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MARLBORO CENTRAL SCHOOL DISTRICT
CURRICULUM MAP
_________Math 6___________________
Course Title
Title or Topics
Concepts
(Unit
(understandings)
organizing idea)
Purposes of numbers
September
Number sense in measurement
Building Number Concepts
October
Multiplying whole & decimal numbers
November
Divide whole numbers, decimals
December
Geometry
January
Fraction concept and number theory adding,
Subtraction
__________Grade 6________________
Grade Levels
Skills
Major Assessments
Time Frame
(What students
(Tests, projects, etc.)
(Number of
actually do)
weeks)
In order of importance
- Tests
- Homework
- Projects
3-4 wks +
In order of importance
- Tests
- Homework
- Projects
3-4 wks +
In order of importance
- Tests
- Homework
- Projects
3-4 wks +
Basic ideas-points, rag, segments, angles etc. angle
measurement-Meaning of a degree
Polygons – triangles, tiles problem
solving by solving a simpler problem
Circles-circumferences, area problem
solve using logical reasoning
Congruent & similar figures,
transformations 3 dimensional figures, surface area
In order of importance
- Tests
- Homework
- Projects
3 wks +
Divisibility rules - Prime & composite numbers
Greatest common fracture-Least common multiples
Prime factorization comparing & ordering fractions,
+- fractions same & differences denominationsEstimating sums & differences
Egyptian & Roman numerals-Problem solve – too
little or too much information-Mixed numbers, add
& subtract
In order of importance
- Tests
- Homework
- Projects
3-4 wks +
First Quadrant Graphing
Number patterns
Problem solving-Guide
Whole numbers & decimals
Number sense
Exponent’s & powers
Multiplying with multiples of 10
Estimating products
Problem solving
a) choosing an operation
b) using table
Multiple decimals
Square roots
Mental math, estimates
Interpret all parts of division, word
problem
Problem solving – write equation,
choosing a strategy, order of
operations
Name whole & decimal numbers
Plot point & ungrid
Rounding whole & decimal
numbers
Estimate add & subtract by
a) Rounding to a place
b) Finding a range
Problem solving using patterns,
table, equations
Add & subtract whole & decimal
numbers
Associative, commutative,
distributive properties
Multiple properties of 1 and 0
Standards & exponent form of a
number
Expanding using exposure
Problem solving . reading a table
Estimating using cluster method
Ordering decimal numbers
Planets = A.U. distances
Estimate quotients
1, 2, 3 digit divisions
O’s in quotient
Decimal & whole numbers
division
Fractions as decimals
Repeating decimals
Ordering fractions & decimals
Word problems
Topics
(Unit Title or
organizing idea)
February
Concepts
(understandings)
See January
Using measurement
April
Relating Geometry & measurement
May
Ratio, Properties, percent, and relating %, fractions,
decimals to each other
June
Statistic, probability, In ledgers
Follow book – homework assignments
from book
Worksheets from book & teacher made
Problem of day – teacher and book
generated
Some hand on activity simulation
Do practice tests, then tests and
sometime re-tests
Major Assessments
(Tests, projects, etc.)
Time Frame
(Number of
weeks)
In order of importance
Tests
Homework
Projects
2-3 wks
Customary & metric units of length,
are, volume – estimating & measuring
with ruler-custom & metric weight &
capacity, mass conversion – custom &
metric problem solve
Use data from table
In order of importance
Tests
Homework
Projects
3-4 wks
Perimeter, circumferences, area of
rectangle, squares, circles, paralleling
… surface area, volume problem solve:
a) Table
2) Use formula
In order of importance
Tests
Homework
Projects
3-4 wks
% & decimal & fractions
Find % of a number
Estimations, multiple step problems,
Find what % one number is of another,
% > than 100% and <1%
In order of importance
Tests
Homework
Projects
3-4 wks
Mean, median, mole, range,
interpreting graphs, circle graphs,
probability, counting, choices, making
………..,+ x divide integers, graphing
in 4 quadrants.
In order of importance
Tests
Homework
Projects
2-3 wks
January continued
March
Skills
(What students
actually do)
MARLBORO CENTRAL SCHOOL DISTRICT
CURRICULUM MAP
_______Math____________________
Course Title
Title or Topics
Concepts
(Unit
(understandings)
organizing idea)
Large numbers with place value greater
September
than 1000
Number sense & whole number operations
Problem solving strategies
October
Number sense & whole number operations
Problem solving strategies
November
Decimal concepts & operations
December
Decimal concepts & operations
January
Measurement
Metric & Customary
(some) Geometry
Skills
(What students
actually do)
_________Grade 6_______________
Grade Levels
Major Assessments
Time Frame
(Tests, projects, etc.)
(Number of
weeks)
Standard & exponents form
Read & write large numbers
Compare & order large numbers
Sequence large numbers
Daily class problems
Class disc.
Individual response checks
Numbers & exponents
Factors, multiples
Prime & composite numbers
Probability
Prime factorization
Solve problems
Least common multiple
Greatest common factor
Probability
Section quizzes
Chapter test
Write about math
Applicable word problems
Decimals are ……whole numbers
Decimal places can be rounded
Decimals can be added, subtracted,
multiplied, & divided
Round decimals
Compare & order decimals
Estimate sums, differences, products
quotients
Daily class problems
Class discussion
Individual response checks
In order of importance
Tests
Homework
Projects
Add, subtract, multiple, divide decimals
Section quizzes
Chapter test
Write about math
Applicable word problems
Metric system
Customary system
Area, volume, perimeter using above
units of measure
Measure with metric & customary rulers
Liquids & moss measurement metric &
Customary
Add & subtract units of measure
Find area, volume, perimeter
Write about math
Daily class problems
Applicable word problems
Class discussion
Individual response checks
Section quizzes
Chapter test
Estimate
Preparation for mental math
Varies about 8 wks
Various about 8 wks
Varies about 4 wks
Topics
(Unit Title or
organizing idea)
February
Concepts
(understandings)
Skills
(What students
actually do)
Fractions as part of a whole
Fractions can be compared, sequenced,
added or subtracted only with like
denominators
Multiply by a fraction < 1 gives a
product smaller than started
Divide by a fraction < 1 gives a
quotient larger than the number
started with
Fractions as part of a whole
Fractions can be compared, sequenced,
added or subtracted only with like
denominators
Multiply by a fraction < 1 gives a
product smaller than started
Divide by a fraction < 1 gives a
quotient larger than the number
started with
Find missing number in equal fractions
Reduce fractions to lowest terms
Find common denominators
Convert between improper fractions and
mixed numbers
Convert between fractions & decimals
Add, subtract, multiply, divide fractions,
whole numbers & mixed numbers
Write about math
Daily class problems
Class discussions
Individual response checks
Section quizzes
Chapter test
Applicable word problems
Find missing number in equal fractions
Reduce fractions to lowest terms
Find common denominators
Convert between improper fractions and
mixed numbers
Convert between fractions & decimals
Add, subtract, multiply, divide fractions,
whole numbers & mixed numbers
Write about math
Daily class problems
Class discussions
Individual response checks
Section quizzes
Chapter test
Applicable word problems
Two quantities can be expressed as a
Ratio
A proportion is made of two ratios
A percent is a ratio that compares to
100
Find missing numbers in equal ratios
Test to see if two ratios form a
Proportion
Solve proportions using cross
Write about math
Daily class problems
Class discussions
Individual response checks
Section quizzes
Chapter test
Varies about 4 wks
Classify lines
Names, describe angles
Measure angles
Classify polygons
Identify quadrants
Find area, volume, perimeter
Write about math
Daily class problems
Class discussion
Individual response checks
Section quizzes
Chapter test
Varies about 4 wks
Geometry
Lines, segments, rays
Angles’ measured in degrees
Line symmetry
Definition of volume, are, perimeter
June
Use graphs to compare numbers over
time + as parts of a whole
Use graphs to organize & display
Information
Construct bar, line, pie graphs
Calculate mean, median, mode
Write about math
Daily class problems
Class discussions
Individual response checks
Section quizzes
Chapter test
Varies about 4 wks
Fraction concepts & operations
March
Fraction concepts & operations
April
Ration, proportion, percent
May
Graphing
Major Assessments
(Tests, projects, etc.)
