Morris Plains School District
Curriculum Document
Unit Title: Descriptive Statistics
Established Goals (CCS)
S.ID.1-9
S.IC.3
S.IC.5
S.CP.1-5,7,8
Enduring Understandings
 The message conveyed by the data depends on the display.
 The results of a statistical investigation can be used to support or refute
an argument.
 When collecting data, it is important for the results to accurately
represent the situation.
 Variables are symbols that take the place of numbers or ranges of
numbers; they have different meanings depending on how they are
being used.
 Tables, charts, tree diagrams and multiplication can be used to
determine how many ways an event can occur.
 Probability is about predictions over the long term rather than
predictions of individual events.
Essential Questions
 How can the collection, organization, interpretation and display of
data be used to answer questions?
 How can you make and interpret different representations of data?
 How can the representation of data influence decisions?
 How can technology be used to investigate properties of linear
functions and their graphs?
 When does order matter?
 How is probability related to real-world events?
 How can experimental and theoretical probabilities be used to make
predictions or draw conclusions?
Essential Knowledge
Students will know…
 How to find measures of central tendency
 How to examine samples and conduct surveys
 How to make predictions based on the data they collect
 How to determine theoretical and experimental probabilities and
compare results
 How to find the probabilities of simple and compound events
Essential Skills
Students will be able to…
 Use matrices as a method of organizing data
 Analyze data that is summarized using a frequency table
 Analyze the central tendency and dispersion of data
 Use matrices, frequency tables, histograms ,box and whisker plots, tree
diagrams and other representations to describe different types of data
sets
 Sort a set of data into subsets based on various criteria
 Use a sampling technique free of bias when collecting data
 Use standard measures to describe data sets and make estimates,
decisions and predictions
 Analyze the composition and results of a statistical survey
 Use two way frequency tables to analyze data and make predictions
 Determine the number of possible ways to choose objects with regard
to order
 Determine and compare the probability of two events
 Determine the probability of a compound event using simple
probability
1
Algebra
Morris Plains School District
Curriculum Document
Assessments
Performance Tasks:
 “Do Have Game?” Students will work together to conduct a survey of middle school students at Borough School and ask: Do you have a home
gaming system, a portable gamin system, neither or both? Students will work together to determine sample size and consider bias. Students will work
together to tabulate results. Each student will display the results with a frequency table and histogram and another type of graph using Excel.
Students will determine which display is preferable in different settings and to answer specific data questions and why. Students will determine the
experimental probability of a student not having a gaming system. Students will write the findings in a typed summary.
Other Evidence:
 Periodic writing prompts on student self- assessment of progress
 Solving open ended real life word problems using T.A.S.C.
 Quizzes
 Chapter and unit tests
 Cooperative problem solving activities
 Classroom discussion
 Technology based assessments
 Projects
 Homework and text examples
Learning Activities
 Identify and define key terms: measures of central tendency, combination, permutation, matrix, event, complement of an event, outcome, outlier,
quartile, sample space, bias,
 Use POD activities to analyze bias in sampling
 Complete graphic organizer that displays data that can be organized in a table or in a matrix
 Complete activity sheet on addition, subtraction, and multiplication of matrices and check results with partner
 Have students calculate mean, median and mode of their own spelling test scores. Explain which measure best represents the data
 Use the spelling test scores of entire class and display the results in a histogram. Introduce the concept of a bell curve
 Use the spelling test scores of the entire class and calculate the measures of central tendency. Graph the results using a box and whisker plot
 Students will answer writing prompt “How can samples be biased? Explain three different ways”
 Explore fitting a line to data. Have students explore rate of change as slope and write equations for real life problems.
 Complete activities with dice, playing cards and spinners to compare theoretical and experimental probabilities.
 Use Venn Diagrams to summarize information concerning compound events with playing cards.
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Students complete worksheet on finding permutations and combinations using tree diagrams and formulas
 Have students play “Deal or no deal” in teams and write how they came up with a strategy based on probability concepts to complete game.
