MORRIS SCHOOL DISTRICT
MORRISTOWN, NJ
2011-2012
GRADE 6 MATHEMATICS
C URRICULUM M AP
1
Grade 6, focus on: (1) connecting ratio and rate to whole number multiplication and division and using concepts of ratio and rate to
solve problems; (2) completing understanding of division of fractions and extending the notion of number to the system of rational
numbers, which includes negative numbers; (3) writing, interpreting, and using expressions and equations; and (4) developing
understanding of statistical thinking.
Grade 6 Overview
Ratios and Proportional Relationships
◦ Understand ratio concepts and use ratio reasoning to solve problems.
The Number System
◦ Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
◦ Multiply and divide multi-digit numbers and find common factors and multiples.
◦ Apply and extend previous understandings of numbers to the system of rational numbers.
Expressions and Equations
◦ Apply and extend previous understandings of arithmetic to algebraic expressions.
◦ Reason about and solve one-variable equations and inequalities.
◦ Represent and analyze quantitative relationships between dependent and independent variables.
Geometry
◦ Solve real-world and mathematical problems involving area, surface area, and volume.
Statistics and Probability
◦ Develop understanding of statistical variability.
◦
Summarize and describe distributions.
2
Curriculum Map
Content/Objective
Unit 1- Expressions and Number Properties
The learner will:
 Write and evaluate numerical expressions
involving whole number exponents (6.EE.1)
 Evaluate expressions at specific values of their
variables. (6.EE.2c)
 Write expressions that record operations with
numbers and with letters standing for numbers.
(6.EE.2a)
 Identify parts of an expression using
mathematical terms (sum, term, product, factor,
quotient, coefficient); view one or more parts of
an expression as a single entity. (6.EE.2b)
 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.6)
 Apply the properties of operations to generate
equivalent expressions (6.EE.3)
 Identify when two expressions are equivalent
(6.EE.4)
 Find the greatest common factor of two whole
numbers less than or equal to 100 and the least
common multiple of two whole numbers less
than or equal to 12. Use the distributive
property to express a sum of two whole
numbers with no common factor. (6.NS.4)
Essential Questions/
Enduring Understandings
Essential Questions:
How can you write and
evaluate an expression that
represents a real-life problem?
Which words correspond to the
four operations of addition,
subtraction, multiplication and
division?
Does the order in which you
perform an operation matter?
How do you multiply two 2digit numbers using mental
math?
How can you use formulas to
find the area of an object with
an unusual shape?
Enduring Understandings:
Apply and extend previous
understandings of arithmetic to
algebraic expressions
Reason about and solve onevariable equations and
inequalities
Represent and analyze
quantitative relationships
between dependant and
independent variables
Suggested Activities
Activities:
 Translate number stories into algebraic expressions.
 Evaluating algebraic expressions using substitution
 Evaluating an Expression substituting two variables
 Evaluating Expressions with Two Operations
 Real-Life Application (Saving for a skateboard)
 Taking Math Deeper: Deck Activity
Activities:
 Words that Imply Addition or Subtraction
 Words that Imply Multiplication or Division
 Find the Intruder Activity
 Writing Numerical Expressions
 Writing Algebraic Expressions
 Standardized Test Practice
 Real-Life Application – Cypress Tree
 Taking Math Deeper- Using Tables to Organize
Information
Evaluation/
Assessment
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Warm-Ups
Checkpoint
Exercises
Oral
Questioning
Exit Tickets
Projects
Tests/Quizzes
TechnologyBased
Assessments
Activities:
 Does Order Matter?
