Algebra Support Lab Scope and Sequence
Grade level: HS /Algebra Lab
Marking Period 1:
Stage 1 – Desired Results
Enduring Understandings/Goals:
 Interpreting numbers as quantities with appropriate units, scales, and levels of accuracy allows one to
and make sense of real world problems.
 Relationship between numbers can be represented by equation, inequalities and systems.
 Equivalent equations can be found using inverse operations and simplification.
Essential Questions:
 In what ways can the choice of units, quantities and levels of accuracy impact a solution?
 How can algebra describe the relationship between sets of numbers?
 Can equations that appear to be different be equivalent?
Mathematical Practices:
1.
Make sense of problems and persevere in solving them.
2.
Reason abstractly and quantitatively.
3.
Construct viable arguments and critique the reasoning of others.
4.
Model with mathematics.
5.
Use appropriate tools strategically.
6.
Attend to precision.
7.
Look for and make use of structure.
8.
Look for and express regularity in repeated reasoning.
Standard:
Student Learning
Prerequisites Necessary for Mastery
Objectives
N.Q.1 Use units as a way 1. Solve multi-step
6.RP.A1 Understand the concept of a ratio and
use ratio language to describe a ratio relationship
to understand problems
problems that can be
between two quantities.
and to guide the solution
represented
of multi-step problems;
algebraically with
6.RP.A2 Understand the concept of a unit rate a/b
choose and interpret units accurate and
associated with a ratio a:b with b ≠ 0, and use rate
consistently in formulas;
appropriately defined
language in the context of a ratio relationship.
choose and interpret the
units, scales, and
6.RP.A3 Use ratio and rate reasoning to solve
1
*M.C. = major content
*S.C. = supporting content
effectively model
Suggested
Resources
Pearson Algebra
1 Common Core
Series (in relation
to Algebra 1
curriculum)
Pearson MathXL
(intervention)
*A.C. = additional content, relative to PARCC assessment ★
scale and the origin in
graphs and data displays.
N.Q.2 Define appropriate
quantities for the purpose
of descriptive modeling.
N.Q.3 Choose a level of
accuracy appropriate to
limitations on
measurement when
reporting quantities.
A.SSE.1 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
real-world and mathematical problems, e.g., by
models (such as
graphs, tables, and data reasoning about tables of equivalent ratios, tape
diagrams, double number line diagrams, or
displays). S.C.
equations.
NJ Center for
teaching and
learning. (group
activities to
develop
mathematical
practices)
2. Interpret terms,
factors, coefficients,
and expressions
(including complex
linear and exponential
expressions) in terms of
context. M.C.
Pearson Algebra
1 Common Core
Series (in relation
to Algebra 1
curriculum)
Pearson MathXL
(intervention)
NJ Center for
teaching and
learning. (group
activities to
develop
mathematical
practices)
A.REI.3 Solve linear
equations and inequalities
in one variable, including
equations with coefficients
represented by letters.
A.CED.4 Rearrange
formulas to highlight a
quantity of interest, using
3. Solve linear
equations and
inequalities in one
variable (including
literal equations).
Justify each step in the
process and solution.
M.C.
6.EE.A.2 Write, read, and evaluate expressions in
which letters stand for numbers.
6.EE.A.3 Apply the properties of operations to
generate equivalent expressions.
6.EE.A.4 Identify when two expressions are equivalent
example, interpret P(1+r)n
as the product of P and a
factor not depending on P.
2
6.EE.A.1 Write and evaluate numerical expressions
involving whole-number exponents.
*M.C. = major content
6.EE.B.5 Understand solving an equation or inequality
as a process of answering a question: which values
from a specified set, if any, make the equation or
inequality true? Use substitution to determine whether
a given number in a specified set makes an equation or
inequality true.
6.EE.B.6 Use variables to represent numbers and write
expressions when solving a real-world or mathematical
problem; understand that a variable can represent an
unknown number, or, depending on the purpose at
hand, any number in a specified set.
6.EE.B.7 Solve real-world and mathematical problems
*S.C. = supporting content
Pearson Algebra
1 Common Core
Series (in relation
to Algebra 1
curriculum)
Pearson MathXL
(intervention)
NJ Center for
*A.C. = additional content, relative to PARCC assessment ★
the same reasoning as in
solving equations. For
by writing and solving equations of the form x + p = q
and px = q for cases in which p, q and x are all
nonnegative rational numbers.
example, rearrange Ohm’s
law V = IR to highlight
resistance R.
