Reporting Category: Data and Analysis
Math: Grade 6
Unit: Data About Us: Statistics
Enduring
Understanding and
Essential Questions
Concepts &
Eligible Content
(6th grade PA Standards)
Big Idea:
Collecting, organizing
displaying and analyzing
data helps us make
informed decisions
about people and the
world around us.
M6.E.1.1.1 Analyze data
and/or answer questions
pertaining to data represented in
frequency tables, double bar
graphs, line plots.
Essential Question:
How is data collected,
analyzed, and displayed
to be useful for informed
decision- making?
M6.E.1.1.3 Display data in
frequency tables, bar graphs or
line plots using a title,
appropriate scale, labels and a
key when needed.
Suggested Length: 5-6 weeks
Competencies
Key
Vocabulary
bar graph
categorical data
coordinate graph
distribution
line plot
mean
median
measures of center
mode
numerical data
Develop strategies for outlier
range
comparing
distributions of data. stem and leaf plot
survey
table
x-axis
y-axis
Understand and use
the process of data
investigation: posing
questions, collecting
and analyzing data
distributions, and
making
interpretations to
answer questions.
Represent
distributions of data
using line plots, bar
graphs, stem and leaf
plots and coordinate
graphs.
Suggested
activities/labs and
assessments (formative
& summative)
Data About Us textbook
Launch
-Discussion
-Pre-assessment
Explore
-Investigation
-Group Activity
Summarize
-Discussion
-Post-assessment
Quizzes
Check Ups
Self-Assessments
Unit Test
Unit Projects
M6.E.2.1.1 Determine/calculate
the mean, median, mode and/or
range of displayed data (data can
be displayed in a table or line
plot – use whole numbers only
up to 2 digits).
Compute the
measures of central
tendency: the mean,
median, mode and
range of the data.
M6.E.1.1.2 Choose the
appropriate representation for a
specific set of data (choices
should be the same type of
graph).
Make informed
decisions about
which graph(s) and
which measures of
center (mean,
median, mode) and
range may be used to
describe a
distribution of data.
Distinguish between
categorical and
numerical data and
identify which graphs
and statistics may be
used to represent
each kind of data.
Reporting Category: Numbers and Operations
Math: Grade 6
Unit: Prime Time: Factors and Multiples
Enduring
Understanding and
Essential Questions
Big Ideas:
The important
properties of whole
numbers are directly
related to properties of
multiplication and
division.
The relationship
between whole number
properties and
multiplication and
division properties are
useful for solving
everyday problems.
Essential Questions:
How are the properties
of whole numbers
related to the properties
of multiplication and
division?
How are properties of
whole numbers used to
solve everyday
problems?
Concepts &
Eligible Content
(6th grade PA Standards)
Suggested Length: 5-6 weeks
Competencies
Key
Vocabulary
abundant number
common factor
common multiple
composite number
conjecture
deficient number
dimensions
Use rectangles to
(whole number)
represent the factor
divisor
pairs of numbers.
even number
exponent
(whole number)
factor
M6.A.1.3.2 Find the Least
Use factors and
factor pair
Common Multiple (LCM) of two multiples to solve
factorization
numbers (through 50) and/or use problems and to
greatest common
the LCM to find the common
explain some
factor (GCF)
denominator of two fractions.
numerical facts of
lowest common
everyday life.
factor (LCM)
multiple
Understand the
odd number
relationships among
perfect number
factors, multiples,
divisors and products. prime factorization
prime number
proper factor
M6.A.1.3.3 Use divisibility
Recognize and use
square number
rules for 2, 3, 5 and/or 10 to
properties of prime
Venn Diagram
draw conclusions and/or solve
and composite
problems.
numbers, even and
odd numbers, and
M6.A.1.3.1 Find the Greatest
Common Factor (GCF) of two
numbers (through 50) and/or use
the GCF to simplify fractions.
Develop strategies for
finding factors and
multiples, and
greatest common
factors.
Suggested
activities/labs and
assessments (formative
& summative)
Prime Time textbook
Launch
-Discussion
-Pre-assessment
Explore
-Investigation
-Group Activity
Summarize
-Discussion
-Post-assessment
Quizzes
Check Ups
Self-Assessments
Unit Test
Unit Projects
square numbers.
M6.A.3.2.1 Solve problems
involving operations (+, -, x, ÷)
with whole numbers,
Recognize and use
the fact that every
whole number can be
written in exactly one
way as a product of
prime numbers.
Develop a variety of
strategies for solving
problems --building
models, making lists
and tables, drawing
diagrams and solving
simpler problems.