 Commutative Properties
 Associative Properties
 Using Properties to Simplify Expressions
 Real Life Application (Basketball)
 Taking Math Deeper (Drawing prisms & Project)
Activities:
 Finding Products Involving Multiples of 10
 Using Mental Math
 Two Ways to Multiply
 Simplifying Algebraic Expressions
 Standardized Test Practice
 Real Life Application (Mark’s age)
 Taking Math Deeper (Marketing Poster)
Activities:
 Using an Area Formula (Polygon Chart)
3
Content/Objective
Essential Questions/
Enduring Understandings
Suggested Activities
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Unit 2- Multiplying and Dividing Fractions
 Interpret and compute quotients of
fractions and solve word problems
involving division of fractions by fractions
(6.NS.1)
 Fluently divide multi-digit numbers using
the standard algorithm (6.NS.2)
Essential Questions:
How can you use estimation to
check that your answer is
reasonable?
What does it mean when a
whole number is multiplied by
a fraction? Will the product be
greater or less than the whole
number?
What does it mean to multiply
fractions?
How do you multiply a mixed
number by a fraction?
How do you divide by a
fraction?
How can you use division by a
mixed number as part of a
story?
When you write a terminating
decimal as a fraction, what type
of denominator do you get?
How can you tell the
denominator of a fraction if its
decimal form is terminating or
repeating?
Enduring Understandings:
Computational fluency includes
Evaluation/
Assessment
Finding an Area
Using a Simple Formula
Using an Area Formula
Taking Math Deeper (Translating words into Math)
Activities:
 Using Models for Fractions
 Estimating Sums and Differences of Fractions
 Estimating Products of Fractions
 Estimating Quotients of Fractions
 Estimating Products and Quotients with Mixed
Numbers
 Using Overestimates
 Using Compatible Numbers
 Taking Math Deeper- Simplifying Questions using a
Racecar
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Warm-Ups
Checkpoint
Exercises
Oral
Questioning
Exit Tickets
Projects
Tests/Quizzes
TechnologyBased
Assessments
Activities:
 Multiplying a Fraction and a Whole Number
 Multiplying a Whole Number and a Fraction
 Standardized Test Practice
 Real-Life Application- Weight of a Watermelon
 Taking Math Deeper- Making Necklaces
Activities:
 Multiplying Fractions
 Multiplying Fractions with Common Factors
 Standardized Test Practice
 Real-Life Application- Bag of Flour
Activities:
 Multiplying a Mixed Number and a Fraction
 Buried Treasure Game
 Using the Distributive Property
 Multiplying Mixed Numbers
 Real-Life Application- Resurfacing a Basketball Court
 Taking Math Deeper- Changing Units
Activities:
 Dividing by a Fraction
4
Content/Objective
Essential Questions/
Enduring Understandings
understanding the meaning and
the appropriate use of
numerical operations.
The magnitude of numbers
affects the outcome of
operations on them.
In many cases, there are
multiple algorithms for finding
a mathematical solution, and
those algorithms are frequently
associated with different
cultures.
Suggested Activities
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Evaluation/
Assessment
Writing Reciprocals
Dividing a Fraction by a Fraction
Dividing a Whole Number by a Fraction
Evaluating an Algebraic Expression
Using Order of Operations
Taking Math Deeper- Glazing Plates and Bowls
Activities:
 Writing a Story
 Dividing by a Mixed Number
 Dividing a Mixed Number by a Fraction
 Dividing Mixed Numbers
 Using Order of Operations
 Real-Life Application- Tortilla Soup
 Taking Math Deeper- Trail Mix
Activities:
 Writing Common Decimals as Fractions
 4 in a Row Game
 Vocabulary Patterns
 Writing Decimals as Fractions
 Writing Decimals as Mixed Numbers
 Real-Life Application- Bird Species
 Taking Math Deeper- Animal Exhibits
Activities:
 Writing a Fraction as a Decimal
 Real-Life Application- 40-yard Dash
 Taking Math Deeper- Turtle Shell Length
Unit 3: Multiplying and Dividing Decimals
Essential Questions:
The learner will:
 Fluently add, subtract, multiply and divide
multi-digit decimals using the standard
algorithm for each operations. (6.NS.3)
 Fluently divide multi-digit numbers using
the standard algorithm. (6.NS.2)
How can you use estimation to
check that your answer is
reasonable?
