ALGEBRA I NJDOE MODEL CURRICULUM
Course:
Algebra I
CONTENT AREA: Mathematics
STUDENT LEARNING
OBJECTIVES
π#
1
2
Interpret parts of expressions in
terms of context including those
that represent square and cube
roots; use the structure of an
expression to identify ways to
rewrite it. ★
Manipulate expressions using
factoring, completing the square
and properties of exponents to
produce equivalent forms that
highlight particular properties
such as the zeros or the
maximum or minimum value of
the function. ★
CCSS
A.SSE.1
A.SSE.2
UNIT #: 3
UNIT NAME: Expressions and Equations
Instructional Strategies, Resources, Projects,
integration of technology
1. Real world examples of quadratic functions:
http://www.mathsisfun.com/algebra/quadratic-equation-real-world.html
1. Properties of exponents: http://www.mathplanet.com/education/algebra-1/exponents-andexponential-functions/properties-of-exponents
2. Completing the square: http://www.mathsisfun.com/algebra/completing-square.html
A.SSE.3
3. Completing the square to find the vertex:
http://www.purplemath.com/modules/sqrvertx.htm
4. Have students “find their match” of their equation in an alternate form
3
Perform addition, subtraction
and multiplication with
polynomials and relate it to
arithmetic operations with
integers.
Page 1 of 6
1. Basic polynomial operations:
http://www.kutasoftware.com/FreeWorksheets/Alg2Worksheets/Polynomial%20Basics.pdf
A.APR.1
2. Multiplying polynomials with a graphic organizer:
http://www.mathguide.com/lessons/Polynomials.html
Curriculum: Algebra 1-Unit 3: EXPRESSIONS AND EQUATIONS
KK, EE July 2013
ALGEBRA I NJDOE MODEL CURRICULUM
Course:
Algebra I
CONTENT AREA: Mathematics
UNIT #: 3
UNIT NAME: Expressions and Equations
3. Tutorials of operations with polynomials: http://www.virtualnerd.com/algebra2/polynomials/operations
4
Write linear and exponential
functions (e.g. growth/decay
and arithmetic and geometric
sequences) from graphs, tables,
or a description of the
relationship, recursively and
with an explicit formula, and
describe how quantities
increase linearly and
exponentially over equal
intervals.
1. How to determine if a graph represents a linear, exponential, or quadratic function:
http://www.virtualnerd.com/algebra-1/quadratic-equations-functions/linear-exponentialcomparison/linear-exponential-comparison-graphing-examples/determine-function-typefrom-graph
F.BF.2
2. Teacher resource for determining an equation of an exponential function:
http://www.youtube.com/watch?v=U27PIX6LFTc
3. Have students use Geogebra or other online software to model a curve ax + c understanding
what effect a and c have on the graph.
4. Writing linear equations from graphs: http://www.mathplanet.com/education/algebra1/formulating-linear-equations/writing-linear-equations-using-the-slope-intercept-form
5
Create equations and
inequalities in one variable and
use them to solve problems.
Include equations arising from
linear and quadratic functions,
simple rational and exponential
functions and highlighting a
Page 2 of 6
A.CED.1,
A.CED.4
1. Basic application of creating a one variable equation:
http://www.khanacademy.org/math/algebra/solving-linear-equations-andinequalities/equations_beginner/v/application-problems-with-equation-in-one-variable
Curriculum: Algebra 1-Unit 3: EXPRESSIONS AND EQUATIONS
KK, EE July 2013
ALGEBRA I NJDOE MODEL CURRICULUM
Course:
Algebra I
CONTENT AREA: Mathematics
6
quantity of interest in a formula.
Create linear and quadratic
equations that represent a
relationship between two or
more variables. Graph equations
on the coordinate axes with
labels and scale.
Derive the quadratic formula by
completing the square and
recognize when there are no
real solutions.
7
UNIT #: 3
UNIT NAME: Expressions and Equations
1. Graphing quadratic functions: http://www.purplemath.com/modules/grphquad.htm
A.CED.2,
1. Derive the quadratic formula: http://www.mathsisfun.com/algebra/quadratic-equationderivation.html
A.REI.4
2. Understanding the discriminant: http://www.mathwarehouse.com/quadratic/discriminantin-quadratic-equation.php
3. Practice with the discriminant:
http://www.kutasoftware.com/FreeWorksheets/Alg2Worksheets/The%20Discriminant.pdf
8
Solve quadratic equations in
one variable using a variety of
methods [including inspection
(e.g. x2 = 81), factoring,
completing the square, and the
quadratic formula].