Time Frame
(Number of
weeks)
Varies about 8 wks
MARLBORO CENTRAL SCHOOL DISTRICT
CURRICULUM MAP
_______Math 7_______
Course Title
Title or Topics
(Unit
organizing idea)
September
Order of operations
Evaluating expressions
Math terminology
Solving 1 step & 2 step equations
Problem solving
October
Decimals
Fractions (a little bit)
Problem solving
Number theory
November
Fractions
Problem solving
Coordinate Geometry
December
Geometry
Problem solving
January
(Measurement)
Customary units
Metric units
Problem solving
__________Grade 6__________
Concepts
(understandings)
Skills
(What students
actually do)
Grade Levels
Major Assessments
Time Frame
(Tests, projects, etc.)
(Number of
weeks)
PEMDAS
Understanding variables & solving for
the variable
Math language
Ex.) addition, sum, plus, total…etc.
Subtraction – decreased by,
Difference
Write expressions using variables
Translate words into mathematical
Sentences
Write & solve equations
Graded homework
Classroom test
Quiz
. Assessment questions
3-4 wks
Place value
Changing decimals to fractions
Changing fractions to decimals
Rules for divisibility
Exponents
Prime & composite
GCF, LCM
Factor tree
Use divisibility rules to find the quotient
Distinguish between prime & composite
Numbers
Find the LCM for 2 numbers
Add, subtract, multiply, divide decimals
Graded homework
Classroom test
Assessment questions
Quiz
3-4 wks
Equal fractions
Improper fractions, mixed numbers
Comparing
Estimation
Adding, subtracting, multiplying,
dividing fractions
Plotting points, setting up y & x axis
Understand basic operations with
Fractions
Understand fractions in real world
Plot points on graph
Graded homework
Classroom test
Assessment questions
Quiz
3-4 wks
Definitions (points, lines, planes, etc.)
Angles (types, measurement)
Triangles classification
Polygons
Congruent & similar
Circles
Quadrilaterals
Corresponding parts
Translations
Classify & describe lines
Name & describe angles
Measure angles
Classify triangles
Classify polygon
Classify quadrilaterals
Graded homework
Classroom test
Assessment questions
Quiz
3-4 wks
Customary units of length, capacity,
Mass
Metric units length, capacity, mass
Metric table
Conversions
Time
Compare measurements of both
customary & metric
Using the appropriate measurement to
Measure
Graded homework
Classroom test
Assessment questions
Quiz
3-4 wks
Topics
(Unit Title or
organizing idea)
February
Ratio & proportions
Problem solving
March
Percents
Problem solving
Measurement of shapes
April
Probability
Problem solving
May
Statistics
Problem solving
June
Negative numbers
Problem solving
Review
Concepts
(understandings)
Skills
(What students
actually do)
Major Assessments
(Tests, projects, etc.)
Time Frame
(Number of
weeks)
Setting up ratios
Writing ratios
Setting up proportions
Word problems (setting up proportion)
(in order to solve)
Similar figures
Solving percent w/proportions)
Scale drawings
Find what % of one number is of another
number
Writing & solving proportions
Tests
Graded homework
Assessment questions
Quiz
3-4 wks
Percents & decimals
Percents & fractions
Finding a % of a number
Interest
Estimation
Multiple step
Area & volume of figures
Surface area
Circumference
Sample space
Combinations, permutations
Chance events
Finding what % of one number is of
another number
Finding interest in real life situation
Tests
Graded homework
Assessment questions
Quiz
3-4 wks
Construct experiments to determine
Probabilities (use of manipulatives)
Made predictions and compare results
Tests
Graded homework
Assessment questions
Quiz
3-4 wks
Histograms
Data collection
Frequency tables
Stem & leaf plots
Mean, median & mode
Use of mean, median & mode
Read & construct displays of data using
graphs
Tests
Graded homework
Assessment questions
Quiz
3-4 wks
Operations with negative numbers
Solving equations
Number sense
Using basic operations with negative
Numbers
Solving equations with negative numbers
Tests
Graded homework
Assessment questions
Quiz
3-4 wks
MARLBORO CENTRAL SCHOOL DISTRICT
CURRICULUM MAP
_________Math 8 - Regular_______________
Course Title
Title or Topics
Concepts
(Unit
(understandings)
organizing idea)
Review whole numbers (operative)
September
Patterns
Order of operations: whole numbers
Integer Review: addition & subtraction
Number line theory: = > <
October
Fractions (Addition & subtraction)
Decimals (All operations)
Rates, ratios, proportions
November
Problem solving
December
Geometry
Basic Polygons – area – volume
January
Geometry continued
Skills
(What students
actually do)
____________Grade 8__________
Grade Levels
Major Assessments
Time Frame
(Tests, projects, etc.)
(Number of
weeks)
Graded homework
Classroom tests
Assessments questions
Take home tests
Textbook exams
Workbook problems
2-3 ongoing
Tables
Word problems
Test – homework assignments
Teacher supplements – dottos
Sample assessment questions
Drill review exercises;
Cumulative reviews and practice
Board and seat work
Multiples/factors
Primes & composite
Round – estimates
Ruler measurement
Cost – products (%) basic
Text – homework assignments
Teacher supplements – dottos
Sample assessment questions
Drill review exercises
Cumulative reviews and practice
Board and seat work
Graded homework
Classroom tests
Assessments questions
Take home tests
Textbook exams
Workbook problems
2+
Making diagrams
View diagrams
Make a list (patterns)
Pick out facts (table)
Text – homework assignments
Teacher supplements – dottos
Sample assessment questions
Drill review exercises
Cumulative reviews and practice
Board and seat work
Graded homework
Classroom tests
Assessments questions
Take home tests
Textbook exams
Workbook problems
2+
Name polygons – def.
Properties also
Basic formulas
Variables usage
Text – homework assignments
Teacher supplements – dottos
Sample assessment questions
Drill review exercises
Cumulative reviews and practice
Board and seat work
Graded homework
Classroom tests
Assessments questions
Take home tests
Textbook exams
Workbook problems
3+
Volume of polyhedrons
Idea of polygons
Perimeter revisit
Measurement (side & angles)
Angle identify fractions
Text – homework assignments
Teacher supplements – dottos
Sample assessment questions
Drill review exercises
Cumulative reviews and practice
Board and seat work
Graded homework
Classroom tests
Assessments questions
Take home tests
Textbook exams
Workbook problems
2+
Topics
(Unit Title or
organizing idea)
February
Percents (+, >, < 100%)
March
Pythagorean: theorem
April
Solving Equations (one variable)
Graphing (coordinate)
Algebra
May
Probability
June
General Review
Concepts
(understandings)
Skills
(What students
actually do)
Major Assessments
(Tests, projects, etc.)
Time Frame
(Number of
weeks)
Pictures – rates, ratios
Revisit rates –ratios proportions
% key on calculator
Text – homework assignments
Teacher supplements – dottos
Sample assessment questions
Drill review exercises
Cumulative reviews and practice
Board and seat work
Graded homework
Classroom tests
Assessments questions
Take home tests
Textbook exams
Workbook problems
3-4 +
Squares (proportion)
Square root (calculator)
Area – Plane figure
P…………………
Coordinate……..
Text – homework assignments
Teacher supplements – dottos
Sample assessment questions
Drill review exercises
Cumulative reviews and practice
Board and seat work
Graded homework
Classroom tests
Assessments questions
Take home tests
Textbook exams
Workbook problems
2+
Equations/Inequalities
Balance equations
…………………..