A.REI.1 Explain each step
in solving a simple
equation as following from
the equality of numbers
asserted at the previous
step, starting from the
assumption that the
original equation has a
solution. Construct a
viable argument to justify
a solution method.
A.CED.1 Create equations
and inequalities in one
variable and use them to
solve problems. Include
4. Create linear
equations and
inequalities in one
variable and use them
to solve problems.
Justify each step in the
process and the
solution. M.C.
equations arising from
linear functions.
A.REI.3 Solve linear
equations and inequalities
in one variable, including
equations with coefficients
represented by letters.
A.CED.2 Create equations
in two or more variables
to represent relationships
between quantities; graph
equations on coordinate
3
6.EE.B.8 Write an inequality of the form x > c or x < c
to represent a constraint or condition in a real-world or
mathematical problem. Recognize that inequalities of
the form x > c or x < c have infinitely many solutions;
represent solutions of such inequalities on number line
diagrams.
6.EE.C.9 Use variables to represent two quantities in a
real-world problem that change in relationship to one
another; write an equation to express one quantity,
thought of as the dependent variable, in terms of the
other quantity, thought of as the independent variable.
Analyze the relationship between the dependent and
independent variables using graphs and tables, and
relate these to the equation. For example, in a problem
involving motion at constant speed, list and graph
ordered pairs of distances and times, and write the
equation d = 65t to represent the relationship between
distance and time.
teaching and
learning. (group
activities to
develop
mathematical
practices)
Pearson Algebra
1 Common Core
Series (in relation
to Algebra 1
curriculum)
Pearson MathXL
(intervention)
NJ Center for
teaching and
learning. (group
activities to
develop
mathematical
practices)
7.EE.A.1 Apply properties of operations as strategies
to add, subtract, factor, and expand linear expressions
with rational coefficients.
5. Create linear
equations in two or
more variables to
represent relationships
between quantities;
*M.C. = major content
7.EE.A.2 Understand that rewriting an expression in
different forms in a problem context can shed light on
the problem and how the quantities in it are related.
7.EE.B.3 Solve multi-step real-life and mathematical
problems posed with positive and negative rational
numbers in any form (whole numbers, fractions, and
*S.C. = supporting content
Pearson Algebra
1 Common Core
Series (in relation
to Algebra 1
curriculum)
*A.C. = additional content, relative to PARCC assessment ★
axes with labels and
scales.
graph equations on
coordinate axes with
labels and scales. M.C.
decimals), using tools strategically. Apply properties of Pearson MathXL
operations to calculate with numbers in any form;
(intervention)
convert between forms as appropriate; and assess the
NJ Center for
reasonableness of answers using mental computation
teaching and
and estimation strategies.
learning. (group
activities to
7.EE.B.4 Use variables to represent quantities in a real- develop
world or mathematical problem, and construct simple
mathematical
equations and inequalities to solve problems by
practices)
reasoning about the quantities.
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. For example,
6. Model and describe
constraints with linear
equations and
inequalities and
systems of equations
and/or inequalities to
determine if solutions
are viable or non-viable.
M.C.
8.EE.A.1 Know and apply the properties of integer
exponents to generate equivalent numerical
expressions.
represent inequalities
describing nutritional and
cost constraints on
combinations of different
foods.
A.REI.1 Explain each step
in solving a simple
equation as following from
the equality of numbers
asserted at the previous
step, starting from the
assumption that the
original equation has a
solution. Construct a
4
*M.C. = major content
8.EE.A.2 Use square root and cube root symbols to
represent solutions to equations of the form x2 = p and
x3 = p, where p is a positive rational number. Evaluate
square roots of small perfect squares and cube roots of
small perfect cubes. Know that √2 is irrational.
8.EE.A.3 Use numbers expressed in the form of a
single digit times an integer power of 10 to estimate
very large or very small quantities, and to express how
many times as much one is than the other.
8.EE.A.4 Perform operations with numbers expressed
in scientific notation, including problems where both
decimal and scientific notation are used. Use scientific
notation and choose units of appropriate size for
measurements of very large or very small quantities
(e.g., use millimeters per year for seafloor spreading).
Interpret scientific notation that has been generated by
technology
*S.C. = supporting content
Pearson Algebra
1 Common Core
Series (in relation
to Algebra 1
curriculum)
Pearson MathXL
(intervention)
NJ Center for
teaching and
learning. (group
activities to
develop
mathematical
practices)
*A.C. = additional content, relative to PARCC assessment ★
viable argument to justify
a solution method.
A.REI.5 Prove that, given
a system of two equations
in two variables, replacing
one equation by the sum
of that equation and a
multiple of the other
produces a system with
the same solutions.