 Complete examples from text involving line plots and stem and leaf plots.
 Have students work with partner to use the internet to find real life examples of data that is displayed in graphic form from advertisements. Have
students evaluate the display, determine if the display is biased and used the display to predict future results.
2
Algebra
Morris Plains School District
Curriculum Document
Unit Title: Algebra 1: Expressions and Equations
Established Goals (CCS)
N.Q.2-3
A.REI.5,6,12
A.CED.3
A.APR.1
A,SSE.1-2
Enduring Understandings
 Graphs and equations are alternate(and often equivalent) ways for
depicting and analyzing patterns of change
 Useful information about equations and inequalities can be found by
analyzing graphs or tables
 Systems of linear equations and inequalities can be used to model
problems. These systems can have two solutions, one solution or no
solutions
 All of the facts of arithmetic and algebra follow from certain properties
 A single quantity may be represented by many different expressions.
The facts about a quantity may be expressed by many different
equations.
Essential Questions
 How can systems of equations be used to solve real-life situations?
 How can you solve a system of equations or inequalities?
 Can two algebraic expressions that appear to be different be
equivalent?
 How are the properties of real numbers related to polynomials?
 How can factoring be used to model real-life applications?
 How can polynomial operations be used to model real-life examples?
Essential Knowledge
Students will know…
 How to write equations or inequalities to model real-life situations
 How to examine constraints placed on real-world situations
 How to solve systems of equations and inequalities by graphing,
substitution and elimination
 How to use the commutative and associative properties to manipulate
polynomial expressions
 How to perform operations with polynomial expressions
 How to factor polynomials
 How to use the distributive property to multiply polynomials and factor
polynomials
 Factoring a polynomial is essentially the opposite of multiplying its
factors
 Different factoring methods are to be used depending on any given
polynomial
 Factoring of a polynomial requires analyzing to ensure the proper
factoring method
 Not all polynomials can be factored
 Simplification of polynomials will not always result in one term
Essential Skills
Students will be able to…
 Model real-world situations with systems of two linear equations with
two variables
 Solve systems of linear equations by graphing, substitution and
elimination
 Graph linear inequalities in one and two variables
 Solve systems of linear inequalities by graphing.
 Obtain the solutions of linear inequalities systems by detecting the
region where the graphs of the individual inequalities overlap
 Classify polynomials by term and degree
 Simplify polynomials by addition and subtraction
 Simplify polynomials by multiplication (binomial x binomial; binomial x
trinomial)
 Find the GCF of a polynomial factor
 Use the difference of two squares to factor polynomials
 Factor polynomials that are perfect square trinomials
 Factor polynomials in other forms
 Apply polynomial operations to solve equations representing real-life
situations
3
Algebra
Morris Plains School District
Curriculum Document
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Apply factoring of polynomials to solve equations representing realworld situations
Assessments
Performance Tasks:
 Students will research the Cape May- Lewes Ferry. It is a ferry that transports people, cars and buses. Students will determine the space allotted for
buses and cars. Using the internet they will determine how many of each can be transported on a single trip. Use variables to represent the
unknowns. (x for cars and y for buses) and develop the graph of the inequality using paper and pencil and a graphing calculator. Recognizing that
solutions must be whole numbers, students should identify the points whose coefficients are non-negative integers and in the first quadrant on or
below the line.
Other Evidence:
 Periodic writing prompts on student self- assessment of progress
 Solving open ended real life word problems using T.A.S.C.
 Quizzes
 Chapter and unit tests
 Cooperative problem solving activities
 Classroom discussion
 Technology based assessments
 Projects
 Homework and text examples
Learning Activities
 Identify and define key terms: systems of linear equations, inconsistent, consistent, dependent, independent, substitution, elimination, binomial,
trinomial, difference of two squares, factoring by grouping, perfect square trinomial
 POD activities solving real-life word problems with two unknowns
 Writing prompt: “How is solving systems of linear equations different from solving systems of linear inequalities?”
