ALGEBRA 1: NJDOE MODEL CURRICULUM
CONTENT AREA: Mathematics
UNIT #: 4
STUDENT LEARNING
OBJECTIVES
CCSS/
NJCCCS
Use properties of integer
exponents to explain and convert
between expressions involving
radicals and rational exponents,
using correct notation. For
example, we define 51/3 to be the
cube root of 5 because we want
(51/3)3 = 5(1/3)3 to hold, so (51/3)3
must equal 5.
N.RN.1
N.RN.2
π#
1
Course:
Algebra1
UNIT NAME: Quadratic Functions and Modeling
Instructional Strategies, Resources, Projects,
integration of technology
Regentsprep.org: Exponents—includes exponent rules (lessons, practice)
http://www.regentsprep.org/Regents/math/ALGEBRA/AO5/indexAO5.htm
Math.com: Exponents – includes exponent rules (lesson, practice)
http://www.math.com/school/subject2/lessons/S2U2L2GL.html
Gomath.com: Laws of Exponents (summary with interactive example, links to lesson,
worksheet)
http://www.gomath.com/exercises/exponents.php
Powers and Exponents (summary, practice, word search, calculator tutorial)
http://argyll.epsb.ca/jreed/math7/strand1/1101.htm
Regentsprep.org: Exponents—includes exponent rules (lessons, practice)
http://www.regentsprep.org/Regents/math/ALGEBRA/AO5/indexAO5.htm
Page 1 of 10
Curriculum: Algebra 1-Unit 4 Quad.Functions & Modeling
KK, EE July 2013
ALGEBRA 1: NJDOE MODEL CURRICULUM
CONTENT AREA: Mathematics
2
3
Course:
Algebra1
UNIT #: 4
Use the properties of rational and
irrational numbers to explain why
the sum or product of two rational
numbers is rational, the sum of a
rational number and an irrational
number is irrational, and the
product of a nonzero rational
number and an irrational number
is irrational.
N.RN.3
Sketch the graph of a function that
models a relationship between
two quantities (expressed
symbolically or from a verbal
description) showing key features
( including intercepts,
minimums/maximums, domain,
and rate of change) by hand in
simple cases and using technology
in more complicated cases and
relate the domain of the function
to its graph. ★
F.IF.4
F.IF.5
F.1F.7
UNIT NAME: Quadratic Functions and Modeling
Regentsprep.org: Properties of Real Numbers (lessons, practice)
http://www.regentsprep.org/Regents/math/ALGEBRA/AN1/indexAN1.htm
Math.com: Properties of Real Numbers (lesson, practice)
http://www.math.com/school/subject2/lessons/S2U2L1GL.html
Explorelearning.com: Standard From of a Linear Equation (interactive investigation)
http://www.explorelearning.com/index.cfm?method=cResource.dspView&ResourceID=159
Regentsprep.org: Equations and Graphing
Lesson: http://www.regentsprep.org/Regents/math/ALGEBRA/AC1/EqLines2.htm
Practice: http://www.regentsprep.org/Regents/math/ALGEBRA/AC1/PracLine.htm
Math.com: Graphing Linear Equations (lesson, practice)
http://www.math.com/school/subject2/lessons/S2U4L3GL.html
Gomath.com: Slope, equation, and Y-intercept (summary with interactive example, links to
Page 2 of 10
Curriculum: Algebra 1-Unit 4 Quad.Functions & Modeling
KK, EE July 2013
ALGEBRA 1: NJDOE MODEL CURRICULUM
CONTENT AREA: Mathematics
Course:
Algebra1
UNIT #: 4
UNIT NAME: Quadratic Functions and Modeling
lesson, worksheet)
http://www.gomath.com/exercises/SlopeEquationYintercept.php
Interactive Slope Demonstration (analyze line by changing m and b) (interactive demonstration)
http://strader.cehd.tamu.edu/Mathematics/Algebra/Cartesian/slope2.html
NLVM: Grapher – tool for graphing and exploring functions (interactive exploration)
http://nlvm.usu.edu/en/nav/frames_asid_109_g_4_t_2.html?open=activities
4
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.