A.REI.6 Solve systems of
linear equations exactly
and approximately (e.g.,
with graphs), focusing on
pairs of linear equations in
two variables.
1. Solve systems of
linear equations in two
variables graphically
and algebraically.
Include solutions that
have been found by
replacing one equation
by the sum of that
equation and a multiple
of the other. A.C.
8.EE.B.5 Graph proportional relationships, interpreting
the unit rate as the slope of the graph. Compare two
different proportional relationships represented in
different ways. For example, compare a distance-time
Pearson Algebra
graph to a distance-time equation to determine which
1 Common Core
of two moving objects has greater speed.
Series (in relation
to Algebra 1
8.EE.B.6 Use similar triangles to explain why the slope
curriculum)
m is the same between any two distinct points on a
Pearson MathXL
non-vertical line in the coordinate plane; derive the
(intervention)
equation y = mx for a line through the origin and the
NJ Center for
equation y = mx + b for a line intercepting the vertical
teaching and
axis at b.
learning. (group
activities to
8.EE.C.7 Solve linear equations in one variable.
develop
mathematical
8.EE.C.8 Analyze and solve pairs of simultaneous
practices)
linear equations
Stage 2 – Assessment Evidence
Suggested Performance Tasks:
Other Evidence:
 Exemplars
 Classwork
 Extended projects
 Exit Slips
 Math Webquests
 Homework
 Writing in Math/Journal
 Open-ended questions
 Portfolio
 Quizzes
Stage 3 – Learning Plan
Lesson Format
10 min: Do Now/Journaling (whole class)
30 min: Individual computer work - intervention
30 min: Group work – Complex problems used to develop a deeper understanding using
mathematical practices
10 min: Closure/Assessment/Evaluation
5
*M.C. = major content
*S.C. = supporting content
*A.C. = additional content, relative to PARCC assessment ★
UNIT NAME: Linear Relationships
Grade level: HS/ALGEBRA LAB
Marking Period 2:
Stage 1 – Desired Results
Enduring Understandings/Goals:
 There is often an optimal method of manipulating equations and inequalities to solve a mathematical problem,
however, other methods which may not be efficient can still provide insight into the problem.
 Equations, verbal descriptions, graphs, and tables provide insight into the relationship between quantities.
 Functions can be represented by using tables, equations and graphs.
 Real-world situations can be modeled by discrete and continuous functions.
Essential Questions:
 In what ways can the problem be solved and why should one method be chosen over another?
 How can the relationship between quantities best be represented?
 How can you represent and describe functions?
 How can functions describe real-world situations?
Mathematical Practices:
1.
Make sense of problems and persevere in solving them.
2.
Reason abstractly and quantitatively.
3.
Construct viable arguments and critique the reasoning of others.
4.
Model with mathematics.
5.
Use appropriate tools strategically.
6.
Attend to precision.
7.
Look for and make use of structure.
8.
Look for and express regularity in repeated reasoning.
6
*M.C. = major content
*S.C. = supporting content
*A.C. = additional content, relative to PARCC assessment ★
Standard:
Student Learning
Objectives
A.REI.11 Explain why the x-coordinates of the
points where the graphs of the equations y = f(x)
and y = g(x) intersect are the solutions of the
equation f(x) = g(x); find the solutions
approximately, e.g., using technology to graph
the functions, make tables of values, or find
successive approximations. Include cases where
f(x) and/or g(x) are linear, polynomial, rational,
absolute value, exponential, and logarithmic
functions.★
2. Find approximate
solutions of linear
equations by making a
table of values, using
technology to graph
and successive
approximations. M.C.
A.REI.10 Understand that the graph of an
equation in two variables is the set of all its
solutions plotted in the coordinate plane, often
forming a curve (which could be a line).
A.REI.11 Explain why the x-coordinates of the
points where the graphs of the equations y = f(x)
and y = g(x) intersect are the solutions of the
equation f(x) = g(x); find the solutions
approximately, e.g., using technology to graph
the functions, make tables of values, or find
successive approximations. Include cases where
f(x) and/or g(x) are linear, polynomial, rational,
absolute value, exponential, and logarithmic
functions.★
A.REI.12 Graph the solutions to a linear
inequality in two variables as a half-plane
(excluding the boundary in the case of a strict
inequality), and graph the solution set to a system
3. Graph equations,
inequalities, and
systems of inequalities
in two variables and
explain that the
solution to an equation
is all points along the
curve, the solution to a
system of linear
functions is the point
of intersection, and the
solution to a system of
inequalities is the
intersection of the
corresponding halfplanes. ★ M.C.