What happens to the decimal
point when you multiply a
whole number by a decimal?
When multiplying decimals,
Activities:
 Newspaper ad activity decimal estimation
 Estimating decimal products
 Writing a estimation of decimal story
 Estimate Decimal products and quotient
 Using Compatible Numbers
 Real-Life Application: Beach Erosion
 Taking it Deeper: Calories Burn
Activities:
 Activity: Multiplying by the powers of 10
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Warm-up
Check point
exercise
Oral Question
Exit Ticket
Tests/
Quizzes
Technology
based
assessments
Projects
5
Content/Objective
Essential Questions/
Enduring Understandings
how do you know where to
place the decimal point in the
product?
How is dividing a decimal by a
whole number similar to
dividing a whole number by a
whole number?
How can you use the base ten
blocks to model decimal
division
Enduring Understandings:
Numeric fluency includes both
the understanding of and the
ability to appropriately use
numbers.
Computational fluency includes
understanding the meaning and
the appropriate use of
numerical operations.
The magnitude of numbers
affects the outcome of
operations on them.
In many cases, there are
multiple algorithms for finding
a mathematical solution, and
those algorithms are frequently
associated with different
cultures.
Unit 4: Fractions, Decimals, Percents
 Find a percent of a quantity as a rate per
Essential Questions:
Suggested Activities
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Evaluation/
Assessment
Activity: Multiplying a Decimal by a Whole NumberSchool Carnival
Activity: Back to School Shopping
Using estimation to find a product
Multiplying decimals and whole numbers
Inserting zeros in the product
Mental Math: product of base ten numbers
Taking it Deeper: Converting building heights from
meters to feet
Activities:
 Activity: Multiplying decimal and converting fractions
to the product
 Activity: Multiplying decimals using the circle maze
 multiplying decimals
 Evaluating Expressions using variables and substitution
 Real-Life Application: Cost to pounds
 Taking it Deeper: Area of a painting find the missing
dimensions
Activities:
 Activity: Dividing a decimal using base ten blocks
 Activity: Where does the decimal go using estimation
 Activity: Using the perimeter formula
 Dividing decimals by whole numbers
 Dividing decimals by adding zeros to have the quotient
terminate
 Real-Life Application: Sport Drink Comparative
Shopping
 Taking it Deeper: Free Style Relay
Activities:
 Activity: Dividing Decimals using Base Ten Blocks
 Dividing Decimals
 Dividing Decimals when there is a decimal in the
divisor
 Real-Life Application: Cellular phone line graph
 Taking it Deeper: Increasing the rectangular
dimensions will effect the area and perimeter
Activities:
 Writing Percents as Fractions
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Warm-Ups
Checkpoint
6
Content/Objective
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100; solve problems involving finding the
whole, given a part and a percent (6.RP.3c)
Understand the concept of a ratio and use
ratio language to describe a ratio
relationship between two quantities
(6.RP.1)
Interpret statements as statements about the
relative position of two numbers on a
number line diagram (6.NS.7a)
Write, interpret and explain statements of
order for rational numbers in real-world
contexts (6.NS.7b)
Essential Questions/
Enduring Understandings
How can you use a model to
write a percent as a fraction or
write a fraction as a percent?
How does the decimal point
move when you rewrite a
percent as a decimal and when
you rewrite a decimal as a
percent?
How can you order numbers
that are written as fractions,
decimals and percents?
How can you use mental math
to find the percent of a number?
How can you use mental math
and estimation to help solve
real-life problems?
Enduring Understanding:
A quantity can be
represented numerically in
various ways. Problem
solving depends upon
choosing wise ways.
Numeric fluency includes
both the understanding of
and the ability to
appropriately use numbers.
Context is critical when
using estimation.
