTIONS THAT ARISE IN APPLICATIONS IN TERMS OF THE CONTEXT
MAFS.912.F-IF.2.AP.4a: Recognize and interpret the key features of a function.
MAFS.912.F-IF.2.AP.4b: Select the graph that matches the description of the relationship between two quantities in the function.
MAFS.912.F-IF.2.AP.5a: Given the graph of a function, determine the domain.
MAFS.912.F-IF.2.AP.6a: Describe the rate of change of a function using words.
MAFS.912.F-IF.2.AP.6b: Describe the rate of change of a function using numbers.
MAFS.912.F-IF.2.AP.6c: Pair the rate of change with its graph.
ANALYZE FUNCTIONS USING DIFFERENT REPRESENTATIONS
MAFS.912.F-IF.3.AP.7a: Select a graph of a function that displays its symbolic representation (e.g., f(x) = 3x + 5).
MAFS.912.F-IF.3.AP.7b: Locate the key features of linear and quadratic equations.
MAFS.912.F-IF.3.AP.8a: Write or select an equivalent form of a function [e.g., y = mx + b, f(x) = y, y – y1 = m(x – x1), Ax + By = C].
MAFS.912.F-IF.3.AP.8b: Describe the properties of a function (e.g., rate of change, maximum, minimum, etc.).
MAFS.912.F-IF.3.AP.9a: Compare the properties of two functions.
2.0
The student will recognize or recall specific vocabulary:
Square root, exponent, linear function, opposite, distributive, area, proof, isolate, function notation, domain, range
The student will:
UNDERSTAND THE CONCEPT OF A FUNCTION AND USE FUNCTION NOTATION
MAFS.912.F-IF.1.AP.1a: Describe the relationship between a domain and a range in a function.
MAFS.912.F-IF.1.AP.1b: Draw the elements of the domain sets.
MAFS.912.F-IF.1.AP.2a: Show correct function notation.
MAFS.912.F-IF.1.AP.3a: Using models of a domain, recognize that it is a subset of the integers.
INTERPRET FUNCTIONS THAT ARISE IN APPLICATIONS IN TERMS OF THE CONTEXT
MAFS.912.F-IF.2.AP.4a: Recognize the key features of a function.
MAFS.912.F-IF.2.AP.4b: Show which graph matches the description of the relationship between two quantities in the function.
MAFS.912.F-IF.2.AP.5a: Given a graph, determine the domain.
MAFS.912.F-IF.2.AP.6a: Describe the rate of change using words.
MAFS.912.F-IF.2.AP.6b: Describe the rate of change using numbers.
MAFS.912.F-IF.2.AP.6c: Show the rate of change on its graph.
ANALYZE FUNCTIONS USING DIFFERENT REPRESENTATIONS
MAFS.912.F-IF.3.AP.7a: Select a graph that displays its symbolic representation (e.g., f(x) = 3x + 5).
MAFS.912.F-IF.3.AP.7b: Locate the key features of equations.
MAFS.912.F-IF.3.AP.8a: Show an equivalent form of a function [e.g., y = mx + b, f(x) = y, y – y1 = m(x – x1), Ax + By = C].
MAFS.912.F-IF.3.AP.8b: Show the properties of a function (e.g., rate of change, maximum, minimum, etc.).
MAFS.912.F-IF.3.AP.9a: Show the properties of two functions.
1.0
The student needs prompting and support to complete 2.0 content.
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ACCESS HS ALGEBRA 1B UNIT 5: INTERPRETING FUNCTIONS
Unpacking the Standard: What do we want students to Know, Understand and Do (KUD):
The purpose of creating a Know, Understand, and Do Map (KUD) is to further the unwrapping of a standard beyond what the MDS
provides and assist PLCs in answering question #1, “What do we expect all students to learn?” It is important for PLCs to study the
focus standards in the unit to ensure that all members have a mutual understanding of what student learning will look like and sound
like when the standards are achieved. Additionally, collectively unwrapping the standard will help with the creation of the unidimensional scale (for use with students). When creating a KUD, it is important to consider the standard under study within a K-12
progression and identify the prerequisite skills, from prior grade level standards, that are essential for mastery of the standard.
Access Algebra 1B
UNDERSTAND THE CONCEPT OF A FUNCTION AND USE FUNCTION NOTATION
MAFS.912.F-IF.1.AP.1a: Demonstrate that to be 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.
MAFS.912.F-IF.1.AP.1b: Map elements of the domain sets to the corresponding range sets of functions and determine the rules in the relationship.
MAFS.912.F-IF.1.AP.2a: Match the correct function notation to a function or a model of a function (e.g., x f(x) y).
MAFS.912.F-IF.1.AP.3a: Recognize that the domain of a sequence is a subset of the integers.
INTERPRET FUNCTIONS THAT ARISE IN APPLICATIONS IN TERMS OF THE CONTEXT
MAFS.912.F-IF.2.AP.4a: Recognize and interpret the key features of a function.
MAFS.912.F-IF.2.AP.4b: Select the graph that matches the description of the relationship between two quantities in the function.
MAFS.912.F-IF.2.AP.5a: Given the graph of a function, determine the domain.
MAFS.912.F-IF.2.AP.6a: Describe the rate of change of a function using words.
MAFS.912.F-IF.2.AP.6b: Describe the rate of change of a function using numbers.
MAFS.912.F-IF.2.AP.6c: Pair the rate of change with its graph.
ANALYZE FUNCTIONS USING DIFFERENT REPRESENTATIONS
MAFS.912.F-IF.3.AP.7a: Select a graph of a function that displays its symbolic representation (e.g., f(x) = 3x + 5).
MAFS.912.F-IF.3.AP.7b: Locate the key features of linear and quadratic equations.
MAFS.912.F-IF.3.AP.8a: Write or select an equivalent form of a function [e.g., y = mx + b, f(x) = y, y – y1 = m(x – x1), Ax + By = C].
MAFS.912.F-IF.3.AP.8b: Describe the properties of a function (e.g., rate of change, maximum, minimum, etc.).
MAFS.912.F-IF.3.AP.9a: Compare the properties of two functions.
Know
Declarative knowledge: Facts, vocabulary,
information
UNDERSTAND THE CONCEPT OF A FUNCTION AND
USE FUNCTION NOTATION