7
*M.C. = major content
*S.C. = supporting content
Prerequisites
Necessary for
Mastery
6.EE
7.EE
8.EE
See standards listed
in unit 1.
6.EE
7.EE
8.EE
See standards
listed in unit 1.
Suggested
Resources
Pearson Algebra 1
Common Core Series
(in relation to
Algebra 1
curriculum)
Pearson MathXL
(intervention)
NJ Center for
teaching and
learning. (group
activities to develop
mathematical
practices)
Pearson Algebra 1
Common Core Series
(in relation to
Algebra 1
curriculum)
Pearson MathXL
(intervention)
NJ Center for
teaching and
learning. (group
activities to develop
mathematical
practices)
*A.C. = additional content, relative to PARCC assessment ★
of linear inequalities in two variables as the
intersection of the corresponding half-planes.
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, evaluates functions
for inputs in their domains, and interprets
statements that use function notation in terms of
a context.
4. Explain and
interpret the definition
of functions including
domain and range and
how they are related;
correctly use function
notation in a context
and evaluate functions
for inputs and their
corresponding outputs.
M.C.
F.IF.3 Recognize that sequences are functions,
sometimes defined recursively, whose domain is a
subset of the integers. For example, the Fibonacci
5. Write a function for
a geometric sequence
defined recursively,
whose domain is a
subset of the integers.
M.C.
F.IF.5 Relate the domain of a function to its
graph and, where applicable, to the quantitative
relationship it describes. For example, if the
6. Graph functions by
hand (in simple cases)
and with technology
(in complex cases) to
describe linear
relationships between
sequence is defined recursively by f (0) = f (1) =
1, f (n+1) = f (n) + f (n-1) for n ≥ 1.
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
8
*M.C. = major content
*S.C. = supporting content
Pearson Algebra 1
Common Core Series
(in relation to
Algebra 1
curriculum)
Pearson MathXL
(intervention)
NJ Center for
teaching and
8.F.A.2 Compare
learning. (group
properties of two
functions each represented activities to develop
mathematical
in a different way
practices)
(algebraically,
Pearson Algebra 1
graphically, numerically
Common Core Series
in tables, or by verbal
(in relation to
descriptions).
Algebra 1
curriculum)
8.F.A.3 Interpret the
Pearson MathXL
equation y = mx + b as
defining a linear function, (intervention)
whose graph is a straight
NJ Center for
line; give examples of
teaching and
functions that are not
learning. (group
linear.
activities to develop
mathematical
8.F.B.4 Construct a
practices)
function to model a linear Pearson Algebra 1
relationship between two
Common Core Series
quantities. Determine the
(in relation to
rate of change and initial
Algebra 1
value of the function from
curriculum)
a description of a
Pearson MathXL
8.F.A.1 Understand that a
function is a rule that
assigns to each input
exactly one output. The
graph of a function is the
set of ordered pairs
consisting of an input and
the corresponding output.
*A.C. = additional content, relative to PARCC assessment ★
for the function.★
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.★
a. Graph linear functions.
F.IF.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
two quantities and
identify, describe, and
compare domain and
other key features in
one or multiple
representations. ★
M.C.
quadratic function and an algebraic expression for
another, say which has the larger maximum.
quadratic function and an algebraic expression for
another, say which has the larger maximum.
9
*M.C. = major content
(intervention)
NJ Center for
teaching and
learning. (group
activities to develop
mathematical
practices)
8.F.B.5 Describe
qualitatively the
functional relationship
between two quantities by
analyzing a graph (e.g.,
where the function is
increasing or decreasing,
linear or nonlinear).
Sketch a graph that
exhibits the qualitative
features of a function that
has been described
verbally.
A.REI.11 Explain why the x-coordinates of the
points where the graphs of the equations y = f(x)
and y = g(x) intersect are the solutions of the
equation f(x) = g(x); find the solutions
approximately, e.g., using technology to graph
the functions, make tables of values, or find
successive approximations. Include cases where
f(x) and/or g(x) are linear, polynomial, rational,
absolute value, exponential, and logarithmic
functions.
F.IF.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
relationship or from two
(x, y) values, including
reading these from a table
or from a graph. Interpret
the rate of change and
initial value of a linear
function in terms of the
situation it models, and in
terms of its graph or a
table of values.
7. Compare properties
of two functions each
represented in a
different way
(algebraically,
graphically, numerically
in tables, or by verbal
descriptions). S.C.