 Use grid slates to solve systems derived from real-life situations by graphing and check by graphing on a calculator
 Complete “find the error” handouts on solving systems of equations and inequalities and justify solutions to a partner
 Writing prompt: “Which method for solving systems do you prefer and why?”
 Complete text exercises on polynomial operations and simplifying
 Use “diamond” model to introduce students to basic factoring of trinomials
 Use five questions inquiry for determining which method of factoring should be utilized
 Complete extensive study of factoring by worksheets, text examples
 Complete POD activities solving area and perimeter with real-life word problems
 Have students work with partner to determine the most cost effective and ascetic type of paver to use to make a patio. Use internet to obtain
prices and layouts for patterns that utilize different size pavers. Have students write a summary of how systems of equations and polynomial
expressions helped model the problem
4
Algebra
Morris Plains School District
Curriculum Document
Unit Title: Algebra 1: Linear and Exponential Relationships
Established Goals (CCS)
N.Q.1-3
A.SSE.1
A.CED.1-3
A.REI.10,11
F.IF.4-6
F.LEI.1-3,6
F.BF.3
G.SRT.6,8
Enduring Understandings
 Graphs can be used to visually represent the relationship between two
variable quantities as they change
 The value of one variable may be uniquely determined by the value of
another variable. These relationships may be represented using, words,
tables, equations, ordered pairs and graphs
 Functional relationships can be expressed in real contexts, graphs,
equations, words and tables; each representation is simply a different
way of expressing the same idea
 Many real-world functional relationships can be represented by
equations and can be used to find solutions
 Properties of exponents make it easier to simplify expressions
 Real-world situations involving exponential relationships can be solved
using multiple representations
Essential Questions
 How can you represent and describe functions?
 How can you use mathematical models to describe change or
change over time?
 Can functions describe real-world situations?
 How can technology be used to investigate properties of linear
functions and their graphs?
 How are patterns of change related to the behavior of functions?
 How can patterns, relations, and functions be used to best describe
and help explain real-life situations?
 What does the slope of a line indicate about the line?
 What information does the equation of a line give you?
 How can you make predictions based on a trend line?
 How can you model situations using exponents?
 How can you represent numbers less than 1 using exponents?
 How can you simplify expressions involving exponents?
 What are the characteristics of exponential functions?
 How are radical expression represented?
 How can you solve a radical equation?
 How can geometric/algebraic relationships best be represented and
verified?
Essential Knowledge
Students will know…
 Ratios can be used to show a relationship between changing
quantities. If this ratio is constant the variables have a special
relationship called a direct variation
 Two sets of numerical data can be graphed as ordered pairs. If the
two sets of data are related, a line on the graph can be used to
predict values
Essential Skills
Students will be able to…
 Use proportional reasoning to understand problem situations
 Determine how quantities vary directly and indirectly
 Use equations and graphs to model variation and solve real-world
variation problems
 Investigate and write recursive(arithmetic) and geometric sequences
 Define and calculate the slope of a line
5
Algebra
Morris Plains School District
Curriculum Document
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Functions are a special type of relation where each value in the
domain is paired with exactly one value in the range
A line on a graph can be represented by a linear equation.
The relationship between two lines can be determined by comparing
their slopes and y-intercepts
Two sets of numerical data can be graphed as ordered pairs. If the
two sets of data are related, a line on the graph can be used to
predict values
A line on a graph can be represented by a linear equation.
The relationship between two lines can be determined by comparing
their slopes and y-intercepts
The idea of exponents can be extended to include zero and negative
exponents
You can use rational exponents to represent radicals
Operations can be performed with radical expressions and radical
expressions can be simplified using the multiplication and division
properties of square roots
An object’s location on a plane or in space can be described
quantitatively.