Text – homework assignments
Teacher supplements – dottos
Sample assessment questions
Drill review exercises
Cumulative reviews and practice
Board and seat work
Graded homework
Classroom tests
Assessments questions
Take home tests
Textbook exams
Workbook problems
2-3+
Outcomes
Tree design
Multiply principal (counting)
In dept. (dept meeting)
Graded homework
Classroom tests
Assessments questions
Take home tests
Textbook exams
Workbook problems
Graded homework
Classroom tests
Assessments questions
Take home tests
Textbook exams
Workbook problems
2+
Graded homework
Classroom tests
Assessments questions
Take home tests
Textbook exams
Workbook problems
Graded homework
Classroom tests
Assessments questions
Take home tests
Textbook exams
Workbook problems
3+
MARLBORO CENTRAL SCHOOL DISTRICT
CURRICULUM MAP
_______Math 8________________
Course Title
Title or Topics
(Unit
organizing idea)
September
Problem solving
Patterns
October
Number and numeration
Algebraic
November
Geometry
December
Probability
January
Statistics &
Data Analysis
Concepts
(understandings)
_______Grade 8____________
Grade Levels
Skills
Major Assessments
Time Frame
(What students
(Tests, projects, etc.)
(Number of
actually do)
weeks)
Develop and apply strategies to solve a
wide variety of problems extending to
multi-step and non-routine problems
5 steps to problem solving
Strategies include:
. patterns, diagrams
. trial and error
. simpler but related problems
. work backwards
Problems of the week
Presentation of Pow’s
Test
Homework
Problem based learning projects
4 wks
Review basic operations with whole
Numbers
Integers
Rational numbers
Patterns
Functions
Order of operations
Using a problem solving foundation
In/our tables
Weekly problems of the week
In/out of class assessments
1-Patterns
2-Probability & s… game of Pig
4 wks
Consecutive sums
Using a counter example
Angle sums in polygons
Types of angles
Diagonals of a polygon
Measuring angles with protractor
Constructing regular polygons with
protractor and straightedge
Weekly problems of the week
In/out of class assessments
1-Patterns
2-Probability & s… game of Pig
4 wks
Use experimental and theoretical
probability to represent and solve
problems involving uncertainty
Frequency histograms
Game strategies
Conduct/predict outcomes of
Experiments
Students …………
Titanic WebQuest
4 wks
Combinations/permutations
Probability modeling
Circle graphs
Sample space
Tree diagrams
Exponents
Mean/median/mode
Student …. For outcomes
Excel
4 wks
Topics
(Unit Title or
organizing idea)
February
Concepts
(understandings)
Skills
(What students
actually do)
Major Assessments
(Tests, projects, etc.)
Indirect measurement
Pythagorean ….
Area/perimeter
Square roots
Locating points on coordinates grid
Perpendicular/parallel links
Find height of school building, flag pole
Using – proportions
Trig ratios
Ratio/similar triangles
Proportional reasoning
Trig ratios (…………..)
Measure the height of building/flagpole
+/-/x/÷ Equations
Two step equations
Write variable expressions
Problem solving
Modeling equations
Using tiles
Graphing calculator to explore lines,
slopes, system or equations
Graphing in computer lab
2 quizzes
4 wks
Graphing equations
Slope intercepts
Systems of equations
Inequalities with one variable
Inequalities with two variables
Battleship using points & lines
Graphing in computer lab
2 quizzes
1 unit test
4 wks
Graphing
Coordinate plane
June
Transformational geometry
Symmetry
Modeling transactions, rotations,
dilations, reflections
1 quiz
1 project – Ana-m….. art
4 wks
Geometry
Measurement
-direct
-indirect
March
Measurement
April
Equations
May
Transformational Geometry
Review
Outside measurements
Performance Assessment on indirect
Measures
Time Frame
(Number of
weeks)
6 wks
6 wks
MARLBORO CENTRAL SCHOOL DISTRICT
CURRICULUM MAP
_________Pre-Sequential___________
Course Title
Title or Topics
Concepts
(Unit
(understandings)
organizing idea)
Addition
September
Subtraction
Whole numbers
Decimals
October
Fractions
November
Decimals <-> Fractions
Percents
December
Integers
Basic Algebra
January
Equation solving
Skills
(What students
actually do)
_______Grade 9_________
Grade Levels
Major Assessments
Time Frame
(Tests, projects, etc.)
(Number of
weeks)
Students can:
. add, subtract, multiply, divide whole
numbers
. write and read whole numbers, decimal
and place values
. round-off whole numbers, decimal
. whole numbers problem solve decimals
– money problems
Students can:
. add, subtract, multiply, divide fractions
. change mixed <-> Improper
. compare using number line
. find % of number
. apply proportions and %
. w.p. finding/using sales tax
2 tests
Homeworks
Worksheets
Quizzes
2
3 tests
Homeworks
Worksheets
Quizzes
4
Compare and order decimals
Conversions of % <->
Decimals <-> fractions
Ratios
Percent of numbers
Sales tax word problems
Students can:
. convert % -decimal –fraction
. problem solve with %
. find % of number
. apply proportion and %
. w.p. finding/using sales tax
3 tests
Homeworks
Worksheets
Quizzes
2
Add/subtract/multiply/divide using
number lines
Absolute value
Variables and expressions
Order of operations
Combining like terms
Substitutions, distributive properties
Students can:
. add-subtract-multiply-divide INT
. use number line to compare integers
. use absolute value
. build vocabulary
. understand PEMDAS
. be able to combine like terms
. be able to distribute
Students can:
. solve one operation linear equation
. solve two operation linear equation
. understand balance and opposite
2 tests
Homeworks
Worksheets
Quizzes
2
2 tests
Homeworks
Worksheets
Quizzes
4
Multiplication
Division
Read & write
Rounding word problems
Add/subtract/multiply/divide
Mix <-> Improper
Compare and order fractions
Word problems
Single operation equation
Double operation equation
2-3
2-3
2
Topics
(Unit Title or
organizing idea)
February
Equation solving II
March
Exponents
April
Writing Algebraic
Expressions & Equations
May
Inequalities
Review
June
Review
Concepts
(understandings)
Skills
(What students
actually do)
Combining like terms within equations
Variables on both sides of the equation
Distributive property within equation
Solving
Students can:
. solve equation with parenthesis,
variables on both sides, and combining
. understand balance/opposite
2-3 tests
Homeworks
Worksheets
Quizzes
4
Bases, exponents and powers
Evaluating exponents
Multiplying & dividing like bases
Power to power
Students can:
. understand exponent and concepts
. expand exponents
. multiply-divide like base
. multiply power to power
. build vocabulary
2 tests
Homeworks
Worksheets
Quizzes
3-4
Translating verbal phrases into
mathematical expressions
Translating verbal sentences into
mathematical sentences
Students can:
. identify variables in word problems
. build computation vocabulary
. write expressions and equations from
words
2 tests
Homeworks
Worksheets
Quizzes
3-4
Number line
Graphing solution sets to single
variable inequalities
Students can:
. build vocabulary
. use a number line to show inequalities
. use rules of inequalities
. find solution sets of inequality
2 tests
Homework
Quizzes
Worksheets
2
Final exam
1-2
Review
Major Assessments
(Tests, projects, etc.)
Time Frame
(Number of
weeks)
2-3
MARLBORO CENTRAL SCHOOL DISTRICT
CURRICULUM MAP
_________Sequential 1A______________
Course Title
Title or Topics
Concepts
(Unit
(understandings)
organizing idea)
September
Integers
Basic Algebra’s
October
Basic Algebra
Exponents
November
Solving equations
December
Inequalities
January
Writing expressions and equations from words
Skills
(What students
actually do)
_______________Grade 9 – 10_________
Grade Levels
Major Assessments
Time Frame
(Tests, projects, etc.)