Unit 5 – Ratios, Rates and Data Analysis
Essential Questions:
How can you tell whether two
Suggested Activities
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Evaluation/
Assessment
Exercises
 Oral
Questioning
 Exit Tickets
 Projects
 Tests/Quizzes
 TechnologyBased
Assessments
Writing Fractions as Percents
Real-Life Application- Digital Cameras
Taking Math Deeper- Comparing Sizes of U.S. States
Activities:
 Writing Percents as Decimals
 Writing Decimals as Percents
 Standardized Test Practice
 Real-Life Application- Ultraviolet Rays
 Taking Math Deeper- Circle Graph Tables
Activities:
 Ordering Numbers
 Using Fractions, Decimals and Percents
 The Game of Math Card War
 Comparing Fractions, Decimals and Percents
 Real-Life Application- Soccer Goals
 Taking Math Deeper- Ordering & Comparing Data
Activities:
 Finding 10% of a Number
 Finding 1% of a Number
 Using Mental Math to find percents of numbers
 Finding the Percent of a Number
 Standardized Test Practice
 Using Mental Math to Find Price of Concert Tickets
 Real-Life Application- Area of a Room
 Taking Math Deeper-Sale Prices
Activities:
 Estimating a Percent
 Using Mental Math to estimate percent of a Number
 Estimating the Percent of a Number
 Using Compatible Numbers
 Real-Life Application- Circle Graphs
 Taking Math Deeper- Ratios
Activities
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Warm Ups
7
Content/Objective
The learner will:
 Understand the concept of a ratio and use ratio
language to describe a ratio relationship
between two quantities. (6.RP.1)
 Understand the concept of a unit rate a/b
associated with a ratio a:b with b not equal to 0,
and use rate language in the context of a ratio
relationship (6.RP.2)
 Solve unit rate problems including those
involving unit pricing and constant speed.
(6.RP.3b)
 Use ratio reasoning to convert measurement
units; manipulate and transform units
appropriately when multiplying or dividing
quantities. (6.RP.3d)
 Make tables of equivalent ratios relating
quantities with whole number measurements,
find missing values in the tables, and plot the
pairs of values on the coordinate plane. Use
tables to compare ratios. (6.RP.3a)
 Recognize a statistical question as one that
anticipates variability in the data related to the
question and accounts for it in the answers.
(6.SP.1)
 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. (6.SP.2)
 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.3)
 Summarize numerical data sets in relation to
their context by reporting the number of
observations (6.SP.5a)
 Summarize numerical data sets in relation to
their context by giving quantitative measures of
center (median and/or mean) and variability
(interquartile range and/or mean absolute
deviation), as well as describing any overall
pattern and any striking deviations from the
overall pattern with reference to the context in
Essential Questions/
Enduring Understandings
recipes make the same mixture?
How can you use rates to
describe changes in real-life
problems?
How can you use rates to help
show how a country can save
valuable natural resources?
What is the meaning of the
word “average”? How can you
find the average of a collection
of numbers.
Describe situations in real life
where the mean is not a good
representation of the average.
How can you use tables and
graphs to help organize data?
Enduring Understandings:
The message conveyed by the
data depends on how the data is
collected, represented, and
summarized.
The results of a statistical
investigation can be used to
support or refute an argument.