F.IF.9
Mathnets.net: Solving Quadratic Equations (interactive practice)
http://www.mathsnet.net/algebra/e31.html
Mathnets.net: Factorising (factoring) (interactive practice)
http://www.mathsnet.net/algebra/e21.html
Regentsprep.org: Definition of a Function (lesson, practice)
http://www.regentsprep.org/Regents/math/ALGEBRA/AP3/indexAP3.htm
Page 3 of 10
Curriculum: Algebra 1-Unit 4 Quad.Functions & Modeling
KK, EE July 2013
ALGEBRA 1: NJDOE MODEL CURRICULUM
CONTENT AREA: Mathematics
Course:
Algebra1
UNIT #: 4
UNIT NAME: Quadratic Functions and Modeling
NLVM: Function Machine (interactive & visual demonstration of input/output concept)
http://nlvm.usu.edu/en/nav/frames_asid_191_g_4_t_2.html
Explorelearning.com: Linear Functions – determining whether a relation represented multiple
ways is a function
http://www.explorelearning.com/index.cfm?method=cResource.dspView&ResourceID=216
5
Calculate (over a specified period
if presented symbolically or as a
table) or estimate (if presented
graphically) and interpret the
average rate of change of a
function. ★
F.IF.6,
Regentsprep.org: Slope and Rate of Change (lesson)
http://www.regentsprep.org/Regents/math/ALGEBRA/AC1/Rate.htm
Regentsprep.org: Straight Lines and Slope (lesson)
http://www.regentsprep.org/Regents/math/ALGEBRA/AC1/Llines.htm
Regentsprep.org: Direct Variation (lesson, practice)
http://www.regentsprep.org/Regents/math/ALGEBRA/AO4/indexAO4.htm
Keymath.com: Direct Variation (dynamic algebra exploration)
Page 4 of 10
Curriculum: Algebra 1-Unit 4 Quad.Functions & Modeling
KK, EE July 2013
ALGEBRA 1: NJDOE MODEL CURRICULUM
CONTENT AREA: Mathematics
Course:
Algebra1
UNIT #: 4
UNIT NAME: Quadratic Functions and Modeling
http://www.keymath.com/x7041.xml
6
Write functions in different but
equivalent forms by manipulating
quadratic expressions using
methods such as factoring and
completing the square, or
exponential expressions using the
properties of exponents, to reveal
and explain properties of the
function.
F.IF. 8
Regentsprep.org: Literal Equations (lesson, practice)
http://www.regentsprep.org/Regents/math/ALGEBRA/AE4/indexAE4.htm
Math.com: Formulas (lesson, practice)
http://www.math.com/school/subject2/lessons/S2U3L5GL.html
Explorelearning.com: Solving Formulas for Any Variable (interactive practice)
http://www.explorelearning.com/index.cfm?method=cResource.dspView&ResourceID=309
Math is fun: How to Complete the Square
http://www.mathsisfun.com/algebra/completing-square.html
Regentsprep.org: Scientific Notation (lessons, practice)
http://www.regentsprep.org/Regents/math/ALGEBRA/AO2/indexAO2.htm
Page 5 of 10
Curriculum: Algebra 1-Unit 4 Quad.Functions & Modeling
KK, EE July 2013
ALGEBRA 1: NJDOE MODEL CURRICULUM
CONTENT AREA: Mathematics
Course:
Algebra1
UNIT #: 4
UNIT NAME: Quadratic Functions and Modeling
Math.com: Exponents – includes scientific notation (lesson, practice)
http://www.math.com/school/subject1/lessons/S1U1L8GL.html
7
Write a function that describes a
linear or quadratic relationship
between two quantities given in
context using an explicit
expression, a recursive process, or
steps for calculation (include
contexts that require a
combination of various function
types). ★For example, build a
function that models the
temperature of a cooling body by
adding a constant function to a
decaying exponential, and relate
these functions to the model.
F.BF.1
Regentsprep.org: Equations of Straight Lines
Lesson: http://www.regentsprep.org/Regents/math/ALGEBRA/AC1/EqLines.htm
Practice: http://www.regentsprep.org/Regents/math/ALGEBRA/AC1/pracEq.htm
Explorelearning.com: Defining a Line with Two Points (interactive investigation)
http://www.explorelearning.com/index.cfm?method=cResource.dspView&ResourceID=63
Regentsprep.org: Parallels and Perpendiculars (lesson, practice)
http://www.regentsprep.org/Regents/math/ALGEBRA/AC3/indexAC3.htm
Regentsprep.org: Scatter Plots and Lines of Best Fit (lessons, practice)
http://www.regentsprep.org/Regents/math/ALGEBRA/AD4/indexAD4.htm
NLVM: Scatter Plot (interactive exploration)
Page 6 of 10
Curriculum: Algebra 1-Unit 4 Quad.Functions & Modeling
KK, EE July 2013
ALGEBRA 1: NJDOE MODEL CURRICULUM
CONTENT AREA: Mathematics
Course:
Algebra1
UNIT #: 4
UNIT NAME: Quadratic Functions and Modeling
http://nlvm.usu.edu/en/nav/frames_asid_144_g_4_t_5.html?open=activities
8
9
Identify the effects of translations
[ f(x) + k, k f(x), f(kx), and f(x + k)]
on a function and find the value of
k given the graphs.