In, Su, Pa:
A function contains a domain and a range that can
be graphed to show a relationship.
A function can be written using function notation.
Subsets exist in sequential domains.
Understand
Do
“Essential understandings,” or
generalizations, and represent ideas
that are transferable to other contexts.
Procedural knowledge: Skills, strategies
and processes that are transferrable to
other contexts.
All students will be able to understand the
properties of a function, determine the
context, apply the function and use function
notation.
UNDERSTAND THE CONCEPT OF A FUNCTION
AND USE FUNCTION NOTATION
Level 1 (Retrieval)
In, Su, Pa:
Show the relationship between a domain and a
range.
Label the elements of a domain.
Recognize correct function notation.
Recognize that a domain is a subset of integers.
Level 2 (Comprehension)
In, Su, Pa:
Describe the relationship between a domain and
a range in a function.
Draw the elements of the domain sets.
Show correct function notation.
Using models of a domain, recognize that it is a
subset of the integers.
Level 3 (Analysis)
In, Su, Pa:
Demonstrate that to be a function, from one set
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ACCESS HS ALGEBRA 1B UNIT 5: INTERPRETING FUNCTIONS
(called the domain) to another set (called the
range) assigns to each element of the domain
exactly one element of the range.
Map elements of the domain sets to the
corresponding range sets of functions and
determine the rules in the relationship.
Match the correct function notation to a
function or a model of a function (e.g., x f(x) y).
Recognize that the domain of a sequence is a
subset of the integers.
Level 4 (Knowledge Utilization)
In, Su, Pa:
INTERPRET FUNCTIONS THAT ARISE IN
APPLICATIONS IN TERMS OF THE CONTEXT
In, Su, Pa:
A function is made up of key features.
A function describes an equation.
Domains are values for the input of the function.
A function and rate of change can be graphed.
INTERPRET FUNCTIONS THAT ARISE IN
APPLICATIONS IN TERMS OF THE CONTEXT
Level 1 (Retrieval)
In, Su, Pa:
Recognize the key features of a function.
Recognize that a graph can describe the
relationship between two quantities in a
function.
Recognize a graph can represent the domain.
Recognize the rate of change using words.
Recognize the rate of change using numbers.
Recognize the rate of change on its graph.
Level 2 (Comprehension)
In, Su, Pa:
Label the key features of a function.
Show which graph matches the description of
the relationship between two quantities in the
function.
Given a graph determine the domain.
Describe the rate of change using words.
Describe the rate of change using numbers.
Show the rate of change on its graph.
Level 3 (Analysis)
In, Su, Pa:
Recognize and interpret the key features of a
function.
Select the graph that matches the description of
the relationship between two quantities in the
function.
Given the graph of a function, determine the
domain.
Describe the rate of change of a function using
words.
Describe the rate of change of a function using
numbers.
Pair the rate of change with its graph.
Level 4 (Knowledge Utilization)
In, Su, Pa:
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ACCESS HS ALGEBRA 1B UNIT 5: INTERPRETING FUNCTIONS
ANALYZE FUNCTIONS USING DIFFERENT
REPRESENTATIONS
In, Su, Pa:
A function can be analyzed many different ways.
A function can be analyzed using its properties.
ANALYZE FUNCTIONS USING DIFFERENT
REPRESENTATIONS
Level 1 (Retrieval)
In, Su, Pa:
Recognize a graph with symbolic representation
(e.g., f(x) = 3x + 5).
Recognize the key features of equations.
Recognize an equivalent form of a function [e.g.,
y = mx + b, f(x) = y, y – y1 = m(x – x1), Ax + By =
C].
Recognize the properties of a function (e.g., rate
of change, maximum, minimum, etc.).
Recognize the properties of two functions.
Level 2 (Comprehension)
In, Su, Pa:
Select a graph that displays its symbolic
representation (e.g., f(x) = 3x + 5).
Locate the key features of equations.
Show an equivalent form of a function [e.g., y =
mx + b, f(x) = y, y – y1 = m(x – x1), Ax + By = C].
Show the properties of a function (e.g., rate of
change, maximum, minimum, etc.).
Show the properties of two functions.
Level 3 (Analysis)
In, Su, Pa:
Select a graph of a function that displays its
symbolic representation (e.g., f(x) = 3x + 5).
Locate the key features of linear and quadratic
equations.
Write or select an equivalent form of a function
[e.g., y = mx + b, f(x) = y, y – y1 = m(x – x1), Ax +
By = C].
Describe the properties of a function (e.g., rate
of change, maximum, minimum, etc.).
Compare the properties of two functions.
Level 4 (Knowledge Utilization)
In, Su, Pa:
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ACCESS HS ALGEBRA 1B UNIT 5: INTERPRETING FUNCTIONS
Uni-Dimensional, Lesson Scale:
The uni-dimensional, lesson scale unwraps the cognitive complexity of a focus standard for the unit, using student friendly language. The
purpose is to articulate distinct levels of knowledge and skills relative to a specific topic and provide a roadmap for designing instruction
that reflects a progression of learning. The sample performance scale shown below is just one example for PLCs to use as a springboard
when creating their own scales for student-owned progress monitoring. The lesson scale should prompt teams to further explore
question #2, “How will we know if and when they’ve learned it?” for each of the focus standards in the unit and make connections to