Suggested Activities
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Comparing Recipes
Finding Equivalent Ratios
Writing a Ratio
Writing and Simplifying Ratios
Writing Equivalent Ratios
Comparing Ratios
Taking Math Deeper (Perimeter and Area)
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Evaluation/
Assessment
Checkpoint
exercises
Oral Questioning
Exit tickets
Projects
Tests/Quizzes,
Technology-based
assessments
Activities
 Stories without Words
 Changing Units in a Rate
 Writing a Rate
 Writing a Unit Rate
 Using a Unit Rate
 Comparing Unit Costs
 Taking Math Deeper (Making a table)
Activities
 Saving Water
 Saving Gasoline
 Finding a Distance
 Finding a Speed
 Solving a Rate Problem
 Solving a Cost Problem
 Taking Math Deeper (Bike Problem)
Activities
 Describing an Average
 Describing a Collection of Shoe Sizes
 Talking About Averages
 Standardized Test Practice
 Comparing Means
 Finding a Mean with and without an Outlier
 Taking Math Deeper (Allowances)
Activities
 Comparing Three Samples
 When the Mean is Misleading
 Finding the Mode
 Standardized Test Practice
 Taking Math Deeper (How does one number affect the
8
Content/Objective
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Essential Questions/
Enduring Understandings
which the data were gathered (6.SP.5c)
Summarize numerical data sets in relation to
their context by relating the choice of measures
of center and variability to the shape of the data
distribution and the context in which the data
were gathered. (6.SP.5d)
Display numerical data in plots on a number
line, including dot plots, histograms, and box
plots. (6.SP.4)
Evaluation/
Assessment
set?)
Activities
 Conducting an Experiment
 Organizing Data
 Developing an Experiment
 Choosing the Best Measure of Central Tendency
 Removing an Outlier
 Standardized Test Practice
 Taking Math Deeper (Baseball)
 Making a Line Plot
 Making a Histogram
 Making a Box-and-Whisker-Plot
 Analyzing a Box-and-Whisker Plot
Essential Questions
Unit 6: Circles and Area
The learner will:
 Evaluate expressions at specific values of
their variables. Include expressions that
arise from formulas used in real world
applications. Perform arithmetic
operations, including those involving
whole-number exponents, the conventional
order when there are no parentheses to
specify a particular order. (Order of
Operations) (6.EE.2c)
 Find the area if right triangles, other
triangles, special quadrilaterals and
polygons by composing into rectangles or
decomposing into triangles and other
shapes; apply these techniques in the
context of solving real-world problems.
(6.G1)
Suggested Activities
How do you find the
circumference of a circle?
How can you find the perimeter
of a composite figure?
How can you find the area of a
circle?
How can you find the area of
composite figure?
Enduring Understandings:
Everyday objects have a
variety of attributes, each of
which can be measured in
many ways.
What we measure affects
how we measure it.
Activities:
 Approximating pi to square
 Approximating pi to hexagons
 Find the radius and a diameter
 Finding the circumference of circles
 Standardized Test Practice: Decreasing the diameter
will effect the circumference
 Finding the perimeter of a semicircular region
 Taking It Deeper: Bicycle Wheel Rotational Turns
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Activities:
 Finding the pattern by finding the perimeter
 Find the distance using scale factor
 Submitting a bid –tiling a pool
 Finding a perimeter using grid paper
 Using tangrams, compare the perimeter of a square to
the perimeter of the house
 Find the perimeter of irregular shapes
 Taking it Deeper: Find compound area of an irregular
shaped garden
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Warm-up
Check point
exercise
Oral Question
Exit Ticket
Tests/
Quizzes
Technology
based
assessments
Projects
Activities:
 Estimating the area of a circle
 Approximating the area of a circle by cutting the circle
into circle
 Find the area of circle using pi
9
Content/Objective
Essential Questions/
Enduring Understandings
Measurements can be used
to describe, compare, and
make sense of phenomena.
Suggested Activities
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Evaluation/
Assessment
Standardized Test Practice: Distance of wheel rotation
Finding the area of a semicircle
Taking it Deeper: The dog path area
Real-life Application: Pool inscribe by a square
Activities:
 Activity: Find the area of irregular shapes using grid
paper
 Find the area of the basketball court
 Find the compound area of irregular shapes
 Taking It Deeper: Find the area of 2d nets of square
pyramid and rectangular prism
Unit 7- Equations
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Identify parts of an expression using
mathematical terms (sum, term, product,
factor, coefficient); view one or more parts
of an expression as a single entity.
