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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 1 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. 2 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 3 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: 4 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: 5 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 9 ACCESS HS ALGEBRA 1B UNIT 5: INTERPRETING FUNCTIONS 10