(Number of
weeks)
Add/subtract/multiply/divide
Number line
Absolute value
Order of operations
Combining like terms
Distributive property
Variables and substitutions
Students can:
. add, subtract, multiply, divide all
integers
. use number line
. use and understand absolute value
. build vocabulary
. understand and use PEMDAS
. use variables and substitutions
. distributive and combine
2 tests
Homework
Quizzes
Worksheets
2
Evaluating expressions
Bases, exponents, powers
Evaluation in exponential form
Multiplying/dividing like bases
Power to power
Negative exponents
Scientific notation
Students can:
. like terms
. understand exponent concepts expanded
notation both positive and negative
exponents
. multiply – divide like bases and power
to power
. apply uses of scientific notation
. recognize the whole number vs.
decimal
Exponential terms
. solve equations with single and multisteps
. Understand the concept of balance and
opposite
. use checks to verify solution
3 tests
Homework
Quizzes
Worksheets
2
3 tests
Homework
Quizzes
Worksheets
4
Number line
Graphing solution sets to single
variable inequalities
Solution of inequalities with graph
Properties of inequalities
Graphing and shading inequalities
Students can:
. show how number lines indicate
inequalities
. solve, work and graph are inequalities
. understand the principles of operation
within inequalities
2 tests
Homework
Quizzes
Worksheets
2-3
Translating verbal phrases into
mathematical expressions
Translating verbal sentences into
mathematical sentences
Students can:
. build vocabulary
. identify variables in word problems
. write expressions and equation from
words
. Problem solve forming equations
2 tests
Homework
Quizzes
Worksheets
3-4
Preparation and set up
Solution of one and multi-step
Operations
Combining like terms
Variables on both sides
Distributive property
Word problems
2
3
Topics
(Unit Title or
organizing idea)
February
Polynomials
March
Polynomials
April
Quadratics
Graphing
May
Graphing
Probability
Statistics
June
Ratio
Proportions
Percents
Review
Concepts
(understandings)
Skills
(What students
actually do)
Major Assessments
(Tests, projects, etc.)
Time Frame
(Number of
weeks)
Classify … polynomials
Basic operation of polynomials
Multiplying binomials
FOIL
Students can:
. identify polynomials by classification
and term
. add-subtract-multiply-divide
polynomial
. use FOIL method for multi binomials
. divide by monomial/binomial
2-3 tests
Homework
Quizzes
Worksheet
4
Finding a common monomial factor
Factoring the difference of binomial
Squares
Basic trinomial factoring
Complete factorization
Students can:
. find common monomial factor
. recognize and factor trinomial
. recognize and factor difference of
binomial sequence
2-3 tests
Homework
Quizzes
Worksheet
4
Standard form
Solution by factoring
Points or coordinate plan
Basic graphing, T-table
X, Y intercept
Slope
Plotting by points
Systems of equations
Using graphing
Mean, median, mode range
Simple probability
Writing & evaluating
Probability using and/or
Predicting outcomes
Permutations combination factorial
Students can:
. solve quadratics by factoring and then
check
. find point on coordinate plane
. recognize and use graph of linear
equation in any method
2 tests
Homework
Quizzes
Worksheet
1-2
Students can:
. graph equation and find solution set at
intersection
. identify, estimate and find mean,
median, mode
. find simple compound probability by
ratio factoring
2-3 tests
Homework
Quizzes
Worksheet
1-2
Forming a ratio
Forming a proportion
Forming percents from fractions and
Decimals
Percent and percentage problems
Students can:
. problem solve using permutations and
combinations
. compare and describe ratio
. form proportions
. find %
. recognize and set proportion for %
problems
. use decimal equivalent for % to
problem solve
1 test
Homework
Final exam
1-2
2
3-4
1-2
MARLBORO CENTRAL SCHOOL DISTRICT
CURRICULUM MAP
_____Sequential Math I – Course I_________
Course Title
Title or Topics
Concepts
(Unit
(understandings)
organizing idea)
Set theory
September
Number line – coordinates/graphing
Skills
(What students
actually do)
___________Grade 9_________
Grade Levels
Major Assessments
Time Frame
(Tests, projects, etc.)
(Number of
weeks)
Graphing on number line
Operations involving rationals/signed
Numbers
Identify properties
Problems of day (POD)
Teacher prepared quiz (TPQ)
Teacher prepared test (TPT)
Homework (HW)
Board presentation (BP)
1-4
5-6
2 wks
2 wks
Numbers and operations
Operations – signed numbers
Rational numbers
Order of operations
Properties
October
Statements
Rules of logic
Tautologies/contradictions
Converse, inverse, contra positive
Evaluating algebraic expressions
Basic equation solving
Complete truth tables
To apply order of operations rules to
algebraic expressions
POD
PPQ
TPT
HW
BP
1-4
2 ½ wks
5-6
1 ½ wks
Equations containing
parenthesis/fractions
Translation process
Integer problems
Perimeter problems
Solve equations
Solve simple word problems
POD
PPQ
TPT
HW
BP
1-2
1 ½ wks
3-4
1 ½ wks
Word problems involving inequalities
Ordered pairs, etc.
Graphing – table/slope intercept
Solve inequality word problems
Graph linear equations
POD
PPQ
TPT
HW
BP
1
1 wk
2, 3______
POD
PPQ
TPT
HW
BP
1, 2
3, 4
Logic
Equation solving
November
Solving equations
Introduction to word problems
December
Solving literal equations
Solving inequalities
Graphing systems of linear equations
January
Graphing continued
Basic concepts of Geometry
Lines parallel to axis
Graphing systems of linear inequalities
Points/lines/planes
Distance/line segments/rays
Graph “special lines”
Graph inequalities
Name sets of points
Short
Month
Rest of December
1 ½ wks
1 ½ wks
Regular week
Topics
(Unit Title or
organizing idea)
February
Concepts
(understandings)
Skills
(What students
actually do)
Major Assessments
(Tests, projects, etc.)
Time Frame
(Number of
weeks)
Angle measures – special angles
Parallel lines – trans………
Classification of triangles
Angles of a triangle
Polygons
Congruent triangles
Isosceles triangles
Recognize various types of angles
Find angles for onerous polygons
POD
PPQ
TPT
HW
BP
1, 2, 3
4, 5, 6, 7
Area formulas
Volume
Circumference/area of circle
Experiments/tree diagrams
Exponents/factoring
Monomial operations
Polynomial operations
Factoring algebraic expressions
Determine area
Determine volume
Factor
POD
PPQ
TPT
HW
BP
1, 2, 3
4
5-8
Polynomials/factoring continued
Introduction to statistics
Quadratic equations
Word problems – quad ratio equations
Charts/graphs
Measures of central tendency
Quartiles/percentiles
Solve quadratic word problems
Deal with statistics
POD
PPQ
TPT
HW
BP
1
1 wk
2
1 wk
3, 4, 5 remainder of
month
May
Simplifying radicals
Operations involving radicals
Complete operations with radicals
POD
PPQ
TPT
HW
BP
1 wk for each entry
POD
PPQ
TPT
HW
BP
2 weeks to finish topics
listed – review built in
also
Geometry continued
March
Geometry continued
Probability
Polynomials/Factoring
April
Solving systems of linear equations – algebraically
Rationals, irrationals
June
Ratio and similarity
Pythagorean theorem
Transformations
Review
Ratios
Proportions
Similar polygons
Pythagorean triples
Complete simple word problems of type
Indicated
Work with Pythagorean theorem
Pass Regents
2 wks
2 wks
1 wk
1 wk
2 wks
2 remaining weeks –
extra time if needed
MARLBORO CENTRAL SCHOOL DISTRICT
CURRICULUM MAP
______Sequential Math Course 1B______
Course Title
Title or Topics
Concepts
(Unit
(understandings)
organizing idea)
General technique for solving problems
September
6. problem solving strategies
Students can solve problems by:
. guess & check
. simpler problem
. working backward
. discovering pictures
. drawing pictures
. making lists and charts
1 test
2 quizzes
Student authored problem
With scenario & solution
Homework
Oral assessment
Board problems
2 ½ wks
Sets and subsets
Union and intersection
Identify set and subset
Perform union & intersection
1 test, 1 quiz,
oral, homework
1 ½ wks
Sentences, statements, and truth values
Negation, conjunction, disjunction,
Conditional
Compound statements, converse,
inverse, contra-positive
Bi-conditional, tautologies
Students can:
. judge the truth value of a statement
. construct a truth table
. determine truth value of a compound
statement by simplifying truth values
. identify tautologies
1 test
homework
2 quizzes
oral assessment
Truth tables on board
Student prepared overheads
“Logic Bingo”
Notebook check
3 wks
Identify set and subset
Perform union & intersection
Students can:
. identify natural, whole, integer, rational
& irrational numbers
Students can:
. identify point, line, plane, line segment,
midpoint, perpendicular bisector, angle
. Use complementary and supplementary
relationships
. Use congruent angle relationships, and
exterior angles of triangles
1 test
2 quizzes
1 ½ wks
1 test
2 quizzes
Cooperative Group Activity
Homework
Peer Assessment
Self-assessment
Student generated test questions
4 wks
Define geometric figures
Congruent Triangles: ASA, SSS, SAS
Quadrilaterals
Line reflections & line symmetry
Point reflection & point symmetry
Translations
Rotations
Students can:
. define and identify polygons, regular
polygons
. show that two triangles are congruent
by ASA, SSS, SAS
. reflect in a line or in a point
. translate a figure in plane
. rotate about a point
1 test
2 quizzes
Homework
Oral assessments
“Party Paper” activities
Board demonstrations by students
Notebook check
4 wks
Ratios
Rates
Word problems involving ratio
Proportion
Direct variation
Percent and percentage problems
Students can:
. express ration, continued ratio
. determine equivalent ratios
. determine rate
. solve problems using ratios and
proportions
. calculate constant of variation
. calculate percents & percentages
1 test
2 quizzes
Homework
Oral assessments
Board problems
Review relay game
3½
Problem solving
Sets
October
Logic
Real Numbers
November
Angle Measure in Geometry
December
Congruence and transformations
January
Ratio and Proportion
Skills
(What students
actually do)
__________Grade 10-12_____________
Grade Levels
Major Assessments
Time Frame
(Tests, projects, etc.)
