INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 01: Introduction to Functions
SUGGESTED DURATION : 5 days
UNIT OVERVIEW
This unit bundles student expectations that address the exploration of data and their representations and relationships. The exploration of functions through data collection and
analysis is a foundation for algebraic reasoning and is introduced at the beginning of Algebra 2.
Prior to this unit, in Algebra 1 Units 01, 04, 05, 09, 11, and 12, students investigated linear and quadratic relationships and were introduced to other nonlinear functions,
including rational functions and exponential functions.
During this unit, students explore a variety of data relationships, represent the relationships in multiple ways, and compare and contrast the relationships. Each of the data
relationships is matched to one of the parent functions to be studied in Algebra II. Students then investigate the data relationships using prior skills, technology, and
experimental investigations.
After this unit, in Algebra 2 Unit 02, students will experience a more in depth study of characteristics and transformations of functions. As students compare and contrast the
characteristics and representations, they will build the foundation for subsequent in-depth studies of families of functions in Algebra 2 and other mathematics coursework.
Analysis of functions is foundational to high school and college mathematics. Focusing on the properties, attributes, and applications of functions using multiple
representations is emphasized in the Texas College Career Readiness Standards (TxCCRS): II. Algebraic Reasoning D1, D2; III. Geometric Reasoning C1, C2; VI. Statistical
Reasoning A1, B1, B2, B4, C1, C2, C3; VII. Functions A2, B1, B2, C1, C2; VIII. Problem Solving and Reasoning B2; IX. Communication and Representation B1, B2, C1;
Connections A1; and STAAR Readiness Standards: 2A.1A and 2A.1B. Identification and investigation of parent functions is addressed in the STAAR Supporting Standard:
2A.4A.
According to research found in Focus in High School Mathematics: Reasoning and Sense Making (2009) from the National Council of Teachers of Mathematics (NCTM),
“Functions are one of the most important mathematical tools for helping students make sense of the world around them, as well as preparing them for further study in
mathematics” (p. 41). According to NCTM (2000), students need to learn to use a wide range of explicitly and recursively defined functions to model the world around them.
Navigating through Data Analysis in Grades 9 – 12 (2003) states, “a fundamental goal of the mathematics curriculum: to develop critical thinking and sound judgment based on
data” (NCTM, p. 1). According to Navigating through Algebra in Grades 9 – 12 (2002), “The Algebra Standard emphasizes relationships among quantities and the ways in
which quantities change relative to one another. To think algebraically, one must be able to understand patterns, relations, and functions; represent and analyze mathematical
situations and structures using algebraic symbols; use mathematical models to represent and understand quantitative relationships; and analyze change in various contexts”
(NCTM, p. 2).
National Council of Teachers of Mathematics. (2002). Navigating through algebra in grades 9 – 12. Reston, VA: National Council of Teachers of Mathematics, Inc.
National Council of Teachers of Mathematics. (2003). Navigating through data analysis in grades 9 – 12. Reston, VA: National Council of Teachers of Mathematics, Inc.
Last Updated 06/11/2014
Print Date 07/16/2014 Printed By Judy Bolen, WYLIE ISD
page 1 of 11 INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 01: Introduction to Functions
SUGGESTED DURATION : 5 days
National Council of Teachers of Mathematics (2009). Focus in high school mathematics: Reasoning and sense making. Reston, VA: National Council of Teachers of
Mathematics, Inc.
Texas Education Agency. (2009). Texas college and career readiness standards. Austin, TX: Author.
PERFORMANCE ASSESSMENT(S)
Algebra II Unit 01 PA 01
Collect and/or organize sets of data in problem
situations representing various function models such
as the following:
OVERARCHING CONCEPTS
UNIT CONCEPTS
Foundations for Functions –
Representations; Properties and
Attributes
UNIT UNDERSTANDINGS
Data relationships in problem situations can be represented by various
parent functions and modeled using multiple representations to make
predictions and critical judgments in terms of the problem situations.
Algebra and Geometry – Parent
Functions
Jason’s grandfather deposited $4,275 into an
account to pay his college expenses. Jason
withdrew $475 each month to meet his costs.
How long will it take Jason to spend all of the
money that his grandfather deposited into his
account?
Sue Ellen throws a basketball towards the hoop
from a height of approximately 6 ft. In 0.1 sec, it
is at 6.8 ft. In 0.2 sec, it is at 7.36 ft. In 0.3 sec,
it is at 7.6 ft. In 0.5 sec, it is at 7.0 ft. In 0.7
sec, it is at 5.2 ft. In 0.9 sec, it is at 2 ft. In 1
sec, it hits the ground. How many seconds had
elapsed when the ball was approximately at 4
ft?