(6.EE.2b)
Solve real-world and mathematical
problems 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. (6.EE.7)
Understand solving an equation or
inequality as a process of answering a
question; which values of 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.5)
Essential Questions:
How does rewriting a word
problem help you solve the
word problem?
How can you use addition or
subtraction to solve an
equation?
How can you use multiplication
or division to solve an
equation?
What is a “two-step” equation?
How can you solve a two-step
equation?
How can you use area and
perimeter formulas to find
missing dimensions of plane
figures?
How can you use a volume
formula to find missing
dimensions of prisms?
Enduring Understandings:
Activities:
 Rewriting a Word Problem
 Standardized Test Practice
 Real-Life Application- Spelling Bee
 Taking Math Deeper- Strawberries
Activities:
 Solving an Equation using Subtraction
 Solving Equations Using Mental Math
 Solving Equations Using Addition or Subtraction
 Checking Solutions
 Real-Life Application – Rock Climbing
 Taking Math Deeper- Amusement Park
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Warm-Ups
Checkpoint
Exercises
Oral
Questioning
Exit Tickets
Projects
Tests/Quizzes
TechnologyBased
Assessments
Activities:
 Writing and Solving Multiplication Equations
 Using an Equation to Model a Story
 Solving Equations Using Multiplication
 Solving an Equation Using Division
 Using the Formula for Distance
 Taking Math Deeper- Frozen Juice Drinks
Activities:
 Identifying Inverse Operations
 Solving Two-Step Equations
 Analyzing a Video Game
 Standardized Test Practice
10
Content/Objective
Essential Questions/
Enduring Understandings
Everyday objects have a variety
of attributes, each of which can
be measured in many ways.
What we measure affects how
we measure it.
Measurements can be used to
describe, compare, and make
sense of phenomena.
Algebraic representation can be
used to generalize patterns and
relationships
The symbolic language of
algebra is used to communicate
and generalize the patterns in
mathematics.
Unit 8 – Inequalities
Essential Questions:
The learner will:
 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? (6.EE.5)
 Write an inequality of the form x >c or x <c to
represent a constraint or condition in a realworld 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.8)
How can you use a number line
to represent solutions of an
inequality?
How can you use an inequality
to describe a real-life situation?
How can you use multiplication
or division to solve an
inequality?
Suggested Activities
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Real-Life Application- Tandem Bikes
Taking Math Deeper- Hardcover Book
Activities:
 Finding Missing Dimensions
 Finding Dimensions
 Drawing a School Logo
 Real-Life Application- Dance Studio
 Taking Math Deeper- Door Dimensions
Activities:
 Finding Missing Dimensions
 Finding Dimensions
 Counting Cubes
 Finding the Volume of a Rectangular Prism
 Finding a Missing Dimension of a Rectangular Prism
 Finding the Surface Area of a Rectangular Prism
 Finding the Surface Area of a Triangular Prism
 Finding the Surface Area of a Square Pyramid
Activities:
 Understanding Inequality Statements
 Understanding Inequality Symbols
 How Close Can you Come to 0?
 Writing Inequalities
 Checking Solutions
 Graphing an Inequality
 Real-Life Application (Solar Probe)
 Taking Math Deeper (Shopping)
Enduring Understandings:
Activities:
 Writing an Inequality
 The Triangle Inequality
 Puzzles
 Solving an Inequality using Addition
 Solving an Inequality using Subtraction
 Real-Life Application
 Taking Math Deeper (Open Ended)
Algebraic representation can be
used to generalize patterns and
Activities:
 Saving Water
How can you use inequalities to
classify different species of
animals?
Evaluation/
Assessment
Evaluation/Assessme
nt
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Warm-Ups
Checkpoint
Exercises
Oral
Questioning
Exit Tickets
Projects
Tests/Quizzes
TechnologyBased
Assessments
11
Content/Objective
Essential Questions/
Enduring Understandings
relationships.
The symbolic language of
algebra is used to communicate
and generalize the patterns in
mathematics.