(Number of
weeks)
Points, lines, planes
Angles, angle measure,
Perpendicularity
Pairs of angles
Angles and parallel lines
Triangles and angles
Triangles with congruent angles
homework
oral assessment
Topics
(Unit Title or
organizing idea)
February
Concepts
(understandings)
Skills
(What students
actually do)
Similar polygons
Similar triangles
Dilations
Ratio of perimeters of similar polygons
Ratio of areas of similar polygons
Students can:
. use proportions to find measures of
similar polygons & triangles
. identify corresponding parts of similar
figures
. use A.A. Theorem to show triangles are
similar
. dilate a figure & determine constant of
dilation
. use ratios of area & perimeter
Students can:
. Find area and perimeter of any
parallelogram or trapezoid
. find area and perimeter of triangle and
reg. Polygons
. use formulas to problem solve
. find areas of shaded regions
. use Pythagorean Theorem to find
lengths needed to find areas
. calculate volumes
Students can:
. find principle square roots
. solve for variable by taking square root
- exact values and approximately values
. 4 basic operation with square root
radicals
1 test
homework
2 quizzes
Board problems
Oral assessment
Worksheet
Review relay game
Notebook check
4 wks
1 test
2 quizzes
Board problems
homework
Oral assessment
Student generated problems & solutions
Notebook check
4 wks
1 test
Worksheets
Oral assessment
Homework
4 quizzes
3 wks
Frequency tables & histograms
Cum. Freq. tables & cum. Histograms
Mean, Media, Mode, Percentiles
Students can:
. construct freq. Table, freq. As
histogram, cum. Freq. Table, cum. Freq.
Histogram
. calculate mean, median, mode and
percentile
1 test
2 quizzes
Music survey – Record
Homework
Display
Analyze
Oral assessment
3 wks
Simultaneous equations
Review graphic solutions
Algebraic solutions
. solve systems by elimination
. solve systems by substitution
June
Test taking strategies
Practice testing
Students can:
. use test taking strategies
. improve performance on practice exams
Similarity
March
Geometric Formulas
April
Operations with Radicals
May
Statistics
Regents Review
Area and perimeter formulas for
Polygons
Area of circle and circumference
Terms and definitions for circle
Problem solving with area, perimeter or
Circumference
Areas of shaded regions
Pythagorean Theorem
Volume formulas
Radicals with rational or irrational
Numbers
Finding principle square roots
Simplifying square root radicals
Adding and subtracting radicals
Multiplying and dividing square root
Radicals
Major Assessments
(Tests, projects, etc.)
Time Frame
(Number of
weeks)
2 wks
1 test
strategies
Oral assessment
Board presentation
3 ½ wks
MARLBORO CENTRAL SCHOOL DISTRICT
CURRICULUM MAP
_____________Math 2_____________
Course Title
Title or Topics
Concepts
(Unit
(understandings)
organizing idea)
Operations – signed numbers
September
Rational numbers
Numbers and operations
Polynomial Review
October
Polynomial review continued
Review factoring
November
Factoring continued
Review equation solving
December
Algebraic fractions
Complex fractions
January
Review Algebraic fractions
Word problems
Equation solving revisited
Skills
(What students
actually do)
__________Mixed Grade___________
Grade Levels
Major Assessments
Time Frame
(Tests, projects, etc.)
(Number of
weeks)
Operations involving rationals/signed
Numbers
Complete basic algebraic tasks
Problem of Day (POD)
Teacher Prepared Quiz (TPQ)
Teacher Prepared Test (TPT)
Homework (HW)
Board Presentation (BP)
1-3
4-6
1 ½ wks
2 ½ wks
Power of a power
Multiplying polynomial by monomial
Multiplying polynomial by polynomials
Division of monomials
Division of polynomial by monomial
Greatest common factor
Complete more difficult algebraic tasks
Factor
Problem of Day (POD)
Teacher Prepared Quiz (TPQ)
Teacher Prepared Test (TPT)
Homework (HW)
Board Presentation (BP)
1-3
2-4
5-7
1 wks
1 ½ wks
1 ½ wks
Difference of 2 squares
Trinomial squares
Factoring trinomials – co-efficient of
quadratic term is one
Factoring trinomials – co-efficient of
quadratic term not equal to one
Factoring completely
Equations with parenthesis
Equations with fractional co-efficients
Factor
Complete the solutions for more difficult
Equations
Problem of Day (POD)
Teacher Prepared Quiz (TPQ)
Teacher Prepared Test (TPT)
Homework (HW)
Board Presentation (BP)
1-5
6, 7
Reduction
Multiplication
Division
Addition/Subtraction
Simplification of complex fractions
Operations involving Algebraic fractions
Problem of Day (POD)
Teacher Prepared Quiz (TPQ)
Teacher Prepared Test (TPT)
Homework (HW)
Board Presentation (BP)
1-4
2 ½ wks
51 wk
Short month
Integer problems
Ratio problems
Literal equations
Word problems
Solving equations – involving formulas
Problem of Day (POD)
Teacher Prepared Quiz (TPQ)
Teacher Prepared Test (TPT)
Homework (HW)
Board Presentation (BP)
1, 2
3
Order of operations
Adding/subtracting monomials
Adding/subtracting polynomials
Multiplying monomials
2 ½ wks
1 ½ wks
Regents week
1 wk
1 ½ wks
Topics
(Unit Title or
organizing idea)
February
Absolute valve
Inequalities
Quadratic equations
March
Real number system
rationals/irrationals
Radicals continued
Quadratic equations revisited
April
Quadratic equations continued
Solving systems of linear equations algebraically
May
Graphing systems of linear equations
Graphing expanded
Introduce imaginary numbers
June
Review for final examination
Concepts
(understandings)
Skills
(What students
actually do)
Major Assessments
(Tests, projects, etc.)
Time Frame
(Number of
weeks)
Derived equations
Solving inequalities
Solutions to quadratic equations – by
Factoring
Work with absolute valve
Solve quadratic equations
Problem of Day (POD)
Teacher Prepared Quiz (TPQ)
Teacher Prepared Test (TPT)
Homework (HW)
Board Presentation (BP)
1
2, 3
1 wk
2 wks
Roots/Radicals
Simplifying radicals
Rationalize denominators
Operations involving radicals
Rationalize binomial radical
Denominators
Solve by factoring
Complete operations involving radicals
Solve quad equations
Problem of Day (POD)
Teacher Prepared Quiz (TPQ)
Teacher Prepared Test (TPT)
Homework (HW)
Board Presentation (BP)
1-5
6
Quadratic formula
Irrational roots
Fractional co-efficients
Quadratic formula
Applied to quadratics of various
difficulty levels
Problem of Day (POD)
Teacher Prepared Quiz (TPQ)
Teacher Prepared Test (TPT)
Homework (HW)
Board Presentation (BP)
3 wks
Scope/intercept
Parabolas – axis of symmetry, etc.