Reporting Category: Numbers and Operations
Math : Grade 6
Unit: Bits and Pieces I: Understanding Fractions, Decimals and Percents
Enduring
Understanding and
Essential Questions
Concepts &
Eligible Content
(6th grade PA Standards)
Big Ideas:
Fractions, decimals, and
percents are related and
they are apart of the set
of rational numbers.
M6.A.1.1.1 Represent common
percents as fractions and/or
decimals (e.g., 25% = ¼ = .25) –
common percents are 1%, 10%,
25%, 50%, 75%, 100%.
Model situations
involving fractions,
decimals and
percents.
Rational numbers are an
essential part of
everyday life.
M6.A.1.1.2 Convert between
fractions and decimals and/or
differentiate between a
terminating decimal and a
repeating decimal.
Move flexibly among
fraction, decimals
and percent
representations.
Essential Questions:
How are fractions
decimals and percents
related?
How is this relationship
useful in everyday life?
M6.A.1.1.3 Represent a number
in exponential form (e.g.,
10x10x10=103).
M6.A.1.1.4 Represent a mixed
number as an improper fraction.
Competencies
Understand and use
equivalent fractions
to reason about
situations.
Use benchmark
fractions and whole
numbers to help
estimate the size of a
number or sum.
Develop and use
benchmarks that
relate different forms
of rational numbers.
Use context, physical
models, drawings,
patterns or estimation
Suggested Length: 5-6 weeks
Key
Vocabulary
benchmark
decimal
denominator
equivalent fraction
fraction
improper fraction
mixed number
numerator
percent
place value
ratio
rational number
Suggested
activities/labs and
assessments (formative
& summative)
Bits and Pieces I
textbook
Launch
-Discussion
-Pre-assessment
Explore
-Investigation
-Group Activity
Summarize
-Discussion
-Post-assessment
Quizzes
Check Ups
Self-Assessments
Unit Test
Unit Projects
top help reason about
real life situations
involving rational
numbers.
M6.A.1.2.1 Compare and/or
order whole numbers, mixed
numbers, fractions and/or
decimals (do not mix fractions
and decimals – decimals through
thousandths).
Compare and order
fractions and
decimals.
Reporting Category: Measurement; Geometry
Math: Grade 6
Unit: Shapes and Designs: Two-Dimensional Geometry
Enduring
Understanding and
Essential Questions
Concepts &
Eligible Content
(6th grade PA Standards)
Big Idea :
Displaying, analyzing,
measuring, and
reasoning about shapes
are important features of
our world
M6.C.1.1.1 Identify, classify
and/or compare polygons (up to
ten sides.)
Competencies
Understand some
important properties
of polygons and
recognize polygonal
shapes both in and
out of the classroom
Draw or sketch
polygons with certain
properties
Essential Questions:
How do we display,
analyze, measure and
reason about shapes?
Find patterns that
help determine angle
sums of polygons
Why is being able to
display, analyze,
measure and reason
about shapes an
important feature of our
world?
Investigate the
symmetries of a
shape—rotation or
reflection
M6.C.1.2.1 Identify, describe
and/or label parallel,
perpendicular or intersecting
lines.
Explore parallel lines
and angles created by
lines intersecting
parallel lines
Suggested Length: 5-6 weeks
Key
Vocabulary
acute angle
angle
angle sum
central angle
degree
diagonal
equilateral triangle
exterior angle
interior angle
isosceles angle
irregular polygon
line of symmetry
line segment
midpoint
obtuse angle
parallel lines
parallelogram
perpendicular lines
polygon
quadrilateral
ray
rectangle
reflection symmetry
regular polygon
rhombus
right angle
rotation symmetry
scalene triangle
square
straight angle
Suggested
activities/labs and
assessments (formative
& summative)
Shapes and Designs
textbook
Launch
-Discussion
-Pre-assessment
Explore
-Investigation
-Group Activity
Summarize
-Discussion
-Post-assessment
Quizzes
Check Ups
Self-assessments
Unit Test
Project: Create your
own design/picture
tiling
transversal
trapezoid
vertex
M6.B.2.1.3 Measure angles
using a protractor up to 180° protractor must be drawn - one
side of the angle to be measured
should line up with the straight
edge of the protractor.
Use an angle ruler or
protractor for making
more accurate angle
measurements
M6.C.1.1.2 Identify and/or
describe properties of all types
of triangles (scalene, equilateral,
isosceles, right, acute, obtuse).
Explain the property
of triangles that
makes them useful as
a stable structure for
building
M6.C.1.1.4 Identify and/or use
the total number of degrees in a
triangle, quadrilateral and/or
circle.
