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Algebra 1 Unit 3 Overview
UNIT 3: Families of Functions
TIME: 4 weeks
UNIT NARRATIVE: This initial unit starts with a treatment of quantities as preparation for work with modeling. The work then shifts to a general look at
functions with an emphasis on representation in graphs, and interpretation of graphs in terms of a context. More emphasis is placed on qualitative analyses
than calculation and symbolic manipulation. Linear and non-linear examples are explored. Only linear, simple quadratic, and simple exponential functions will
be explored in this unit with an emphasis on distinguishing between linear and exponential growth patterns. Additional work with quadratic functions will
occur in later math courses. Features of graphs will emphasize increasing/decreasing behavior and intercepts and interpreting their meaning in the context of
a situation. Domain and range will be described verbally and symbolically with students able to identify a reasonable domain based on the context given a
function represented in multiple ways.
Textbook Correlations:
Additional Resources
HOLT Algebra 1: Chapter 4
Utah Math I Module 4 Linear and Exponential Functions
Utah Math I Module 5 Features of Functions
ACADEMIC VOCABULARY: domain, range, function notation,
fibonacci sequence, recursive process, intercepts, increasing intervals,
decreasing intervals, positive intervals, negative intervals, relative
maximum, relative minimum, symmetries, end behavior, periodicity,
rate of change, step function, absolute value function, asymptote,
exponential function logarithmic function, trigonometric function,
period, midline, amplitude, exponential growth, exponential decay,
constant function, arithmetic sequence, geometric sequence, invertible
function, radian measure, arc, sine cosine, tangent, conditional relative
frequency, residuals, correlation, causation, correlation coefficient,
sample survey, experiment, observational studies, margin of effort,
simulation models, subsets, unions, intersections, complements,
independent, conditional probability, 2-way frequency table, addition
rule, multiplication rule
ESSENTIAL QUESTIONS:
1. How are equations used to describe numbers or relationships and solve
problems?
2. How does a graphed solution of equations and inequalities in two variables
indicate the set of all its solutions?
3. What do the symbols (parentheses, brackets, braces) represent when evaluating
an expression?
4. What is a function, how is it written and interpreted?
5. What essential information is indicated when graphing linear and quadratic
functions?
6. What essential information is indicated when graphing square root, cube root
and piecewise-defined functions?
7. What essential information is indicated when graphing polynomial functions?
8. How can multiple representations of functions help reveal and explain different
properties of the function?
9. What method can be used to develop and define inverse functions?
10. How can I describe the relationship between two quantitative variables
represented on a scatterplot?
11. How does a function fitted to data help solve problems?
12. What information is needed to interpret linear models?
FUSD Unit Overview 2014-2015
Algebra 1 Unit 3
Algebra 1 Unit 3 Overview
CLUSTER HEADING & STANDARDS:
Understand the concept of a function and use function notation
F.IF.1 Understand that 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. If f is a function and x is an element of its domain, then f(x) denotes the
output of f corresponding to the input x. The graph of f is the graph of the equation
y = f(x).
F.IF.2 Use function notation, evaluate functions for inputs in their domains, and
interpret statements that use function notation in terms of a context.
F.IF.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
F.IF.5 Relate the domain of a function to its graph and, where applicable, to the
quantitative relationship it describes.
Analyze functions using different representations
F.IF.7 Graph functions expressed symbolically and show key features of the graph,
by hand in simple cases and using technology for more complicated cases.
F.IF.9 Compare properties of two functions each represented in a different way
(algebraically, graphically, numerically in tables, or by verbal descriptions).
MATHEMATICAL PRACTICE:
All mathematical practice standards are addressed in every unit.
Those receiving special attention in this unit are bolded.
MP 1 Make sense of problems and persevere when solving them.
S.ID.7
MP 2 Reason quantitatively and abstractly.
F.IF.1, F.IF.2, F.IF.4, F.IF.5, S.ID.7, A.CED.2, A.CED.3, A.REI.10, F.BF.4,
F.LE.2, S.ID.6
MP 3 Construct viable arguments and critique the reasoning of
others.
S.ID.6
MP 4 Model with mathematics.
F.IF.4, F.IF.5, S.ID.7, A.CED.2, A.CED.3, A.REI.10, F.IF.6, F.BF.4, S.ID.6
MP 5 Use appropriate tools strategically.