*S.C. = supporting content
Pearson Algebra 1
Common Core Series
(in relation to
Algebra 1
curriculum)
Pearson MathXL
(intervention)
NJ Center for
teaching and
learning. (group
activities to develop
*A.C. = additional content, relative to PARCC assessment ★
A.SSE.1 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.
1. 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. ★
M.C.
6.EE
7.EE
8.EE

See standards
listed in unit 1.
A.SSE.2 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).
A.SSE.3 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%
10
*M.C. = major content
2. 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. ★ S.C.
*S.C. = supporting content
6.EE
7.EE
8.EE
 See standards
listed in unit 1.
mathematical
practices)
Pearson Algebra 1
Common Core Series
(in relation to
Algebra 1
curriculum)
Pearson MathXL
(intervention)
NJ Center for
teaching and
learning. (group
activities to develop
mathematical
practices)
Pearson Algebra 1
Common Core Series
(in relation to
Algebra 1
curriculum)
Pearson MathXL
(intervention)
NJ Center for
teaching and
learning. (group
activities to develop
mathematical
practices)
*A.C. = additional content, relative to PARCC assessment ★
Stage 2 – Assessment Evidence
Suggested Performance Tasks:
Other Evidence:
 Exemplars
 Classwork
 Extended projects
 Exit Slips
 Math Webquests
 Homework
 Writing in Math/Journal
 Open-ended questions
 Portfolio
 Quizzes
Stage 3 – Learning Plan
Lesson Format
10 min: Do Now/Journaling (whole class)
30 min: Individual computer work - intervention
30 min: Group work – Complex problems used to develop a deeper understanding using
mathematical practices
10 min: Closure/Assessment/Evaluation
UNIT NAME: Expressions and Equations
11
*M.C. = major content
*S.C. = supporting content
*A.C. = additional content, relative to PARCC assessment ★
Grade level: HS/ALGEBRA LAB
Marking Period 3:
Stage 1 – Desired Results
Enduring Understandings/Goals:
 Expressions can be written in multiple ways using the rules of algebra: each version of the expression tells something
about the problem it represents.
 The relationships between numbers can be represented by equations, inequalities and systems.
 Quadratic equations can be solved by graphing, factoring, completing the square, and using the quadratic formula.
Essential Questions:
 Why structure expressions in different ways?
 How can algebra describe the relationship between sets of numbers?
 How can you solve a quadratic equation?
Mathematical Practices:
1.
Make sense of problems and persevere in solving them.
2.
Reason abstractly and quantitatively.
3.
Construct viable arguments and critique the reasoning of others.
4.
Model with mathematics.
5.
Use appropriate tools strategically.
6.
Attend to precision.
7.
Look for and make use of structure.
8.
Look for and express regularity in repeated reasoning.
Standard:
Student Learning
Prerequisites for Mastery
Suggested
Objectives
Resources
A.APR.1 Understand that
3. Perform addition,
6.EE
Pearson
polynomials form a system
subtraction and
7.EE
Algebra 1
analogous to the integers, namely, multiplication with
8.EE
Common
they are closed under the
polynomials and relate it
Core Series
operations of addition, subtraction, to arithmetic operations
See standards listed in MP1
(in relation to
and multiplication; add, subtract,
Algebra 1
with integers. M.C.
and multiply polynomials.
curriculum)
8.F.A.1
F.BF.2 Write arithmetic and
4. Write linear and
8.F.A.2
Pearson
geometric sequences both
exponential functions
12
*M.C. = major content
*S.C. = supporting content
*A.C. = additional content, relative to PARCC assessment ★
recursively and with an explicit
formula,, use them to model
situations, and translate between
the two forms.
(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. M.C.
A.CED.1 Create equations and
5. Create equations and
inequalities in one variable and use inequalities in one
them to solve problems. Include
variable and use them to
equations arising from linear and
solve problems. Include
quadratic functions, and simple
equations arising from
rational and exponential functions. linear and quadratic
A.CED.4 Rearrange formulas to
functions, simple rational
highlight a quantity of interest,
and exponential functions
using the same reasoning as in
and highlighting a
solving equations. For example,
quantity of interest in a
rearrange Ohm’s law V = IR to
formula. M.C.
8.F.A.3
8.F.B.4.
8.F.B.5
A.CED.2 Create equations in two
or more variables to represent
relationships between quantities;
graph equations on coordinate
axes with labels and scales
6.EE
7.EE
8.EE
See standards listed in MP 2
MathXL
(intervention)
NJ Center for
teaching and
learning.