Determine if a function has an
inverse, and if so, write the
expression for it.
F.BF.3 F.BF.4
PurpleMath.com: shifting of graphs of functions
http://www.purplemath.com/modules/fcntrans.htm
For Dummies.com: how to shift graphs of functions
http://www.dummies.com/how-to/content/how-to-translate-a-functions-graph.html
F.BF.4
Purple Math: finding the inverse of a function
http://www.purplemath.com/modules/invrsfcn3.htm
Math is Fun: finding and verifying inverses
http://www.mathsisfun.com/sets/function-inverse.html
Cool Math: using the vertical line test
http://www.coolmath.com/algebra/15-functions/03-vertical-line-test-01.htm
10
Compare (using graphs and tables)
linear, quadratic, and exponential
models to determine that a
quantity increasing exponentially
eventually exceeds a quantity
increasing linearly, quadratically,
or (more generally) as a
polynomial function, include
interpretation of parameters in
terms of a context.
Page 7 of 10
F.LE.3 F.LE.5
TI.com: comparing linear to exponential models
http://education.ti.com/en/timathnspired/us/detail?id=DEF0603B173F4EDBBD542188
8C18310E&sa=2D7AB06424004125A392EB9A075CABC0&t=655EACD6D73F40D7B49EE
840D89DA06A
Virtual Nerd.com: comparing linear, quadratic and exponential graphs
http://www.virtualnerd.com/algebra-1/quadratic-equations-functions/linearexponential-comparison/linear-exponential-comparison-graphingexamples/determine-function-type-from-graph
Curriculum: Algebra 1-Unit 4 Quad.Functions & Modeling
KK, EE July 2013
ALGEBRA 1: NJDOE MODEL CURRICULUM
CONTENT AREA: Mathematics
Course:
Algebra1
UNIT #: 4
UNIT NAME: Quadratic Functions and Modeling
Analyze Math.com: applying parameters to polynomial functions
http://www.analyzemath.com/polynomial2/polynomial2.htm
Major Content (Identified by PARCC Model Content Frameworks).
Page 8 of 10
Curriculum: Algebra 1-Unit 4 Quad.Functions & Modeling
KK, EE July 2013
ALGEBRA 1: NJDOE MODEL CURRICULUM
CONTENT AREA: Mathematics
Code #
N.RN.1
N.RN.2
N.RN.3
F.IF.4
F.IF.5
F.IF.6
F.IF.7
F.IF.8
Page 9 of 10
Course:
Algebra1
UNIT #: 4
UNIT NAME: Quadratic Functions and Modeling
Common Core State Standards
Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents
to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 51/3 to be the cube
root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so (51/3)3 must equal 5.
Rewrite expressions involving radicals and rational exponents using the properties of exponents.
Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational
number is irrational; and that the product of a non-zero rational number and an irrational number is irrational.
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.★
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.★
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.★
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for
more complicated cases.★
a. Graph linear and quadratic functions and show intercepts, maxima, and minima.
b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
Exponential, growth or decay.
e. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions,
showing period, midline, and amplitude
F.IF.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of
the function.
Curriculum: Algebra 1-Unit 4 Quad.Functions & Modeling
KK, EE July 2013
ALGEBRA 1: NJDOE MODEL CURRICULUM
CONTENT AREA: Mathematics
F.IF.9
F.BF.1
F.BF.3
F.BF.4
F.LE.3
F.LE.5
Course:
Algebra1
UNIT #: 4
UNIT NAME: Quadratic Functions and Modeling
a. Use the process of factoring and completing the square in a quadratic
function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.
c. Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent
rate of change in functions such as y = (1.02)t, y = (0.97)t, y = (1.01)12t, y = (1.2)t/10, and classify them as
representing exponential growth or decay.
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.
Write a function that describes a relationship between two quantities.★
a. Determine an explicit expression, a recursive process, or steps for calculation from a context.
b. Combine standard function types using arithmetic operations. For example, build a function that models the
temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to
the model.
Identify the effect on the graph of replacing f(x) by f(x) + k, k f(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.
Find inverse functions.
a. Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the
inverse. For example, f(x) = 2 x3 or f(x) = (x+1)/(x-1) for x ≠ 1.
Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly,
quadratically, or (more generally) as a polynomial function.
Interpret the parameters in a linear or exponential function in terms of a context.
Major Content (Identified by PARCC Model Content Frameworks).
Page 10 of 10
Curriculum: Algebra 1-Unit 4 Quad.Functions & Modeling
KK, EE July 2013