Design Question 1, “Communicating Learning Goals and Feedback” (Domain 1: Classroom Strategies and Behaviors). Keep in mind that
a 3.0 on the scale indicates proficiency and includes the actual standard. A level 4.0 extends the learning to a higher cognitive level. Like
the multidimensional scale, the goal is for all students to strive for that higher cognitive level, not just the academically advanced. A
level 2.0 outlines the basic declarative and procedural knowledge that is necessary to build towards the standard.
Understand the Concept of a Function and Use Function Notation
MAFS.912.F-IF.1.AP.1a, MAFS.912.F-IF.1.AP.1b, MAFS.912.F-IF.1.AP.2a, MAFS.912.F-IF.1.AP.3a
Learning Progression
Score
4.0
3.0
Target
Standard
I can determine that to be 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.
I can solve equations using elements of the domain sets to the corresponding range sets of functions and determine the rules in the
relationship.
I can develop a strategy to use the correct functional notation with a function or a model of a function (e.g., x f(x) y).
I can generate and test that the domain of a sequence is a subset of the integers.
I can demonstrate that to be 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.
I can map elements of the domain sets to the corresponding range sets of functions and determine the rules in the relationship.
I can match the correct function notation to a function or a model of a function (e.g., x f(x) y).
I can recognize that the domain of a sequence is a subset of the integers.
2.0
I can describe the relationship between a domain and a range in a function.
I can draw the elements of the domain sets.
I can show correct function notation.
I can use models of a domain and recognize that it is a subset of the integers.
1.0
I need prompting and support to complete 2.0 tasks.
6
ACCESS HS ALGEBRA 1B UNIT 5: INTERPRETING FUNCTIONS
Interpret Functions that Arise in Applications in Terms of the Context
MAFS.912.F-IF.2.AP.4a, MAFS.912.F-IF.2.AP.4b, MAFS.912.F-IF.2.AP.5a, MAFS.912.F-IF.2.AP.6a, MAFS.912.F-IF.2.AP.6b, MAFS.912.F-IF.2.AP.6c
Score
Learning Progression
4.0
3.0
Target
Standard
I can develop a strategy to recognize and interpret the key features of a function.
I can select the best equation from examples and use a graph that matches the description of the relationship between two
quantities in the function.
I can use a strategy given a graph of a function determine the domain.
I can develop a strategy to determine the rate of change of a function using words.
I can develop a strategy to determine the rate of change of a function using numbers.
I can generate and test the rate of change with its graph.
I can recognize and interpret the key features of a function.
I can select the graph that matches the description of the relationship between two quantities in the function.
Given the graph of a function, I can determine the domain.
I can describe the rate of change of a function using words.
I can describe the rate of change of a function using numbers.
I can pair the rate of change with its graph.
2.0
I can label the key features of a function.
I can show which graph matches the description of the relationship between two quantities in the function.
I can determine the domain on a graph.
I can describe the rate of change using words.
I can describe the rate of change using numbers.
I can show the rate of change on its graph.
1.0
I need prompting and support to complete 2.0 tasks.
7
ACCESS HS ALGEBRA 1B UNIT 5: INTERPRETING FUNCTIONS
Analyze Functions Using Different Representations
Score
4.0
3.0
Target
Standard
MAFS.912.F-IF.3.AP.7a, MAFS.912.F-IF.3.AP.7b, MAFS.912.F-IF.3.AP.8a, MAFS.912.F-IF.3.AP.8b, MAFS.912.F-IF.3.AP.9a
Learning Progression
I can develop a strategy to graph a function that displays its symbolic representation (e.g., f(x) = 3x + 5).
I can develop a strategy to locate the key features of linear and quadratic equations.
I can develop a strategy to write or select an equivalent form of a function [e.g., y = mx + b, f(x) = y, y – y1 = m(x – x1), Ax + By = C].
I can develop a strategy to describe the properties of a function (e.g., rate of change, maximum, minimum, etc.).
I can develop a strategy to compare the properties of two functions.
I can select a graph of a function that displays its symbolic representation (e.g., f(x) = 3x + 5).
I can locate the key features of linear and quadratic equations.
I can write or select an equivalent form of a function [e.g., y = mx + b, f(x) = y, y – y1 = m(x – x1), Ax + By = C].
I can describe the properties of a function (e.g., rate of change, maximum, minimum, etc.).
I can compare the properties of two functions.
2.0
I can select a graph that displays its symbolic representation (e.g., f(x) = 3x + 5).
I can locate the key features of equations.
I can show an equivalent form of a function [e.g., y = mx + b, f(x) = y, y – y1 = m(x – x1), Ax + By = C].
I can show the properties of a function (e.g., rate of change, maximum, minimum, etc.).
I can show the properties of two functions.
1.0
I need prompting and support to complete 2.0 tasks.
8
ACCESS HS ALGEBRA 1B UNIT 5: INTERPRETING FUNCTIONS
Recommended Resources:
These recommended instructional materials are designed to provide flexible options for instruction, but are not intended to be a prescriptive curriculum.
This set of recommended texts and resources offer a range of materials from which teachers may choose.
Recommended Resources:
In
SRA Algebra Readiness
Su, Pa
Equals Math
Understand the Concept of a Function and Use Function Notation