F.IF.4, F.IF.7, S.ID.7, A.CED.2, A.CED.3, F.IF.6, F.BF.4, S.ID.6
MP 6 Attend to precision.
F.IF.4, F.IF.5, F.IF.7, S.ID.7, S.ID.6
MP 7 Look for and make use of structure.
F.IF.9, F.BF.4, S.ID.6
MP 8 Look for and express regularity in repeating reasoning
S.ID.6
Interpret linear models
S.ID.7 Interpret the slope (rate of change) and the intercept (constant term) of a
linear model in the context of the data.
Supporting Standards
Create equations that describe numbers or relationships
A.CED.2 Create equations in two or more variables to represent relationships
between quantities; graph equations on coordinate axes with labels and scales.
A.CED.3 Represent constraints by equations or inequalities, and by systems of
equations and/or inequalities, and interpret solutions as viable or non-viable
options in a modeling context.
FUSD Unit Overview 2014-2015
Algebra 1 Unit 3
Algebra 1 Unit 3 Overview
Interpret functions that arise in applications in terms of the context
F.IF.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.
Build a function that models a relationship between two quantities
F.BF.1 Write a function that describes a relationship between two quantities.
Construct and compare linear, quadratic, and exponential models and solve
problems
F.LE.3 Observe using graphs and tables that a quantity increasing exponentially
eventually exceeds a quantity increasing linearly
Summarize, represent, and interpret data on two categorical and
quantitative variables
S.ID.6 Represent data on two quantitative variables on a scatter plot, and describe
how the variables are related.
Learning Outcomes: By the end of course one level, students should be able to explain the following: Linear – x/y-intercepts and slope as
increasing/decreasing at a constant rate and also understand the concept that exponential- y-intercept and increasing at an increasing rate or decreasing at a
decreasing rate, Quadratics – x-intercepts/zeroes, y-intercepts, vertex, intervals of increase/decrease, the effects of the coefficient of x2 on the concavity of
the graph, symmetry of a parabola. Students should manipulate a quadratic function to identify its different forms (standard, factored, and vertex) so that
they can show and explain special properties of the function such as; zeros, extreme values, and symmetry. Students should be able to distinguish when a
particular form is more revealing of special properties given the context of the situation. Students should be able to write equations for functions by
developing the NOW-NEXT form or use the context in which the problem is given to find the equation. Use addition, subtraction, multiplication, and division
to combine functions to create other functions. When used in context, interpret the effect the combination of the functions had on the given situation.
Students should also be able to identify the effect transformations have on functions in multiple modalities or ways. Student should be fluent with
representations of functions as equations, tables, graphs, and descriptions. They should also understand how each representation of a function is related to
the others. For example, the equation of the line is related to its graph, table, and when in context, the problem being solved.
End of the Unit Assessment: AC Driven
INTERDISCIPLINARY CONNECTIONS:
FUSD Unit Overview 2014-2015
LITERACY CONNECTIONS: optional
Algebra 1 Unit 3
Algebra 1 Unit 3 Overview
REMEDIATION
Visual aids
Scaffolding of basic functions from Common
Core Unit 1 and Unit 2
Real-world situations where students can
work problems through linear input/output
data tables
Revisit 7th/8th grade Common Core
Standards
Start with equations and move into functions
Develop lessons with graph vocabulary based
on earlier units.
Talk moves
FUSD Unit Overview 2014-2015
DIFFERENTIATION
ACCELERATION
Technology
Functions applied in the real world
Student presentation of self-made
applications
Start with equations and move into
functions
Talk moves
ENGLISH LEARNERS
ELD Literacy Standards
Graphic organizers
Highlighting : “cloze” activities
SIOP strategies
Real-world visuals
Group collaboration
Number talks
SPECIAL EDUCATION
Small group instruction
One on one peer support
Smaller size quantities
Number Talks
Scaffolding of basic functions from
Common Core Unit 1 and Unit 2
Real-world situations where
students can work problems through
linear input/output data tables
Revisit 7th/8th grade Common Core
Standards
Start with equations and move into
functions
Develop lessons with graph
vocabulary based from earlier units.
Algebra 1 Unit 3