After taking a prescription medication, trace
Last Updated 06/11/2014
Print Date 07/16/2014 Printed By Judy Bolen, WYLIE ISD
page 2 of 11 INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 01: Introduction to Functions
PERFORMANCE ASSESSMENT(S)
SUGGESTED DURATION : 5 days
OVERARCHING CONCEPTS
UNIT CONCEPTS
UNIT UNDERSTANDINGS
amounts stay in your system for an extended
period of time. For example, on Wednesday,
Daphne takes an allergy pill containing 128
milligrams of medicine. The next day, half of the
medicine still remains in her system (64 mg).
Assume that each day Daphne’s body
processes half of the medicine in her system
from the day before. Determine the amount left
in Daphne's system on the 8th day, and explain
why the amount of the drug left in the system
will never reach zero.
Create a chart for each situation that includes a table
and a scatterplot over the appropriate domain and
range. Use the representation to make predictions and
draw conclusions in each problem situation. Identify
the representative parent function, and write an
explanation of why it was chosen for each relation.
Standard(s): 2A.1A , 2A.1B , 2A.4A ELPS.c.1C ,
ELPS.c.5B , ELPS.c.5G
MISCONCEPTIONS / UNDERDEVELOPED CONCEPTS
UNDERDEVELOPED CONCEPTS:
Some students may only be able to create situations representing linear and quadratic models at the beginning of Algebra 2, since these are the functions covered in
depth in Algebra 1. Other functions will be explored and developed throughout Algebra 2.
Last Updated 06/11/2014
Print Date 07/16/2014 Printed By Judy Bolen, WYLIE ISD
page 3 of 11 INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 01: Introduction to Functions
SUGGESTED DURATION : 5 days
UNIT VOCABULARY
Parent function – simplest graph of a function family with similar characteristics (e.g., linear parent function y = x)
Representations – concrete models, tables, graphs, verbal descriptions, and algebraic generalizations of data
SYSTEM RESOURCES
Algebra II Transition Alignment Guide (TAG) Tool
OTHER RESOURCES
Fostering Algebraic Thinking: Introduction and Analyzing Written Student Work,
Introductory Session – Postage Stamp, Closing Session – Peasant Algorithm, Session
1 – Crossing the River, Session 2 Sum of Consecutive Numbers, Session 3 – The
Staircase Problem, Session 4 – Golden Apples; Asking Questions of Students,
Session 1 – The Candles Problem, Session 2 – Towering Numbers, Session 3 –
Toothpick Squares, Session 4 – More Postage Stamps; Documenting Patterns of
Student Thinking, Session 1 – Marcy’s Dots, Session 4 – More Postage Stamps;
Listening to Students, Session 1 – Carnival Bears, Session 2 – Difference of Squares,
Session 3 – Lots of Squares, Session 4 – More Postage Stamps
Maximizing Algebra 2 Performance: Explore/Explain 3: Absolute Value Functions –
Part 1 (The Fire Station Problem), Part 2 (The Relay Race), Part 3 (Transformations of
the Parent Function); Student Lesson – Absolute Value
Functions http://ritter.tea.state.tx.us/math/training/materials/Algebra_II/index.htm
TEA STAAR Mathematics
Resources: http://www.tea.state.tx.us/student.assessment/staar/math/
TEA STAAR Released Test
Questions: http://www.tea.state.tx.us/student.assessment/staar/testquestions/
TEKS#
SE#
TEKS
UNIT LEVEL SPECIFICITY
Last Updated 06/11/2014
Print Date 07/16/2014 Printed By Judy Bolen, WYLIE ISD
page 4 of 11 INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 01: Introduction to Functions
SUGGESTED DURATION : 5 days
TEKS#
TEKS
SE#
Legend:
Bold black text in italics: Knowledge and
Skills Statement (TEKS)
UNIT LEVEL SPECIFICITY
Legend:
Blue text: Supporting Information / Clarifications from TCMPC (Specificity)
Blue text in italics: Unit-specific clarification
Bold black text: Student Expectation (TEKS)
Bolded red text in italics: Student
Expectation identified by TEA as a
Readiness Standard for STAAR
Black text: Texas Education Agency (TEA); Texas College and Career Readiness Standards
(TxCCRS)
Bolded green text in italics: Student
Expectation identified by TEA as a
Supporting Standard for STAAR
Strike-through: Indicates portions of the Student
Expectation that are not included in this unit but
are taught in previous or future unit(s)
2A.1
Foundations for functions. The student uses
properties and attributes of functions and applies
functions to problem situations. The student is
expected to:
2A.1A
Identify the mathematical domains and ranges of
functions and determine reasonable domain and
range values for continuous and discrete
situations.