Parabolas/imaginaries
Graph linear equations
Graph quadratic equations
Problem of Day (POD)
Teacher Prepared Quiz (TPQ)
Teacher Prepared Test (TPT)
Homework (HW)
Board Presentation (BP)
2 weeks graphing
1 ½ wks imaginary
numbers
Review for final examination
Pass final
Teacher prepared final
Remaining time for
review
3 wks
1 wk
Short month
MARLBORO CENTRAL SCHOOL DISTRICT
CURRICULUM MAP
_________Math II__________
Course Title
Title or Topics
(Unit
organizing idea)
September
The Real Number System
October
Operations on Polynomials
November
Factoring and Operations on Rational Expressions
December
First-Degree Equations and Inequalities
January
First-Degree Equations and Inequalities (cont.)
Begin Linear Relations and Functions
Concepts
(understandings)
Sets, Subsets, Union, Intersection
Subsets of Real Numbers
Solution sets of open sentences
-one variable
Properties of Real Numbers
Properties of Equality
Proof in algebra
_____________________________
Grade Levels
Skills
Major Assessments
Time Frame
(What students
(Tests, projects, etc.)
(Number of
actually do)
weeks)
Students can:
-create sets and subsets
-perform union & intersection
-graph solution sets of open sentences
one variable
-identify properties of real numbers &
equality
-use properties to prove truth of solutions
-subsets of Real Numbers
Students can:
-evaluate expressions and formulas
-add, subtract, multiply & divide two
monomials, a monomial and
polynomial, two polynomials
-use properties of reals to simplify
operations on polynomials
1 test
Homework
Board problems
Oral assessment
2 quizzes
4 wks
1 test
Homework
Board problems
Oral assessment
2 quizzes
4 wks
Factoring polynomials
Transforming Rational Expressions into
Equivalent Expressions
Simplifying Rational Expressions
4 operations on Rational, Complex
Fractions Expressions
Rational Equations
Students can:
-factor polynomials
-change algebraic fractions to equivalent
fractions
-simplify rational expressions
-perform 4 basic operations on 2 rational
expressions
-solve rational equations
1 test
2 quizzes
Homework
Board problems
Oral assessment
Algebra-Tile Geometric Activity
5 wks
Literal Equations
First-Degree Inequalities in one
variable
Problem solving with Literal Equations
and First-Degree Inequalities
Students can:
-solve literal equations
-solve first-degree inequalities
-solve “word problems” involving literal
equations and first-degree inequalities
1 test
2 quizzes
Algebra “Proof”
Students Authored Test Questions
Homework
Oral assessments
Board problems
3 wks
Absolute value equation
Absolute value inequalities
Students can:
-solve absolute value equations and
inequalities
-graph the results
1 Quiz
Homework
Oral assessment
Board problems
1 ½ wks
Finding solution sets of open sentences
in two variables
Students can:
-find the solution set of an open sentence
when domain is real numbers
-find the solution set of an open sentence
when the domain is other than TR
1 Quiz
Homework
Oral assessment
1 ½ wks
Evaluation algebraic expressions and
Formulas
4 operations for monomials and
polynomials
Applying properties of Real Numbers
to simplify polynomials
Topics
(Unit Title or
organizing idea)
February
Linear Relations and Functions
March
More Linear Relations and Functions
April
Real Numbers and Radicals
May
Quadratic Equations and Functions
June
Concepts
(understandings)
Review graphing ordered pairs
Review graphing lines using table, x
and y intercepts, slope – intercept
form
Slope
Writing equations for lines
Major Assessments
(Tests, projects, etc.)
Time Frame
(Number of
weeks)
Students can:
-graph ordered pairs
-graph lines using 3 methods
-choose the best method
-find slope of a line
-write an equation for a line
a) given M and A
b) given M and ordered pair
c) given two ordered pairs
Students can:
-graph inequalities
-graph inequalities using other
replacement sets
-graph systems of inequalities
-solve systems of equations algebraically
-solve problems using systems
1 test
3 quizzes
Cooperative Learning Activity
Peer Evaluation
Self-evaluation
Graphing Calculator Activity
4 wks
1 test
3 quizzes
Homework
Oral assessment
Student Prepared overheads
Board problems
4 wks
Students can:
-Perform 4 operations on irrational
numbers
-Rationalize radical denominators
-Perform 4 operations on polynomials
with radicals
-Rationalize binomial radical
denominators
-Solve irrational equations
Students can:
-graph parabolas
-solve quadratic equations by factoring
and formula
-connect solutions of equations to xintercepts of function
-solve quadratic-linear systems
graphically and algebraically
1 test
3 quizzes
Homework
Oral assessment
Board problems
4 wks
1 test
2 quizzes
Homework
Oral assessment
T1-92 graphing calculator project
Board problems
Overhead presentation
4 wks
Laws of Exponents
Students can:
-perform 4 basic operations on positive,
negative, and 0 exponents
1 test
1 quiz
Homework
Oral assessment
Board problems
1 ½ wks
Review of Final Examination
Students can:
-Do everything!
Worksheets
Calculator activities
1 ½ wks
Inequalities in Two Variables
Comparing Inequalities Using Different
Replacement Sets
Systems of Equations
Systems of Inequalities
Problem Solving
Roots and Radicals
4 Operations on Radicals
Rationalizing Radical Denominators
Polynomials with Radicals
Rationalizing Binomial Radical
Denominator
Irrational Equations
Quadratic Functions
Quadratic Equations
Relating Quadratic Function to
Quadratic Equation
Quadratic – Linear Systems
Exponents
Review
Skills
(What students
actually do)
MARLBORO CENTRAL SCHOOL DISTRICT
CURRICULUM MAP
_____Intermediate Sequential Course III___
Course Title
Title or Topics
Concepts
(Unit
(understandings)
organizing idea)
Sets
September
Math Systems
Rational Numbers
Rational Expressions
October
Relations Functions
Irrational Numbers
Radical EQ
November
Imaginary & complex numbers
Equations with complex roots
Graphing Parabola
Quadratic Inequalities
December
Finis conic section
Invwerse & composition of functions
Basic transformations
January
Exponential Function
Skills
(What students
actually do)
______Grade 10-11__________
Grade Levels
Major Assessments
Time Frame
(Tests, projects, etc.)
(Number of
weeks)
Identify properties of sys
Classify elements as Mem of sets
Factor
Perform oper w/rat exp
Simp complex fract
Solve fractional EQ
Written tests (WT)
Homework (HWK)
Oral Assessment (OA)
Board Problems (BP)
Student Seat Work (SSW)
Sets of systems
1 wk
Relation
Domain Range
Functions
Absolute Value = < >
Review Radicals
Radical =
Classify Rotation as Function or NonFnct.
Iden Domain/Range
Eval. Funct for specific element
Solve equations & iner with absd value
simp rad
Written tests (WT)
Homework (HWK)
Oral Assessment (OA)
Board Problems (BP)
Student Seat Work (SSW)
Week per topic
Imaginary numbers
Powers of I
Quad eq with imag roots
Parabola …../prod roots
Solving Quad < >
Diff between imag & complex
Evaluate powers of I
Solve Quad EQ with complex roots
Draw graph of parabola
Ident if mat min
Solve ineq w/quad
Written tests (WT)
Homework (HWK)
Oral Assessment (OA)
Board Problems (BP)
Student Seat Work (SSW)
Imag & compl
1 wk
Graphing
1 + wk
Ineq
1 wk
Conic Sections
Circle Hyperbola Eclipse
Revisit fract
Inverse, composition
Basic transformations
Identify graph from EQ
Draw resp graph
Write inv. Of fnct
Oper with composition
Review transformation
Written tests (WT)
Homework (HWK)
Oral Assessment (OA)
Board Problems (BP)
Student Seat Work (SSW)
Conic sect
1.5 wks
ino & comp
wk
trans wk
Exponential functions
Fractional & neg exp
Exponential EQ
Perform operations in exp form
Eval exp with fractional & neg exp
Solve equations w/ exp
Written tests (WT)
Homework (HWK)
Oral Assessment (OA)
Board Problems (BP)
Student Seat Work (SSW)
Exp 1 wk
Exp EQ 1-2 wks
Number Prop.