Unit 4 Symbolic Notation /Equations and Functions (p. 278)
Textbook Key
Example = 3-D-4, 5, 6 represents Chapter 3, Section D, Lessons 4, 5 and 6
Understand the Concept of a Function and Use Function Notation

Chapter 6-B-2, 3, 8, 9
Interpret Functions that Arise in Applications in Terms of the Context

Unit 4 Symbolic Notation /Equations and Functions (p. 278)
Interpret Functions that Arise in Applications in Terms of the Context

Chapter 6-A-1-6
Analyze Functions Using Different Representations

Unit 4 Symbolic Notation /Equations and Functions (p. 278)
Analyze Functions Using Different Representations

Chapter 5-C-5, 6

Chapter 6-A-4-6
In
Pacemaker Algebra I
Understand the Concept of a Function and Use Function Notation

Chapter 4 Introducing Functions (p. 94)

Chapter 5 Linear Equations and Functions (p.116)
Interpret Functions that Arise in Applications in Terms of the Context

Chapter 4 Introducing Functions (p. 94)

Chapter 5 Linear Equations and Functions (p.116)
Analyze Functions Using Different Representations

Chapter 4 Introducing Functions (p. 94)

Chapter 5 Linear Equations and Functions (p.116)
Website Resources
General Resources:
http://www.cpalms.org/
www.Math-Aids.com
www.mathslice.com
www.mathworksheetwizard.com
http://illuminations.nctm.org/
Concept Specific Resources:
https://www.mathsisfun.com/definitions/function.html
http://www.virtualnerd.com/tutorials/?id=Alg1_9_2_17
www.coolmath.com/algebra/15-functions
https://www.khanacademy.org/math/algebra2/functions_and_graphs/function-introduction/v/what-is-a-function
Literacy Resources – Found on Pasco MIND
Literacy:
http://mind.pasco.k12.fl.us/index.html
Math on Call
Algebra to Go
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ACCESS HS ALGEBRA 1B UNIT 5: INTERPRETING FUNCTIONS
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