Readiness Standard
Use, Apply, Identify, Determine
REASONABLE MATHEMATICAL DOMAINS AND RANGES
Including, but not limited to:
Last Updated 06/11/2014
Print Date 07/16/2014 Printed By Judy Bolen, WYLIE ISD
page 5 of 11 INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 01: Introduction to Functions
SUGGESTED DURATION : 5 days
TEKS#
SE#
TEKS
UNIT LEVEL SPECIFICITY
Comparison of discrete and continuous domain
Representations of domain and range with and without technology
Tables
Graphs
Verbal descriptions
Connections among the representations
Determination of scales for graphs and windows on graphing calculators using domain and
range
Contextual domain and range of real-world problem situation
Note:
In Algebra 1, students determine domain and range using various representations of functions.
TxCCRS Note:
VII. Functions B1 – Understand and analyze features of a function.
2A.1B
Collect and organize data, make and interpret
scatterplots, fit the graph of a function to the data,
interpret the results, and proceed to model,
predict, and make decisions and critical
judgments.
Readiness Standard
Collect, Organize
DATA
Including, but not limited to:
Data sets and real-world problem situations
Data collection and analysis with and without the use of technology (e.g., CBR/CBL, graphing
calculators, and computers)
Ex: measurement activities, experiments, simulations, Internet, etc.
Representations of data with and without technology
Tables
Last Updated 06/11/2014
Print Date 07/16/2014 Printed By Judy Bolen, WYLIE ISD
page 6 of 11 INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 01: Introduction to Functions
SUGGESTED DURATION : 5 days
TEKS#
SE#
TEKS
UNIT LEVEL SPECIFICITY
Graphs including scatterplots
Verbal descriptions
Use, Make, Interpret, Fit, Model, Apply
SCATTERPLOTS AND REPRESENTATIVE FUNCTIONS FOR DATA
Including, but not limited to:
Data sets and real-world problem situations
General trends in data
Data collection and analysis with and without the use of technology (e.g., CBR/CBL, graphing
calculators, and computers)
Ex: measurement activities, experiments, simulations, Internet, etc.
Representations of data with and without technology
Tables
Graphs, including scatterplots
Verbal descriptions
Parent functions as representations of scatterplots of data with and without technology
Linear
Quadratic
Square root
Rational
Exponential
Logarithmic
Absolute value
Linear or nonlinear scatterplots using graphing technology
Model, Predict, Make
Last Updated 06/11/2014
Print Date 07/16/2014 Printed By Judy Bolen, WYLIE ISD
page 7 of 11 INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 01: Introduction to Functions
SUGGESTED DURATION : 5 days
TEKS#
SE#
TEKS
UNIT LEVEL SPECIFICITY
DECISIONS AND CRITICAL JUDGMENTS IN PROBLEM SITUATIONS
Including, but not limited to:
Data sets and real-world problem situations
General trends in the data with and without technology
Data collection and analysis with and without the use of technology (e.g., CBR/CBL, graphing
calculators, and computers)
Ex: measurement activities, experiments, simulations, Internet, etc.
Representations of data with and without technology
Tables
Graphs including scatterplots
Verbal descriptions
Parent functions as representations of scatterplots of data with and without technology
Linear
Quadratic
Square root
Rational
Exponential
Logarithmic
Absolute value
Linear or nonlinear scatterplots using graphing technology
Predictions and critical judgments in terms of the scatterplots and representative functions
Note:
In Algebra 1, students collect and analyze data using various representations, which are then
used to make predictions and critical judgments.