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Write an equation for a line in slope intercept form given a recursive
pattern, a graph or data
Write equations in standard, point slope or slope intercept forms
Solve and graph linear equations
Interpret graphs of real-world situations using terminology(linear,
nonlinear, increasing, decreasing, rate of change, continuous,
discrete)
Evaluate functions by substitution
Work with absolute values, absolute value functions and its graph
Work with the squaring and square root functions and their graphs
Simplify expressions involving negative and zero exponents
Use properties of exponents to rewrite expressions
Write exponential equations that model real-world growth and decay
Write numbers in scientific notation
Extend knowledge about slopes to parallel and perpendicular lines
Determine the midpoint and distance between points on a coordinate
plane
Identify and use the Pythagorean Theorem and its applications
geometrically and algebraically
Work with radical expressions; squaring, simplifying and applying to
solve radical equations
Assessments
Performance Tasks:
 “Buying a car project” Students will finance the purchase of their first car. They will assume they have graduated from college and are working at a
job that pays a yearly salary of $45000. Students will create a realistic budget of living expenses. They will create an equation for their expenses and
income and represent the break- even point graphically. They will use the internet to find a car that fits their lifestyle and financial needs. They will
use the finance calculation (growth formula) to determine the monthly cost of financing their car.
Other Evidence:
 Periodic writing prompts on student self- assessment of progress
 Solving open ended real life word problems using T.A.S.C.
 Quizzes
 Chapter and unit tests
 Cooperative problem solving activities
 Classroom discussion
 Technology based assessments
 Projects
 Homework and text examples
Learning Activities
 Identify and define key terms: arithmetic sequence, recursive sequence, common difference, second difference, function notation, linear function,
6
Algebra
Morris Plains School District
Curriculum Document
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vertical line test, correlation, line of best fit, slope, x and y intercept, slope intercept form, compound interest, growth factor, exponential function,
absolute value function, decay, radical, square root function
Students will work with partner and use sales flyers from newspapers or internet to justify best buy purchases. They will determine discount rate and
percentage change from one store to another for similar products
POD activities that have students solve word problems involving absolute value, linear, exponential and square root functions to reveal the shapes
of their graphs.
Students will complete calculator activities that show how graphs of lines change when coefficients and intercepts change
Use grid slates to graph linear equations to develop concept of slope and x and y intercepts.
Use word problems about speed and distance to derive concept of rate of change over time. Check results with partner
Complete workbook pages on slopes of all types of lines
Students will answer writing prompt” When is a relation also a function?”
Students will complete text examples that involve writing equations of lines in slope intercept form, point slope form and standard form
Students will use linear graphs and trend lines to make predictions about data and present findings to class.
Students will use graphing calculator to find the slopes of perpendicular and parallel lines and derive a rule for obtaining their slopes
Students will manipulate an absolute value parent function to see effects of translations using grid slates and calculators
Students will complete worksheets to become proficient in simplifying radicals and performing operations with radicals
Students will answer writing prompt:” How does a square root function differ from other functions?”
Students will connect geometry and algebra concepts by working with triangles to find missing side lengths using the Pythagorean Theorem,
distance and midpoint formulas.
Use maps from internet to show how traveling the “hypotenuse” is the shortest distance between two cities or two points
Complete text activities to explore properties and operations with exponents
Use calculator and banking interest rates to show how money can grow exponentially. Use example of National Debt to demonstrate the
acceleration and write growth in scientific notation
Connect exponential decay to carbon dating and fossils in conjunction with science activity
7
Algebra
Morris Plains School District
Curriculum Document
Unit Title: Algebra 1: Quadratic Functions and Modeling
Established Goals (CCS)
A.SSE.3
A.CED.1-3
A.APR.3
A.REI 1,4,7,11
F.BF.1
F.IF.4,5,7,8
F.LE.1-3
Enduring Understandings
 A function that models a real-world situation can be used to make
estimates or predictions about future occurrences
 Linear, quadratic or exponential functions can be used to model
various data sets
 Functions can be represented in a variety of ways, such as graphs,
tables, equations or words. Each representation is particularly useful in
certain situations. Some important families of functions are developed
through transformations of the simplest form of the function
 Graphs and equations are alternative)and often equivalent) ways for
depicting and analyzing patterns of non-linear change
 Mathematical models can be used to describe physical relationships;
these relationships are often non-linear
 Real-world situations involving quadratic relationships can be solved
using multiple representations
Essential Questions
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What situations can be analyzed using transformations and
symmetries?