Suggested Activities
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Evaluation/
Assessment
Matching inequalities
Writing an Inequality
Spaceman Game
Solving an Inequality using Multiplication
Solving an Inequality using Division
Real-Life Application
Taking Math Deeper (Estimating Time)
Activities:
 Classifying Dinosaurs
 Solving Two-Step Inequalities
 Real-Life Application
 Taking Math Deeper (“Equality Problem”)
Unit 9 – Tables, Graphs and Functions
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Essential Questions:
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 the
independent variable using graphs and
tables and relate these to the equation.
(6.EE.9)
What is a mapping diagram?
How can it be used to represent
a function?
How can you describe a
function with words? How can
you describe a function with an
equation?
How can you use a table to
describe a function?
How can you use a graph to
describe a function?
How can you analyze a
function from its graph?
Enduring Understandings:
Patterns and relationships can
be represented graphically,
numerically, symbolically, or
verbally
The symbolic language of
algebra is used to communicate
Activities:
 Constructing Mapping Diagrams
 Interpreting Mapping Diagrams
 Listing Ordered Pairs
 Drawing a Mapping Diagrams
 Describing a Mapping Diagram
 Real-Life Application- Songs Played
 Taking Math Deeper- Scuba Diving
Activities:
 Describing a Function
 Writing an Equation in Two Variables
 Evaluating a Function
 Checking Solutions
 Real-Life Application- “maXair Ride”
 Taking Math Deeper-Bracelets
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Warm-Ups
Checkpoint
Exercises
Oral
Questioning
Exit Tickets
Projects
Tests/Quizzes
TechnologyBased
Assessments
Activities:
 Using a Function Table
 Making a Function Table
 Completing Input-Output Tables
 Standardized Test Practice
 Finding a Missing Input
 Taking Math Deeper-Geography
Activities:
 Interpreting a Graph
12
Content/Objective
Essential Questions/
Enduring Understandings
and generalize the patterns in
mathematics.
Algebraic representation can be
used to generalize patterns and
relationships
Unit 10
The Number Line
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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 in
each situation. (6.NS.5)
Recognize opposite signs of numbers as
indicating locations on opposite sides of 0
on the number line; recognize that the
opposite of the opposite of a number is the
number itself, and that 0 is its own
opposite. (6.NS.6a)
Find and position integers and other
rational numbers on a horizontal or vertical
number line diagram; find and position
pairs of integers and other rational numbers
on a coordinate plane. (6.NS.6c)
Unit 11 – Comparing Numbers
Essential Questions:
How can you write and graph
positive and negative integers?
Suggested Activities
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Evaluation/
Assessment
Conducting an Experiment
Graphing a Function
Taking Math Deeper- Furniture Sale
Activities:
 Analyzing Graphs
 Conducting an Experiment
 Identifying Linear Functions
 Comparing Linear Functions
 Taking Math Deeper- Foot Race
Activities:
 Writing Positive and Negative Integers
 Graphing Integers
 Real-Life Application- Delivering Flowers
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Enduring Understandings:
The symbolic language of
algebra is used to communicate
and generalize the patterns in
mathematics.
Algebraic representation can be
used to generalize patterns and
relationships
Warm-Ups
Checkpoint
Exercises
Oral
Questioning
Exit Tickets
Projects
Tests/Quizzes
TechnologyBased
Assessments
A quantity can be represented
numerically in various ways.
Problem solving depends upon
choosing wise ways.
Numeric fluency includes both
the understanding of and the
ability to appropriately use
numbers.
Essential Questions:
How can I compare rational
Activities:
 Comparing Integers
Warm Ups,
Checkpoint exercises,
13
Content/Objective
The learner will:
 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 in each situation. (6.NS.5)
 Find and position integers and other rational
numbers on a horizontal or vertical number line
diagram; find and position pairs of integers and
other rational numbers on a coordinate plane.
