Algebra 1 Unit 2 Overview
UNIT: 2 Linear Functions
TIME: 4 weeks
UNIT 2 NARRATIVE: In this unit, students will focus on patterns in tables, graphs, and rules of the simplest and one of the most important relationships
among variables; linear functions. Students will gain understanding and skills needed to analyze and use linear functions. They will persevere through building
new functions based from existing functions. Students will also write functions and analyze functions using different representations found in the real-world.
They will identify problem conditions, numeric patterns, and symbolic rules of functions with graphs that are straight lines. Students will be able to write rules
for linear functions given a problem situation or data in a table or a graph.
ESSENTIAL QUESTIONS:
ACADEMIC VOCABULARY: finite, infinite, function, range, domain,
1. How do variables and the concepts of relation and function help to represent,
critical point, linear equation, logarithm, derivative, differentials, glide
analyze, and extend numerical and geometrical patterns, and to understand
reflection, oblique, matrices, integral, matrix, exponent, exponential,
input/output relationships?
parabola, linear, slope, hyperbola, velocity, increase, decrease, natural
2. How can algebraic symbols be used to represent and model mathematical
logarithm.
situations?
3. How can tables, graphs, and equations be used to represent verbal descriptions
of quantitative relationships, and vice versa?
4. How can the rate of change be found in various representations of linear data?
CLUSTER HEADING & STANDARDS:
MATHEMATICAL PRACTICE:
Build a function that models a relationship between two quantities
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
F-BF 1a Determine an explicit expression, a recursive process, or steps for
3. Construct a viable argument and critique the reasoning of others.
calculation from a context.
F-BF 1b Combine standard function types using arithmetic operations. For example, 4. Model with mathematics.
5. Use appropriate tools strategically.
build a function that models the temperature of a cooling body by adding a
6. Attend to precision.
constant function to a decaying exponential, and relate these functions to the
7. Look for and make use of structure.
model.
8. Look for and express regularity.
F-BF.2 Write arithmetic and geometric sequences both recursively and with an
explicit formula, use them to model situations, and translate between the two
forms
Build new functions from existing functions
F-BF.3 Identify the effect on the graph of replacing f(x) by f(x)+k, kf(x), f(kx),
and f(x+k) for specific values of k (both positive and negative); find the value
of k given the graphs. Experiment with cases and illustrate an explanation of the
effects on the graph using technology. Include recognizing even and odd functions
from their graphs and algebraic expressions for them.
F-BF.4 Find inverse functions. Solve an equation of the form f(x)=c for a simple
FUSD Unit Overview 9/19/13
Algebra 1Unit 2 Draft
Algebra 1 Unit 2 Overview
function f that has an inverse and write an expression for the inverse. For
example, f(x)=2x3 or f(x)=(x+1)/(x−1) for x≠1.
Interpret functions
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.
Analyze functions using different representations
F-LF. 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-LF.8 Write a function defined by an expression in different but equivalent forms
to reveal and explain different properties of the function
ASSESSMENT: By the end of this unit, students should be able to 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. They should be able to use function notation, evaluate functions for inputs in their domains, and interpret
statements that use function notation in terms of a context. Students should be able to interpret the intercepts; intervals where the function is increasing,
decreasing, positive, or negative; and end behavior (including equations of asymptotes) of exponential functions. They should be able to compare and graph
characteristics of a function represented in a variety of ways. Characteristics include domain, range, vertex, and axis of symmetry, zeros, and intercepts,
intervals of increase and decrease, and rates of change. The student’s ability to combine standard function types using arithmetic operations and distinguish
between situations that can be modeled with linear functions and with exponential functions.
INTERDISCIPLINARY CONNECTIONS:
LITERACY CONNECTIONS: optional
DIFFERENTIATION
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Algebra 1Unit 2 Draft
Algebra 1 Unit 2 Overview
REMEDIATION
 Visual aids
 Scaffolding of basic functions
from Common Core Unit 1
 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
 Talk moves
FUSD Unit Overview 9/19/13
ACCELERATION
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Technology
Functions applied in the real
world
Student presentation of selfmade applications
Start with equations and
move into functions
Talk moves
ENGLISH LEARNERS
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Graphic organizers
Highlighting : “cloze”
activities
SIOP strategies
Real-world visuals
Group collaboration
Number talks
SPECIAL EDUCATION
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Small group instruction
One on one peer support
Smaller size quantities
Number Talks
Algebra 1Unit 2 Draft