Algebra II - Unit #1
RELATIONS & FUNCTIONS
UNIT OVERVIEW
Unit Title
Unit Designer
Relations & Functions
Duration
IA Period
16 days
#1
Stage 1: Identify Desired Results
1) Take standards from the AF Scope and Sequence. 2) Unpack the standards into Unit Aims
Standard # Standard
Unit Aims (SWBAT)
Explain pattern relations, either for repeating patterns or
A2.A.1
Describe, extend, and generalize from
increasing patterns.
patterns (including visual patterns as well as
Predict future iterations of patterns (what would the fifth
situations)
increase look like?)
A2.A.2
Explain why function rules used to generalize
about patterns make sense given the situation.
A2.A.3
Make conjectures about generalities by testing
examples and by finding counter-examples.
A2.A.4
Define a relation and function & determine
when a relation is a function by analyzing its
equation, graph, or table.
A2.A.5
Determine the domain and range of a function
from its equation and from its graph. Justify
the domain and range using mathematical
arguments.
A2.A.6
Explain and use the procedure for finding xintercepts (roots) and y-intercepts
algebraically.
A2.A.7
Explain end behavior of a function and find
the equations of asymptotes.
A2.A.8
Describe the graph mathematically, including
finding vertices, axes of symmetry,
maximums and minimums, slopes of lines,
and increasing and decreasing sections.
A2.A.9
Sketch the graph of a function, given its
equation (may use calculator).
A2.A.10
Write functions using function notation and
Create an incremental pattern relation and write their own
generalization.
Identify pattern relations that can be written in function
form.
Describe function rules and their applications to patterns.
Write function rules based upon a given pattern.
Write pattern identities based upon a given examples.
Compare function rules against future patterns, to check
for predicting ability.
Define both a function and a non-function.
Compare data in tables and determine whether the data
represents a function.
Use the vertical-line test to check for graphs of functions.
Identify equations that represent functions.
Define domain and range as the possible values for both
the x and y values of a function.
Identify the domain and range of a function using either a
table or the graph.
Use interval notation to describe mathematically the
domain and range.
Define x-intercept and y-intercepts as the point(s) where a
function crosses each axes.
Identify an intercept when given an equation’s graph.
Solve equations algebraically to solve for the x-intercept or
y-intercept.
Define end behavior of a function and asymptotes.
Determine end behavior of a function and describe a
function’s end behavior using interval notation.
Identify asymptotes of functions and write their equations.
Define vertex, axis of symmetry, maximum, minimum,
slope, increasing, and decreasing.
Identify the vertex, axis of symmetry, slope, and
maximum/minimums of a graph.
Determine the sections of a graph that are increasing or
decreasing.
Identify and graph basic equations of graphs
(y
 mx  b, y  x2 , y  x3 , y  x ).
Use a data table to make a basic sketch of an equation.
Compare and check sketches using a graphing calculator.
Analyze data tables to describe functional relationships.
Algebra II - Unit #1
explain why function notation is important.
A2.A.11
Use function notation to evaluate functions
for given values in the domain.
A2.A.12
Explain whether a function is odd or even and
whether a function is one-to-one, onto, or
both.
Translate verbal relationships to mathematical statements.
Write mathematical statements in function notation.
Compare the uses of function notation and tables.
Describe the relationship between function notation and
points on a graph.
Evaluate functions for given domain values (x-values).
Define odd and even functions and identify examples of
each.
Explain the differences between odd and even functions
and give a non-example.
Define “one-to-one” functions and “onto” functions.
Explain the differences between one-to-one and onto
functions and give an example of each.
Enduring Understandings: What do you want students to know in 10 years about this topic?
1. Scholars will be able to identify pattern relations both in objects and real-life situations and apply
algebraic reasoning.
2. Scholars will understand how graphs represent data and the different forms of a graph and their
characteristics.
3. Scholars will be able to interpret functions and the relations they represent.
Essential Questions: What questions will guide this unit and focus learning and thinking?
1. How can quickly explaining a pattern or event be useful?
2. Why are their relations in life and patterns?
3. Why do humans use graphical interpretations of data?
Stage 2 : Assessment
Summative assessment: Write the final unit exam that assesses all EUs and standards. Give a description of
this assessment in the space below, but the write the final exam before moving onto stage 3.
Exam: Unit Assessment will consist of a 60-minute exam. Exam questions will consist of analytical questions,
which will ask scholars to think about the conceptual concepts they are learning and vocabulary, a multiplechoice section, and word-problems section. In each section, scholars will be expected to show their work and/or
give explanations for their graphs.
Formative assessment: How will you check for student understanding throughout the unit? (Quizzes, exit
tickets, independent work products, etc)
Exit Slips: At the end of each lesson, scholars will complete a short exit slip to check for understanding of the
aims taught during the lesson. Information from these slips will be used to gage review time and practice
problems.
Quiz: Scholars will be given an announced quiz half-way through the unit to assess comprehensive
Algebra II - Unit #1
understanding. A review session will be held the day before the quiz to allow for questions and
clarifications.
Homework: Each night, scholars will be assigned a selection of problems from the textbook to be completed
and checked for effort the next day.
Unit Vocabulary
*Remember to include both new terms and cumulative review
Pattern
Relation
Function
Non-Function
Function Rules
Vertical Line Test
Domain
Range
Interval Notation
x-intercepts
y-intercepts
End Behavior
Asymptote
Vertex
Axis of Symmetry
Maximum
Minimum
Slope
Increasing/Decreasing
Odd Function
Even Function
Onto Function
One-to-One Function
Optional Sections
Performance Tasks (optional)
Determine product criteria and develop a rubric to evaluate student understanding.
1. Students will work collaboratively on the 48 Hour Project. During this project, students complete a
large number of interrelated tasks in a short amount of time. This involves the skill of breaking up work
into sub-tasks, negotiating equitable distributions of work, and helping each other by giving support and
critical advice.
2. Students will improve their communication skills during the 48 Hour Project and the Seminar Problem.
Algebra II - Unit #1
Over the course of the unit, they will work collaboratively on a poster, presentation, and write-up, and
they will create one write-up on their own.
Prior Knowledge and Prerequisite Skills (optional)
List prior skills and knowledge that students would need to access to be successful in this unit.
Common Misunderstandings (optional)
Anticipate potential misunderstandings and incorporate this information in your lesson planning.
Misconception
Clarification
Aim
Lesson Plan Ideas (optional)
Brainstorm potential activities, resources, and materials.
Idea
Reflections to Capture for the Future (optional)
What would I do differently if I were to teach this again? Where do I need to go from here?