Factoring Polynomial
Rational Exp Division
Reduce +, -, x, ÷
Complex Fr
Fract EQ
Rat Exp
2 wks
Topics
(Unit Title or
organizing idea)
February
Logarithmic functs
Statistics
March
Probability & Binom Them
Geography of 0……..
Radian meas
April
Initial trig functions
Trig graphs
May
Trig applications
Trig equations & identities
Solving
June
Review for Regents
Concepts
(understandings)
Skills
(What students
actually do)
Major Assessments
(Tests, projects, etc.)
Time Frame
(Number of
weeks)
Logs des ……
Use for computations
Use to solve exp EQ Stat.
Mean, median mode
Range variance
Standard dev normal curve
Review ….prob
Exactly R outcomes in N trials
At least, at mort
Bionomial expansion
Circle ………………….?
Convert expression log <-> exp
Use logs to compute ans to problems
Draw graph of log functs
Compute mean, med mode
Use normal curve to eval outcomes
Written tests (WT)
Homework (HWK)
Oral Assessment (OA)
Board Problems (BP)
Student Seat Work (SSW)
Convert < 1 wk
Log comp & graph 1-2
wks
Stat 1 wk
Complete prob of outcomes of stated
events
Find indicated term of a binomial to
given power
Compute lengths of …. In 0 ralations
Written tests (WT)
Homework (HWK)
Oral Assessment (OA)
Board Problems (BP)
Student Seat Work (SSW)
Prob 1 wk
Binom exp 1 wk
& app
) xs sag 1 wk
radian < 1 wk
ARC length
Basic ……………………?
Inverse fncts …………?
Unit 0, stand pos
Angles any size
Res A
Trig graphs amp freq period
State trig ratios
Iden reciprocal & inv
Relations compute trig value of any size
Use trig ret to find missing lengths use
trig to solve…………?
Draw graphs
Written tests (WT)
Homework (HWK)
Oral Assessment (OA)
Board Problems (BP)
Student Seat Work (SSW)
Basic rel 1 wk
Graphs < 1 wk
Comp 1-2 wks
Rect c…………?
Inverse trig
Trig equations
1st degree 2nd degree
1 & 2 variable
Law sines cosinos
…………………case?
Vector prob
Trig identities
Regents Review prob
Solve eq with trig functs
Linear & Quad single & dual fncts
Written tests (WT)
Homework (HWK)
Oral Assessment (OA)
Board Problems (BP)
Student Seat Work (SSW)
1 wk
per topic
Regents quad from previous yrs
Homework (HWK
Board Problems (BP)
Oral Assessment (OA)
Student Seat Work (SSW)
2 wks
MARLBORO CENTRAL SCHOOL DISTRICT
CURRICULUM MAP
_____Intermediate Sequential Course II_______
Course Title
Title or Topics
Concepts
(Unit
(understandings)
organizing idea)
Algebra Review
September
Equations Inequalities
Algebra Review
Quadratic EQ
Factoring
October
Systems of EQ
Irrational numbers
Quad Formula
Basic Graphing
November
Graphic soln to system
Rational Expressions
December
Coord Geo
Slope, Dist. Mdpt
Write EQ for line
January
Probability & Math Systems
Skills
(What students
actually do)
_________Grade 9-10__________
Grade Levels
Major Assessments
Time Frame
(Tests, projects, etc.)
(Number of
weeks)
Solve 1st Deg EQ in one Var
Factor polynomials
Solve Quad EQ by factoring
Written Test (WT)
Homework (HWK)
Oral Assessment (OA)
Board Problems (BP)
Student Seat Work (SSW)
Review
wk
Oper
wk
Factoring 1-2 wks
Solve EQ
Quad Linear Sys
Irrational numbers
+, -, x, ÷ Radicals
Quadratic Formula
Discrim & nature of roots
Review Graph Line
Graph Parabola
Solve sys of EQ in 2 variables
algebraically
Perform operations with radicals
Use Quad Formula to solve 2nd deg EQ
Written Test (WT)
Homework (HWK)
Oral Assessment (OA)
Board Problems (BP)
Student Seat Work (SSW)
Systems
Radicals
Quad Form
Graph
Graphic soln to Quad/Linear system
Soln of Quad EQ from GR
Rational Exp (underlined)
Reduce, mul, div
Add & subtract Fract EQ
Use graphs to solve systems of EQ
Use Factoring to simp rat exp
Perform operations / rat ex
Written Test (WT)
Homework (HWK)
Oral Assessment (OA)
Board Problems (BP)
Student Seat Work (SSW)
Systems
Rat exp
Coord slope ???????
Parallel & perpend lines
Write EQ of line
Pythag thrm review
Dist forumula
Midpoint
Use slopes to determine if lines are “ or 1
Write EQ of line
Given slope & ???????
Slope & point
2 pts.
Use pythag thrm (dist Form) to find
length
Written Test (WT)
Homework (HWK)
Oral Assessment (OA)
Board Problems (BP)
Student Seat Work (SSW)
One topic
Flows to other
Time month
Probability
Permutations combinations
Prob with perm & comb
Math systems
Closure, ident. Inverse
Comm Assoc Group
Compute prob of stated event
Diff between comb & ??????????
Compute number of comb perm under
stated cond.
State profs of math system
Ident diff elementary
Written Test (WT)
Homework (HWK)
Oral Assessment (OA)
Board Problems (BP)
Student Seat Work (SSW)
Prob (basic
P………..
Prob
Systems
Operations with polynomials (+, -, x, ÷)
Factoring
Solve Quad EQ by factoring
wk
wk
wk
wk
wk
2 wks
wk
wk
wk
Topics
(Unit Title or
organizing idea)
February
Math Systems
Logic
March
Geometry
Basic Terms
Introduce Proof
Relations
Relations
Parallel
& perp lin…..
April
Polygons
Congruent & other polygons
Propertied of Quads
May
Similar poly
Right trib
Constructions
Locus
June
Review
Concepts
(understandings)
Skills
(What students
actually do)
Major Assessments
(Tests, projects, etc.)
Time Frame
(Number of
weeks)
Finish math systems
Logic
Rules of Inf
2 col ded proof
Inverse, converse etc
Use T.T. to establish logical EQ & Kaws
if Ubs
Ident conn inv & contra
Pos of conditional
Use laws of ind for a formal proof
Written Test (WT)
Homework (HWK)
Oral Assessment (OA)
Board Problems (BP)
Student Seat Work (SSW)
TT
wk
Law of inf wk
Proofs 1-2 wks
Begin Geo
Basic def, lines, segs
Angle relations
Relations
Parallel &
lines
& Converses
Use proper notation to ident geo elem
Solve probelsm using relations discussed
Supply reasons for ded proof
Written Test (WT)
Homework (HWK)
Oral Assessment (OA)
Board Problems (BP)
Student Seat Work (SSW)
Basic terms wk
Proofs
wk
Relations 1-2 wks
Lines 1-2 wks
Polygons
Reg polygons
Sides & relations
Quadrilaterals
Ident diff types of poly
Compute sc…….
& ???? of each int
Proofs for
Use
to estab prop of QUAD
Written Test (WT)
Homework (HWK)
Oral Assessment (OA)
Board Problems (BP)
Student Seat Work (SSW)
Poly
Similar poly
Right triangle prop
Special ratios
30-60-90, 45,45,90
RG & Trib sin cos tan
Constructions locus
Use prop sin to solve prob
Use prop
to derive phthag thrm
Use pythag therm for special r……….
