Common Core Algebra 2 Unit 1 Starting Points
Unit 1: Introduction to Families of Functions
Essential Questions:
o What are the key features of a graph of a function?
o What commonalities do the functions within the same family have? What makes a
particular function family unique from other types of functions?
o What types of data may be represented with a given function family?
o How can we determine if a given function family is an appropriate model for a set of
data? How can we determine if a regression equation best models a set of data?
o What is the inverse of a function? How can an inverse be displayed graphically?
Curriculum Standards:
Interpret functions that arise in applications in terms of a context.
F.IF.B.4 For a function that models a relationship between two quantities, interpret key features of graphs
and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the
relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or
negative; relative maximums and minimums; symmetries; end behavior; and periodicity.* (Cross-cutting)
(Emphasize the selection of a model function based on behavior of data and context.)
Summarize, represent, and interpret data on quantitative variables.
S.ID.B.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are
related. (Cross-cutting)
a Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use
given functions or choose a function suggested by the context. Emphasize linear and exponential
models.
b Informally assess the fit of a linear function by plotting and analyzing residuals.
c Fit a linear function for a scatter plot that suggests a linear association.
Analyze functions using different representations.
F.IF.C.9 Compare properties of two functions each represented in a different way (algebraically, graphically,
numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an
algebraic expression for another, say which has the larger maximum. (Cross-cutting)
Overarching Standards (will be embedded in each unit):
Reason quantitatively and use units to solve problems.
N.Q.A.2 Define appropriate quantities for the purpose of descriptive modeling. (Cross-cutting)
Interpret the structure of expressions.
A.SSE.A.2 Use the structure of an expression to identify ways to rewrite it. (Cross-cutting)
Create equations that describe numbers or relationships.
A.CED.A.1 Create equations and inequalities in one variable and use them to solve problems. (Cross-cutting)
Create equations that describe numbers or relationships.
A.CED.A.2 Create equations in two or more variables to represent relationships between quantities; graph
equations on coordinate axes with labels and scales. (Cross-cutting)
Interpret functions that arise in applications in terms of a context.
This document represents one sample Starting Points for the Unit. It is not all-inclusive and is only one
planning tool. Please refer to the wiki for more information and resources.
F.IF.B.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it
describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a
factory, then the positive integers would be an appropriate domain for the function.* (Cross-cutting)
Interpret linear and exponential functions that arise in applications in terms of a context.
F.IF.B.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table)
over a specified interval. Estimate the rate of change from a graph. (Cross-cutting)
Approximate Length of Unit: 10-13 days
Instructional Notes:
This unit is meant to be an introduction to other function families. Students will be working on
many of these skills throughout the course. Do not require mastery of everything, rather use this
as an opportunity to pre-assess strengths and plan for future units of study.
In addition, modeling is strongly emphasized in this and subsequent units and will be a major
focus of the PARCC exam.
It is necessary to pre-assess student fluency with linear, exponential, and quadratic functions.
Students will expand understanding of exponential functions (Unit 2) and quadratic functions
(Unit 3). Use homework assignments to address remediation of pre-requisite skills as needed.
Standard(s)
F.IF.B.4
F.IF.C.9
Days
1-3
Families of
Function Intro
& Toolbox
Notes
Big Ideas:
Introduction to families of functions
Review known function families (linear, exponential,
and quadratic)
Explore the Function Family Toolbox to compare and
contrast shapes of graphs
(Pre-assess student fluency with linear, exponential
and quadratic functions. Exponential functions will be
explored in Unit 2 and Quadratic (and linear) will be
explored in Unit 3.)
Resources:
 Lesson: Introduction to Families of Functions
S.ID.B.6
The Wave
1
Big Ideas:
Gather data and determine a model of best fit. (Data
should be fairly linear.) Review how to determine if a
linear model is best fit for a set of data.
Resources:
 Task: The Wave
This document represents one sample Starting Points for the Unit. It is not all-inclusive and is only one
planning tool. Please refer to the wiki for more information and resources.
F.IF.B.4
F.IF.B.5
F.IF.B.6
F.IF.C.9
3
Big Ideas:
Graphical analysis of functions
Describe key feature of a graph
Identify domain and range of a function
Resources:
 Lesson: Graphical Analysis of Functions
 Lesson: Domain and Range
F.BF.B.4
1-2
Big Ideas:
Introduction to concept of an inverse
Graphing the inverse of a function and determine if the
inverse graph is a function
(Algebraic work with functions will be explored in the
beginning of Unit 2 as a means to introduce inverse
function families.)
Resources:
 Lesson Seed: The Family Undone
S.ID.B.6
2
Big Ideas:
Gather data using a ball drop experiment
Determine an appropriate model to fit the data
Check the reasonableness of the model
Resources:
 Task: Ball Drop
S.ID.B.6a
2
Big Ideas:
Explore real-world data sets
Determine which function family (or families) may
appropriately model the real-world data
Resources:
 Lesson: Analyzing Real-World Data
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has
licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0
Unported License.
This document represents one sample Starting Points for the Unit. It is not all-inclusive and is only one
planning tool. Please refer to the wiki for more information and resources.