TxCCRS Note:
Last Updated 06/11/2014
Print Date 07/16/2014 Printed By Judy Bolen, WYLIE ISD
page 8 of 11 INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 01: Introduction to Functions
SUGGESTED DURATION : 5 days
TEKS#
SE#
TEKS
UNIT LEVEL SPECIFICITY
II. Algebraic Reasoning D1 – Interpret multiple representations of equations and relationships.
II. Algebraic Reasoning D2 – Translate among multiple representations of equations and relationships.
III. Geometric Reasoning C2 – Make connections between geometry, statistics, and probability.
VI. Statistical Reasoning A1 – Plan a study.
VI. Statistical Reasoning B1 – Determine types of data.
VI. Statistical Reasoning B2 – Select and apply appropriate visual representations of data.
VI. Statistical Reasoning B4 – Describe patterns and departure from patterns in a set of data.
VI. Statistical Reasoning C1 – Make predictions and draw inferences using summary statistics.
VI. Statistical Reasoning C2 – Analyze data sets using graphs and summary statistics.
VI. Statistical Reasoning C3 – Analyze relationships between paired data using spreadsheets,
graphing calculators, or statistical software.
VII. Functions A2 – Recognize and distinguish between different types of functions.
VII. Functions B2 – Algebraically construct and analyze new functions.
VII. Functions C1 – Apply known function models.
VII. Functions C2 – Develop a function to model a situation.
VIII. Problem Solving and Reasoning B2 – Use various types of reasoning.
IX. Communication and Representation B1 – Model and interpret mathematical ideas and concepts
using multiple representations.
IX. Communication and Representation B2 – Summarize and interpret mathematical information
provided orally, visually, or in written form within the given context.
IX. Communication and Representation C1– Communicate mathematical ideas, reasoning, and their
implications using symbols, diagrams, graphs, and words.
X. Connections A1 – Connect and use multiple strands of mathematics in situations and problems.
2A.4A
Identify and sketch graphs of parent functions,
including linear (f (x) = x), quadratic (f (x) = x2),
Connect, Identify, Sketch
exponential (f (x) = ax), and logarithmic (f (x) =
logax) functions, absolute value of x (f (x) = |x|),
PARENT FUNCTIONS AND THEIR GRAPHS
square root of x (f (x) = √x), and reciprocal of x (f
Including, but not limited to:
Last Updated 06/11/2014
Print Date 07/16/2014 Printed By Judy Bolen, WYLIE ISD
page 9 of 11 INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 01: Introduction to Functions
SUGGESTED DURATION : 5 days
TEKS#
TEKS
SE#
UNIT LEVEL SPECIFICITY
(x) = 1/x).
General forms of parent functions (including equation and function notation)
Linear: f(x) = x
Quadratic: f(x) = x²
Supporting Standard
Exponential: f(x) = ax
Logarithmic: f(x) = logax
Absolute value: f(x) = |x|
Square root: f(x) =√x
Rational (reciprocal of x): f(x) =
Representations of parent functions with and without technology
Tables
Graphs
Verbal descriptions
Connections between representations
Similarities and differences in the parent functions
Note:
In Algebra 1, students identified the characteristics of the linear and quadratic parent functions.
TxCCRS Note:
III. Geometric Reasoning C1 – Make connections between geometry and algebra.
VII. Functions A2 – Recognize and distinguish between different types of functions.
X. Connections A1 – Connect and use multiple strands of mathematics in situations and problems.
2A.4
Algebra and geometry. The student connects
algebraic and geometric representations of
functions. The student is expected to:
Last Updated 06/11/2014
Print Date 07/16/2014 Printed By Judy Bolen, WYLIE ISD
page 10 of 11 INSTRUCTIONAL FOCUS DOCUMENT
Algebra II
TITLE : Unit 01: Introduction to Functions
ELPS#
SUGGESTED DURATION : 5 days
SUBSECTION C: CROSS-CURRICULAR SECOND LANGUAGE ACQUISITION ESSENTIAL KNOWLEDGE AND SKILLS.
The English Language Proficiency Standards (ELPS), as required by 19 Texas Administrative Code, Chapter 74, Subchapter A, §74.4, outline English language
proficiency level descriptors and student expectations for English language learners (ELLs). School districts are required to implement ELPS as an integral part of
each subject in the required curriculum.
School districts shall provide instruction in the knowledge and skills of the foundation and enrichment curriculum in a manner that is linguistically accommodated
commensurate with the student’s levels of English language proficiency to ensure that the student learns the knowledge and skills in the required curriculum.
School districts shall provide content-based instruction including the cross-curricular second language acquisition essential knowledge and skills in subsection (c) of the
ELPS in a manner that is linguistically accommodated to help the student acquire English language proficiency.
http://ritter.tea.state.tx.us/rules/tac/chapter074/ch074a.html#74.4
Choose appropriate ELPS to support instruction.
Last Updated 06/11/2014
Last Updated 06/11/2014
Print Date 07/16/2014 Printed By Judy Bolen, WYLIE ISD
page 11 of 11