Solve related prob
Written Test (WT)
Homework (HWK)
Oral Assessment (OA)
Board Problems (BP)
Student Seat Work (SSW)
Wk
Pythag therm & app
2-3 wks
Review
Use Previous Regents Exams to review
years work
Written Test (WT)
Homework (HWK)
Oral Assessment (OA)
Board Problems (BP)
Student Seat Work (SSW)
2 wks
1wk
Wk
Prop Quads 1-2 wks
MARLBORO CENTRAL SCHOOL DISTRICT
CURRICULUM MAP
________Sequential Math III_______
Course Title
Title or Topics
Concepts
(Unit
(understandings)
organizing idea)
Factoring polynomials
September
Add, Multiple, divide
Real Numbers
Polynomials
Polynomial Fractions
October
Real Numbers
Irrational Numbers
November
Imaginary Numbers
December
Conic Sections
Exponents
January
Logarithms
Statistics
Skills
(What students
actually do)
________Grade 11_________
Grade Levels
Major Assessments
Time Frame
(Tests, projects, etc.)
(Number of
weeks)
Operations on polynomials
Review activities
Work sheets
Board Work
Tests
3 wks
Solve & graph inequalities
Simplify radicals
Add, subtract, multiple, divide
Rationalize radicals
Solving quadratic inequalities
Operations on radicals
Review activities
Worksheets
Board Work
Tests
4 wks
Add, subtract, multiply, divide, powers
of complex numbers
Solve Quadratics
Def, types composite inverse of
Functions
Operations on complex numbers
Composition of functions
Review activities
Worksheets
Board work
Tests
4 wks
Circle, eclipse
Parabola, hyperbola
Properties of exponent
Scientific notation
Exponential Equations
Identify and graph conic sections and
exponential equations
Review activities
Worksheets
Board work
Tests
4 wks
Logarithmic and exponential notation
Properties of logarithms
Graph exp and log functions
Sigma notation
Mean, median, mode
Standard deviation
Graph, multiply, divide and do powers
with logarithms
Mean, median, mode standard deviation
Review activities
Worksheets
Board work
Tests
5 wks
Polynomial Fractions
Simplify complex fractions
Topics
(Unit Title or
organizing idea)
February
Statistics
Probability
Geometry of the Circle
March
Trigonometry
April
Right triangles
Scalene and obtuse triangles
Vectors
May
Trigonometric
Identities
June
Review
Concepts
(understandings)
Skills
(What students
actually do)
Major Assessments
(Tests, projects, etc.)
Time Frame
(Number of
weeks)
Permutations, combinations
Binomial expansion
Probabilities from binomial expansion
Find measure of various arcs, chords,
and angles of the circle and tangents
and secants to the circle
Find mean and standard deviation
Make a frequency distribution
Review activities
Worksheets
Board work
Tests
4 wks
Sine, cosine, and tangent values and
Graphs
Radian and degree measure
Reciprocal, Quotient, co-functions
Draw trig ????
Construct trig table
Review activities
Worksheets
Board work
Tests
4 wks
Law of sines
Law of cosines
Ambiguous case
Resolution of forces
Area of triangle
Solve triangle problems
Review activities
Worksheets
Board work
Tests
5 wks
Deprive identities
Solve trigonometric equations
Prove identities
Inverse variation
Prove identities
Solve equations
Review activities
Worksheets
Board work
Tests
4 wks
Review for Regents
Practice for Regents
Review activities
Worksheets
Board work
Tests
3 wks
MARLBORO CENTRAL SCHOOL DISTRICT
CURRICULUM MAP
_______Pre-Calculus A____________
Course Title
Title or Topics
Concepts
(Unit
(understandings)
organizing idea)
Linear Equations
September
Complex numbers
Pre-requisite topics
Quadratics
Matrices
October
Matrix algebra
Math induction
Sequences and series
November
Binomial Expansion
Vectors
December
Polar coordinates
January
Trigonometry
Skills
(What students
actually do)
_________Grade 12__________
Grade Levels
Major Assessments
Time Frame
(Tests, projects, etc.)
(Number of
weeks)
Solve polynomial and high degree
equations
Write Quadratic equations
Review activities
Work sheets
Board work
Tests
4 wks
Row-reduction
Cramer’s Rule
Determinants
Inductive proofs
Arithmetic and geometric
Solve system of equations by various
Techniques
Review activities
Work sheets
Board work
Tests
4 wks
Sequences and series
Terms of expansion
DOT product
3 dimensional vectors
Cross product
Equation of a plane
Sketch vectors and perform vector
Operations
Review activities
Work sheets
Board work
Tests
5 wks
Rectangular and polar coordinates
Multiply, divide polar coordinates
De Moivre’s theorem
Graphing Polar coordinates
Review activities
Work sheets
Board work
Tests
4 wks
Graphs, tables, proofs, equations
Law of sines
Law of cosine
Translating
Graphs
Proving identities
Solving equations
Review activities
Work sheets
Board work
Tests
3 wks
Quadratics
Long Division synthetic Division
Rational Root theorem
Systems of Equation
MARLBORO CENTRAL SCHOOL DISTRICT
CURRICULUM MAP
___________Pre-Calculus B___________
Course Title
Title or Topics
Concepts
(Unit
(understandings)
organizing idea)
Graphs: Bar, component, histogram
September
Ogive, pie
Statistics
October
Hypothesis testing
Logic
November
Computer project
Matrices
December
Compile numbers
January
Review
Skills
(What students
actually do)
___________Grade 12_________
Grade Levels
Major Assessments
Time Frame
(Tests, projects, etc.)
(Number of
weeks)
Graph and design histogram
Review activities
Work sheets
Board work
Tests
4 wks
Frequency distribution
Normal curve
Z-Table
Student T-test
Laws of Logic
Logical Proofs
Boolean Disjunctive form
Logic circuits
Karnaughn maps
Conduct large sample hypothesis test
Conduct small sample hypothesis test
Review activities
Work sheets
Board work
Tests
4 wks
Graph with excel
Row reduction Cramer’s Rule
Add, multiply matrices
Inverse of a matrix
Construct logical proofs
Design logical circuits
Review activities
Work sheets
Board work
Tests
5 wks
Polar coordinates
Rectangular coordinate
DeMoivre’s theorem
Polar graphs
Solve system of equations
Graphing in polar coordinates
Review activities
Work sheets
Board work
Tests
4 wks
Review all topics
Pre-calculus A
And pre-calculus B for calculus
Solve Quadratics
Use synthetic
Division
Rationalize Quadratic
Review activities
Work sheets
Board work
Tests
3 wks
Mean, median, mode, standard
Deviation
MARLBORO CENTRAL SCHOOL DISTRICT
CURRICULUM MAP
_______Calculus________________
Course Title
Title or Topics
(Unit
organizing idea)
September
Graphs
Limits
October
Derivatives
November
Derivatives
December
Derivatives
Integrals
January
Integrals
Concepts
(understandings)
Skills
(What students
actually do)
_________Grade 12_______________
Grade Levels
Major Assessments
Time Frame
(Tests, projects, etc.)
(Number of
weeks)
Graph polynomial functions
Graph rational functions
Limits by Direct
Substitution, algebraic manipulation,
near infinity
Difference Quotient
Define limit
Limit theorems
Review activities
Work sheets
Board work
Tests
4 wks
Derivative by: ∆ x process
X  a process, power race continuity
Product and quotient rules
Chain rule
Continuous & discontinuous functions
Rules for differentiation
Review activities
Work sheets
Board work
Tests
4 wks
Higher order derivatives
Velocity, acceleration
Derivative of trig f….
Implicit differentiation
Logs and Exponents
Applications of the chain rule
Implicit differentiation
Review activities
Work sheets
Board work
Tests
5 wks
Curve tracing
Applications
Optimization
Exponent and logarithm functions
Indefinite integrals
Finding max and mins
Critical points and points of inflection
Optimization
Review activities
Work sheets
Board work
Tests
4 wks
General power rule
Word problems
Definite Integrals
Area and volume
Application of techniques
Review activities
Work sheets
Board work
Tests
3 wks