(group
activities to
develop
mathematical
practices)
6.EE
7.EE
8.EE
See standards listed in MP 1
highlight resistance R
A.REI.4 Solve quadratic equations
in one variable.
a. Use the method of completing
13
*M.C. = major content
6. Create linear and
quadratic equations that
represent a relationship
between two or more
variables. Graph
equations on the
coordinate axes with
labels and scale. M.C.
7. Derive the quadratic
formula by completing
the square and recognize
*S.C. = supporting content
See standards listed in MP1
6.EE
7.EE
8.EE
*A.C. = additional content, relative to PARCC assessment ★
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.
A.APR.3 Identify zeros of
polynomials when suitable
factorizations are available,
and use the zeros to
construct a rough graph of the
function defined by the
polynomial.
when there are no real
solutions.
M.C.
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].
M.C.
1. Identify zeros of
polynomials when
suitable factorizations are
available, and use the
zeros to
construct a rough graph
of the function defined by
the polynomial. S.C.
N.RN.1 Explain how the definition 2. Use properties of
integer exponents to
of the meaning of rational
explain and convert
exponents follows from extending
the properties of integer exponents between expressions
involving radicals and
to those values, allowing for a
rational exponents, using
notation for radicals in terms of
correct notation. For
rational exponents. For example,
1/3
example, we define 51/3
we define 5 to be the cube root
to be the cube root of 5
of 5 because we want (51/3)3 =
14
*M.C. = major content
*S.C. = supporting content
See standards listed in MP1
6.EE
7.EE
8.EE
See standards listed in MP1
6.NS.A.1 Interpret and compute quotients of
fractions, and solve word problems involving
division of fractions by fractions,
6.NS.C.5 Understand that positive and negative
numbers are used together to describe quantities
having opposite directions or values use positive
and negative numbers to represent quantities in
real-world contexts, explaining the meaning of 0
*A.C. = additional content, relative to PARCC assessment ★
5(1/3)3 to hold, so (51/3)3 must
equal 5.
N.RN.2 Rewrite expressions
involving radicals and rational
exponents using the properties of
exponents.
N.RN.3 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.
because we want (51/3)3
= 5(1/3)3 to hold, so
(51/3)3 must equal 5. A.C.
3. 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. A.C.
in each situation.
6.NS.C.6 Understand a rational number as a
point on the number line. Extend number line
diagrams and coordinate axes familiar from
previous grades to represent points on the line
and in the plane with negative number
coordinates.
6.NS.C.7 Understand ordering and absolute
value of rational numbers.
7.NS.A.1 Apply and extend previous
understandings of addition and subtraction to
add and subtract rational numbers; represent
addition and subtraction on a horizontal or
vertical number line diagram.
7.NS.A.2 Apply and extend previous
understandings of multiplication and division
and of fractions to multiply and divide rational
numbers.
7.NS.A.3 Solve real-world and mathematical
problems involving the four operations with
rational numbers.
8.NS.A.1 Know that numbers that are not
rational are called irrational. Understand
informally that every number has a decimal
expansion; for rational numbers show that the
decimal expansion repeats eventually, and
convert a decimal expansion which repeats
eventually into a rational number.
8.NS.A.2 Use rational approximations of
15
*M.C. = major content
*S.C. = supporting content
*A.C. = additional content, relative to PARCC assessment ★
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; and
periodicity. ★
F.IF.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. ★
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. ★
a. Graph linear and quadratic
16
*M.C. = major content
4. 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.
★M.C.
*S.C. = supporting content
irrational numbers to compare the size of
irrational numbers, locate them approximately
on a number line diagram, and estimate the
value of expressions (e.g., π2).
8.F.A.1
8.F.A.2
8.F.A.3
8.F.B.4.
8.F.B.5
See standards listed in MP 2
Pearson
Algebra 1
Common
Core Series
(in relation to
Algebra 1
curriculum)
Pearson
MathXL
(intervention)
NJ Center for
teaching and
learning.
(group
activities to
develop
mathematical
practices)
*A.C. = additional content, relative to PARCC assessment ★
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
Stage 2 – Assessment Evidence
Other Evidence:
 Classwork
 Exit Slips
 Homework
 Open-ended questions
 Portfolio
 Quizzes
Stage 3 – Learning Plan
Lesson Format
10 min: Do Now/Journaling (whole class)
30 min: Individual computer work - intervention
30 min: Group work – Complex problems used to develop a deeper understanding using
mathematical practices
10 min: Closure/Assessment/Evaluation
Suggested Performance Tasks:
 Exemplars
 Extended projects
 Math Webquests
 Writing in Math/Journal
UNIT NAME: Functions and Descriptive Statistics
Grade level: HS/ALGEBRA LAB
17
*M.C. = major content
*S.C. = supporting content
*A.C. = additional content, relative to PARCC assessment ★
Marking Period 4:
Stage 1 – Desired Results
Enduring Understandings/Goals:
 Statisticians summarize, represent and interpret categorical and quantitative data in multiple ways.