 How can transformations be described mathematically?
 How can mathematical language be used to describe non-linear
change?
 What are characteristics of quadratic functions?
 How can you solve a quadratic equation?
 How can you use quadratic functions to model real-life situations?
Essential Knowledge
Students will know…
 That the family of quadratic functions models certain situations where
rate of change is not constant. These functions are graphed by a
symmetric curve with a highest or lowest point corresponding to a
minimum or maximum value
 That in the quadratic function, the value of b translates the position of
the axis of symmetry
 Quadratic equations can be solved by a variety of methods, including,
graphing, finding the square root, using the zero product property or
the quadratic formula
 Systems of linear and quadratic equations can be solved graphically
and algebraically. The system can have two solutions, one solution or
no solutions.
Essential Skills
Students will be able to…
 Write equations of transformed functions and graph them
 Explore concept of a parent function and its family
 Model real-world data with transformed equations
 Investigate rational functions and explore basic transformations
 Use quadratic functions to model and solve equations based on
relationships for projectiles (time and height)
 Solve quadratic equations using graphs, tables, symbolic methods,
factoring and the quadratic formula
 Find the x intercepts and vertex of a parabola by graphical and
symbolic methods
 Convert quadratic equations among vertex, factored and general
forms
 Determine that extraneous solutions exist
8
Algebra
Morris Plains School District
Curriculum Document
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Students will use the discriminant of a quadratic equation to analyze
the number of times a function crosses the x axis
Assessments
Performance Tasks:
 “What size box?” Students investigate what size square to cut from each corner of a rectangular piece of cardboard in order to make the largest
possible open-top box. Students make models, record the size of the square and the volume for each model, plotting the points on a graph using
spreadsheet software. They note the relationship is not linear and make a conjecture about maximum volume. Students also generate an algebraic
expression and equation describing this situation
Other Evidence:
 Periodic writing prompts on student self- assessment of progress
 Solving open ended real life word problems using T.A.S.C.
 Quizzes
 Chapter and unit tests
 Cooperative problem solving activities
 Classroom discussion
 Technology based assessments
 Projects
 Homework and text examples
Learning Activities
 Identify and define key terms: axis of symmetry, completing the square, discriminant, minimum, maximum, parabola, quadratic formula, vertex, zero
of a quadratic function
 POD activities that use quadratic equations to solve projectile word problems, work with partner to verify solutions
 Writing prompt: “How is a quadratic function different than a linear or an absolute value function?”
 Use grid slates to graph quadratic equations. Demonstrate how vertex form and standard form are derived
 Complete text book examples on using the zero product property to find the zeros of a function and how to obtain zeros using the quadratic
formula
 Use calculator to show the translations of the parent quadratic equation
 Complete “find the error” handouts with partner on solving real life quadratic equations
 Writing prompt:” Describe a method for obtaining solutions to quadratic functions.”
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Students will work with partner to plan a fireworks display. They will plan the height and timing of each display using the projectile formula and use
maximum values and vertex points to create a unique display sequence
9
Algebra
Morris Plains School District
Curriculum Document
Unit Title: Algebra 1: Relationships between Quantities and reasoning with Equations
Established Goals (CCS)
N.RN.1-3
N.Q.1-3
A.CED.1-3
A.REI.1-7,10-12
A.SSE.1
Enduring Understandings
 Algebra uses symbols to represent quantities that are unknown or that
vary
 Mathematical phrases and real world relationships can be
represented using symbols and operations
 Logical patterns exist and are a regular occurrence in mathematics
and the world around us
 Algebraic representation can be used to generalize patterns and
relationships
 Properties of geometric patterns can be analyzed and described
mathematically/algebraically
 Equations and inequalities can be solved by isolation, inverse
operations and mathematical equality
 Inequalities represent multiple solutions
 Algebraic representations exist for many real-life problems
Essential Questions
 How can you represent quantities, patterns and relationships?