(6.NS.6c)
 Interpret statements of inequality as statements
about the relative position of two numbers on a
number line diagram. (6.NS.7a)
 Write, interpret, and explain statements of order
fro rational numbers in real-world contexts.
(6.NS.7b)
Essential Questions/
Enduring Understandings
numbers on a number line?
Enduring Understandings:
Suggested Activities
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Comparing Decimals
Comparing Fractions and Mixed Numbers
Real-Life application (Temperature)
The symbolic language of
algebra is used to communicate
and generalize the patterns in
mathematics.
Evaluation/
Assessment
Oral Questioning, Exit
tickets, Projects,
Tests/Quizzes,
Technology-based
assessments
Algebraic representation can be
used to generalize patterns and
relationships
A quantity can be represented
numerically in various ways.
Problem solving depends upon
choosing wise ways.
Numeric fluency includes both
the understanding of and the
ability to appropriately use
numbers.
Unit 12: Absolute Value
The learner will:
 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
applications, explaining the meaning of 0
in each situation (6.NS.5)
 Find the position of integers and other
rational numbers on a horizontal or vertical
number line diagram; find the position of a
pairs of integers and other rational numbers
on the coordinate plane (6.NS.6c)
 Interpret statements of inequalities as
statements about the relative position of
two numbers on a number line diagram
(6.NS.7a)
 Write, interpret, and explain statements of
order for rational numbers in real-world
Essential Questions:
How does absolute value relate
to distance on a number line?
How do you find value of an
integer on the number line?
Activities:
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Finding the absolute value on a number line
Comparing integers to absolute value
Real-life Application: Elevations of several animals
and relate it to sea levels
Taking It Deeper: Apply integers to checking accounts
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Enduring Understandings:
The symbolic language of
algebra is used to communicate
and generalize the patterns in
mathematics.

Warm-up
Check point
exercise
Oral Question
Exit Ticket
Tests/
Quizzes
Technology
based
assessments
Projects
Algebraic representation can be
used to generalize patterns and
relationships
14
Content/Objective
contexts. (6.NS.7c)
Distinguish comparisons of absolute value from
statements about order (6.NS.7d)
Essential Questions/
Enduring Understandings
A quantity can be represented
numerically in various ways.
Problem solving depends upon
choosing wise ways.
Suggested Activities
Evaluation/
Assessment
Numeric fluency includes both
the understanding of and the
ability to appropriately use
numbers.
Unit 13
The Coordinate Plane
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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 in
each situation. (6.NS.5)
Understand signs of numbers in ordered
pairs as indicating locations in quadrants of
the coordinate plane; recognize that when
two ordered pairs differ only by signs, the
locations of the points are related by
reflections across one or both axes.
(6.NS.6b)
Find and position integers and other
rational numbers on a horizontal or vertical
number line diagram; find and position
pairs of integers and other rational numbers
on a coordinate plane. (6.NS.6c)
Solve real-world and mathematical
problems by graphing points in all four
quadrants of the coordinate plane. Include
use of coordinates and absolute value to
find distances between points with the
same first coordinate or the same second
coordinate. (6.NS.8)
Draw polygons in the coordinate plane
Essential Question:
How can you plot points on a
coordinate plane?
Enduring Understandings:
Coordinate geometry can be
used to represent and verify
geometric/ algebraic
relationships.
Activities:
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Plotting Ordered Pairs
Real-Life Application- Finding Area on a Coordinate
Plane
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Warm-Ups
Checkpoint
Exercises
Oral
Questioning
Exit Tickets
Projects
Tests/Quizzes
TechnologyBased
Assessments
Shape and area can be
conserved during mathematical
transformations.
15
Content/Objective
Essential Questions/
Enduring Understandings
Suggested Activities
Evaluation/
Assessment
given coordinates for the vertices; use
coordinates to find the length of a side
joining points with the same first
coordinate or the same second coordinate.
Apply these techniques in the context of
solving real-world and mathematical
problems.
16