 Data can be collected and analyzed to help you make decisions and predictions
Essential Questions:
 How can the properties of data be communicated to eliminate its important features?
 How can data be collected and analyzed to help you make and predictions?
Mathematical Practices:
1.
Make sense of problems and persevere in solving them.
2.
Reason abstractly and quantitatively.
3.
Construct viable arguments and critique the reasoning of others.
4.
Model with mathematics.
5.
Use appropriate tools strategically.
6.
Attend to precision.
7.
Look for and make use of structure.
8.
Look for and express regularity in repeated reasoning.
Standard:
Student Learning
Prerequisites Needed for Mastery
Objectives
8.F.A.1
F.IF.9 Compare properties 5. Compare
8.F.A.2
of two functions each
properties of two
8.F.A.3
represented in a different
functions each
8.F.B.4.
way (algebraically,
represented in a
8.F.B.5
graphically, numerically in
different way
tables, or by verbal
(algebraically,
See standards listed in MP 2
descriptions). For example, graphically,
given a graph of one
numerically in tables,
quadratic function and an
or by verbal
algebraic expression for
descriptions). For
another, say which has the example, given a
larger maximum.
graph of one
quadratic function
18
*M.C. = major content
*S.C. = supporting content
Suggested
Resources
Pearson
Algebra 1
Common
Core Series
(in relation to
Algebra 1
curriculum)
Pearson
MathXL
(intervention)
*A.C. = additional content, relative to PARCC assessment ★
and an algebraic
expression for
another, say which
has the larger
maximum. S.C.
F.IF.6 Calculate and
6. Calculate (over a
interpret the average rate
specified period if
of change of a function
presented
(presented symbolically or
symbolically or as a
as a table) over a specified table) or estimate (if
interval. Estimate the rate
presented graphically)
of change from a graph. ★ and interpret the
average rate of
change of a function.
★M.C.
F.IF.8 Write a function
7. Write functions in
defined by an expression in different but
different but equivalent
equivalent forms by
forms to reveal and explain manipulating
different properties of the
quadratic expressions
function.
using methods such
a. Use the process of
as factoring and
factoring and completing
completing the
the square in a quadratic
square, or
function to show zeros,
exponential
extreme values, and
expressions using the
symmetry of the graph, and properties of
interpret these in terms of
exponents, to reveal
a context.
and explain properties
c. Use the properties of
of the function. S.C.
exponents to interpret
expressions for exponential
functions. For example,
8.F.A.1
8.F.A.2
8.F.A.3
8.F.B.4.
8.F.B.5
NJ Center for
teaching and
learning.
(group
activities to
develop
mathematical
practices)
See standards listed in MP 2
8.F.A.1
8.F.A.2
8.F.A.3
8.F.B.4.
8.F.B.5
See standards listed in MP 2
identify percent rate of
19
*M.C. = major content
*S.C. = supporting content
*A.C. = additional content, relative to PARCC assessment ★
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.
F.BF.1 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.
F.BF.3 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
20
8. 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
8.F.A.1
8.F.A.2
8.F.A.3
8.F.B.4.
8.F.B.5
See standards listed in MP 2
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. S.C.
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
*M.C. = major content
8.F.A.1
8.F.A.2
8.F.A.3
8.F.B.4.
8.F.B.5
*S.C. = supporting content
*A.C. = additional content, relative to PARCC assessment ★
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.LE.3 Observe using
graphs and tables that a
quantity increasing
exponentially eventually
exceeds a quantity
increasing linearly,
quadratically, or (more
generally) as a polynomial
function.
F.LE.5 Interpret the
parameters in a linear or
exponential function in
terms of a context.
graphs. A.C.
See standards listed in MP 2
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. S.C.
8.F.A.1
8.F.A.2
8.F.A.3
8.F.B.4.
8.F.B.5
S.ID.4 Use the mean and
standard deviation of a data
set to fit it to a normal
distribution and to estimate
population percentages.
Recognize that there are
data sets for which such a
procedure is not
appropriate. Use
3. Use the mean and
standard deviation of a
data set to fit it to a
normal distribution and
to estimate population
percentages. Recognize
that there are data sets
for which such a
procedure is not
6.SP.A.1 Recognize a statistical question as one that
anticipates variability in the data related to the question and
accounts for it in the answers.