1. Methods to solving a quadratic equation:
http://www.mathwarehouse.com/quadratic/solve-quadratic-equation.php
A.REI.4
2. Practice with quadratics:
http://regentsprep.org/Regents/math/algtrig/ATE3/quadpractice.htm
Major Content Supporting Content Additional Content (Identified by PARCC Model Content Frameworks).
Bold type indicates grade level fluency requirements. (Identified by PARCC Model Content Frameworks).
Page 3 of 6
Curriculum: Algebra 1-Unit 3: EXPRESSIONS AND EQUATIONS
KK, EE July 2013
ALGEBRA I NJDOE MODEL CURRICULUM
CONTENT AREA: Mathematics
Course:
Algebra I
UNIT #: 3
UNIT NAME: Expressions and Equations
Selected Opportunities for Connection to Mathematical Practices
1.
2.
Make sense of problems and persevere in solving them. *
Reason abstractly and quantitatively.
SLO 1 Analyze expressions by examining their parts in context.
3. Construct viable arguments and critique the reasoning of others.
SLO 7 Examine the steps in the derivation of the quadratic formula to determine if they are logical and ask questions to improve the clarify.
4. Model with mathematics. *
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
SLO 2 Look for structural similarities when writing equivalent expressions.
8. Look for and express regularity in repeated reasoning.
SLO 4 Determine the relationship between quantities over time and express the relationship in a general algebraic abstract expression
*MP.1 and MP.4 are overarching practices relevant to Algebra 1. (PARCC Model Content Frameworks)
All of the content presented in this course has connections to the standards for mathematical practices.
Bold type identifies possible starting points for connections to the SLOs in this unit.
Code #
A.SSE.1
Page 4 of 6
Common Core State Standards
Interpret expressions that represent a quantity in terms of its context.★
a. Interpret parts of an expression, such as terms, factors, and coefficients.
b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret
P(1+r)n as the product of P and a factor not depending on P.
Curriculum: Algebra 1-Unit 3: EXPRESSIONS AND EQUATIONS
KK, EE July 2013
ALGEBRA I NJDOE MODEL CURRICULUM
CONTENT AREA: Mathematics
A.SSE.2
A.SSE.3
F.BF.2
A.APR.1
A.CED.1
A.CED.2
A.CED.4
A.REI.4
Page 5 of 6
Course:
Algebra I
UNIT #: 3
UNIT NAME: Expressions and Equations
Use the structure of an expression to identify ways to rewrite it. For example, see x4 – y4 as (x2)2 – (y2)2, thus recognizing it as a
difference of squares that can be factored as (x2 – y2)(x2 + y2).
Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the
expression.★
a. Factor a quadratic expression to reveal the zeros of the function it defines.
b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
c. Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15t
can be rewritten as (1.151/12)12t 1.01212t to reveal the approximate equivalent monthly interest rate if the annual
rate is 15%.
Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and
translate between the two forms.★
Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition,
subtraction, and multiplication; add, subtract, and multiply polynomials.
Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and
quadratic functions, and simple rational and exponential functions.
Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with
labels and scales.
Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange
Ohm’s law V = IR to highlight resistance R.
Solve quadratic equations in one variable.
a. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x –
p)2 = q that has the same solutions. Derive the quadratic formula from this form.
b. Solve quadratic equations by inspection (e.g., for x2 = 49), taking
square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the
equation. Recognize when the quadratic formula gives complex solutions and write them as a ±
bi for real numbers a and b.
Curriculum: Algebra 1-Unit 3: EXPRESSIONS AND EQUATIONS
KK, EE July 2013
ALGEBRA I NJDOE MODEL CURRICULUM
CONTENT AREA: Mathematics
Course:
Algebra I
UNIT #: 3
UNIT NAME: Expressions and Equations
A.REI.7
Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For
example, find the points of intersection between the line y = –3x and the circle x2 + y2 = 3.
Major Content Supporting Content (Identified by PARCC Model Content Frameworks).
Bold type indicates grade level fluency requirements. (Identified by PARCC Model Content Frameworks).
Page 6 of 6
Curriculum: Algebra 1-Unit 3: EXPRESSIONS AND EQUATIONS
KK, EE July 2013