 How are properties related to algebra?
 How can we use algebraic representations and expressions to analyze
patterns?
 How can you use an algebraic model to represent a real-life problem?
 What kind of relationships can proportions represent?
 How can you solve equations and inequalities?
 Can equations and inequalities that appear to be different be
equivalent?
Essential Knowledge
Students will know…
 That the relationships between quantities can be represented in
different ways, including tables, equations and graphs
 That powers can be used to shorten the representation of repeated
multiplication
 That equivalent equations and inequalities have the same solutions
 That properties of numbers and equality can be used to find solutions
 That proportional reasoning can be used to find unknown quantities
 That equations and inequalities can describe, explain and predict
various aspects of the real world
 How to solve percent problems and find percent increase and
decrease
 That real-life problems can be represented and solved by using
absolute value equations and inequalities
Essential Skills
Students will be able to…
 Investigate numeric, algebraic and geometric patterns
 Review operations with rational numbers
 Use exponents to represent repeated multiplication
 Use variables in different ways
 Use numerical and algebraic expressions
 Use rates, ratios and percents to solve real-life problems
 Add, subtract and multiply polynomial expressions
 Factor simple polynomial expressions by applying the principles of the
distributive property
 Use a graphing calculator and resources to evaluate expressions
 Solve equations using inverse operations
 Solve and graph inequalities in one variable
 Solve absolute value equations
 Translate real life problems to algebraic equations and inequalities and
find the solutions
10
Algebra
Morris Plains School District
Curriculum Document
Assessments
Performance Tasks:
 “Let’s take Stock” Students will track the stock performance of 2 companies listed on the New York Stock Exchange. They will create graphs, find
percentage change over time, profit/loss and use the data collected to determine future performance. They will also compare the companies’
performance to that of the Dow Jones Industrial Average and use this information to decide if investing money in the stock market is advisable.
Other Evidence:
 Periodic writing prompts on student self- assessment of progress
 Solving open ended real life word problems using T.A.S.C.
 Quizzes
 Chapter and unit tests
 Cooperative problem solving activities
 Classroom discussion
 Technology based assessments
 Projects
 Homework and text examples
Learning Activities
 Identify and define key terms: absolute value, equation, expression, inequality, coefficient, radical, rational number, irrational number, inverse,
distributive property, literal equations, relative error, set notation, interval notation, subset, complement of a set, union, intersection, disjoint sets
 Use POD activities to solve real-life word problems involving equations, absolute value and inequalities.
 Complete workbook and textbook examples of solving all types of equations and inequalities.
 Use Venn Diagrams to introduce set notation, subsets, union and intersection of sets
 Students answer writing prompt: “Compare different representations for an irrational number you would expect to encounter in everyday life.
Discuss appropriate circumstances for the use of each”
 View and discuss online video of the Fibonacci Sequence and how this special sequence is found in nature.
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Work with partner to derive a method to write expressions for function tables to introduce rate of change concept
 Use slates to play math millionaire game with partners to ensure mastery of solving equations and inequalities
 Use grid slates to graph solutions to compound inequalities
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Students answer writing prompt: “Compare the process of solving equations and inequalities. How are they similar? How are they different?”
 Complete “find the error “ worksheets for translating expressions, absolute value equations, set notation, inequalities and proportion and percent
problems
 Explore the applications of Pascal’s triangle for solving problems related to combinations and fractals. Complete activity with partner
 Review list of common literal equations and solve problems with their applications. Check results with partner Examples: mass and density,
Fahrenheit/Celsius conversion, rate/time/distance and various geometric formulas
11
Algebra