21
*M.C. = major content
See standards listed in MP 2
6.SP.A.2 Understand that a set of data collected to answer a
statistical question has a distribution which can be described
by its center, spread, and overall shape.
*S.C. = supporting content
*A.C. = additional content, relative to PARCC assessment ★
calculators, spreadsheets,
and tables estimate areas
under the normal curve.
appropriate. Use
calculators,
spreadsheets, and
tables estimate areas
under the normal curve.
A.C.
S.ID.5 Summarize
categorical data for two
categories in two-way
frequency tables. Interpret
relative frequencies in the
context of the data
(including joint, marginal,
and conditional relative
frequencies). Recognize
possible associations and
trends in the data.
S.ID.6 Represent data on
two quantitative variables
on a scatter plot, and
describe how the variables
are related.
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 function by plotting
and analyzing residuals.
c. Fit a linear function for a
scatter plot that suggests a
4. Summarize and
interpret categorical
data for two
categories in two-way
frequency tables;
recognize associations
and trends in the
data. S.C.
22
5. Represent and
describe data for two
variables on a scatter
plot, fit a function to
the data, analyze
residuals (in order to
informally assess fit),
and use the function
to solve problems.
Uses a given function
or choose a function
suggested by the
context. Emphasize
linear and exponential
models. S.C.
*M.C. = major content
6.SP.A.3 Recognize that a measure of center for a numerical
data set summarizes all of its values with a single number,
while a measure of variation describes how its values vary
with a single number.
6.SP.B.4 Display numerical data in plots on a number line,
including dot plots, histograms, and box plots.
7.SP.A.1 Understand that statistics can be used to gain
information about a population by examining a sample of the
population; generalizations about a population from a
sample are valid only if the sample is representative of that
population. Understand that random sampling tends to
produce representative samples and support valid inferences.
7.SP.A.2 Use data from a random sample to draw inferences
about a population with an unknown characteristic of
interest. Generate multiple samples (or simulated samples)
of the same size to gauge the variation in estimates or
predictions.
7.SP.B.3 Informally assess the degree of visual overlap of
two numerical data distributions with similar variability,
measuring the difference between the centers by expressing
it as a multiple of a measure of variability.
7.SP.B.4 Use measures of center and measures of variability
for numerical data from random samples to draw informal
comparative inferences about two populations.
8.SP.A.1 Construct and interpret scatter plots for bivariate
measurement data to investigate patterns of association
between two quantities. Describe patterns such as clustering,
outliers, positive or negative association, linear association,
and nonlinear association.
*S.C. = supporting content
*A.C. = additional content, relative to PARCC assessment ★
linear association.
8.SP.A.2 Know that straight lines are widely used to model
relationships between two quantitative variables. For scatter
6. Interpret the slope, plots that suggest a linear association, informally fit a
intercept and
straight line, and informally assess the model fit by judging
correlation coefficient the closeness of the data points to the line.
(compute using
technology) of a
8.SP.A.3 Use the equation of a linear model to solve
linear model. M.C.
problems in the context of bivariate measurement data,
interpreting the slope and intercept.
S.ID.7 Interpret the slope
(rate of change) and the
intercept (constant term) of
a linear model in the
context of the data.
S.ID.8 Compute (using
technology) and interpret
the correlation coefficient of
a linear fit.
S.ID.9 Distinguish between 7. Distinguish
correlation and causation.
between correlation
and causation in a
data context. M.C.
Suggested Performance Tasks:
 Exemplars
 Extended projects
 Math Webquests
 Writing in Math/Journal
8.SP.A.4 Understand that patterns of association can also be
seen in bivariate categorical data by displaying frequencies
and relative frequencies in a two-way table. Construct and
interpret a two-way table summarizing data on two
categorical variables collected from the same subjects. Use
relative frequencies calculated for rows or columns to
describe possible association between the two variables.
Stage 2 – Assessment Evidence
Other Evidence:
 Classwork
 Exit Slips
 Homework
 Open-ended questions
 Portfolio
 Quizzes
Stage 3 – Learning Plan
Lesson Format
10 min: Do Now/Journaling (whole class)
30 min: Individual computer work - intervention
30 min: Group work – Complex problems used to develop a deeper understanding using
mathematical practices
10 min: Closure/Assessment/Evaluation
23
*M.C. = major content
*S.C. = supporting content
*A.C. = additional content, relative to PARCC assessment ★
24
*M.C. = major content
*S.C. = supporting content
*A.C. = additional content, relative to PARCC assessment ★