Find that the sum of
two side lengths of a
triangle is greater
than the third side
length
Estimate the measure
of any angle using
reference to a right
angle and other
benchmark angles
Find that the sum of
three side lengths of a
quadrilateral is
greater than the
fourth side length
M6.B.2.3.1 Define, label and/or
Reason about and
identify right, straight, acute and
obtuse angles.
solve problems
involving shapes
M6.C.1.2.2 Identify, draw
and/or label points, planes, lines,
line segments, rays, angles and
vertices.
Determine which
polygons fit together
to cover a flat surface
and why
Reporting Category: Numbers and Operations
Math: Grade 6
Unit: Bits and Pieces II: Using Fraction Operations
Enduring
Understanding and
Essential Questions
Concepts &
Eligible Content
(6th grade PA Standards)
Big Idea:
Develop an
understanding of and
strategies for
computations involving
fractions.
M6.A.3.2.1 Solve problems
involving operations (+, -, x, ÷)
with whole numbers, decimals
(through thousandths) and
fractions (avoid complicated
LCDs) - straight computation or
word problems.
Essential Question:
What strategies and
skills are useful for
students to be able to
perform fractional
computations?
Suggested Length: 5-6 weeks
Competencies
Key
Vocabulary
Use benchmarks and
other strategies to
estimate the
reasonableness of
results of operations
with fractions
algorithm
benchmark
denominator
equivalent fractions
fact family
numerator
reciprocal
unit fraction
Use estimates and
exact solutions to
make decisions
Suggested
activities/labs and
assessments (formative
& summative)
Bits and Pieces II
textbook
Launch
-Discussion
-Pre-assessment
Explore
-Investigation
-Group Activity
Solve problems using
arithmetic operations
on fractions
Summarize
-Discussion
-Post-assessment
Develop ways to
model sums,
differences, products,
and quotients with
areas, strips, and
number lines
Quizzes
Check Ups
Self-Assessments
Unit Test
Look for and
generalize patterns in
numbers
Use knowledge of
fractions and
equivalence of
fractions to develop
algorithms for
adding, subtracting,
multiplying and
dividing fractions
Recognize when
addition, subtraction,
multiplication, or
division is the
appropriate operation
to solve a problem
Write fact families to
show the inverse
relationship between
addition and
subtraction, and
between
multiplication and
division
Reporting Category: Numbers and Operations
Math: Grade 6
Unit: Bits and Pieces III: Computing with Decimals and Percents
Suggested Length: 5-6 weeks
Enduring
Understanding and
Essential Questions
Concepts &
Eligible Content
(6th grade PA Standards)
Competencies
Key
Vocabulary
Big Idea:
Develop an
understanding of and
strategies for
computations involving
decimals.
M6.A.3.1.1 Use estimation to
solve problems involving whole
numbers and decimals (up to 2digit divisors and 4 operations).
Build on knowledge
about operations with
fractions and whole
numbers
dividend
divisor
powers of 10
quotient
repeating decimal
terminating decimal
Essential Question:
What strategies and
skills are useful for
students to be able to
perform decimal
computations?
M6.A.3.2.1 Solve problems
involving operations (+, -, x, ÷)
with whole numbers, decimals
(through thousandths) and
fractions (avoid complicated
LCDs) - straight computation or
word problems.
Develop and use
benchmarks and other
strategies to estimate
the answers to
computations with
decimals
Develop meaning or
and algorithms for
operations with
decimals
Use the relationship
between decimals and
fractions to develop
and understand why
decimal algorithms
work
Use the place value
interpretations of
decimals to make
sense of shortcut
algorithms for
Suggested
activities/labs and
assessments (formative
& summative)
Suggested activities:
Bits and Pieces III
Investigations 1-5.2
Launch
-Discussion
-Pre-assessment
Explore
-Investigation
Group Activity
Summarize
-Discussion
-Post-assessment
Suggested assessments:
Quizzes
Check Ups
Self-assessments
Unit Test
operations
Generalize number
patterns to help make
sense of decimal
operations
Choose between
addition, subtraction,
multiplication, or
division as an
appropriate operation
to use to solve a
problem
Understand that
decimals are often
associated with
measurements in realworld situations
Solve problems using
operations with
decimals
Big Idea:
Develop an
understanding of and
strategies for
computations involving
percents.
Essential Question:
What strategies and
skills are useful for
students to be able to
perform computations
involving percents?
Use understanding of
operations and the
meaning of percents
to solve percent
problems of the form
a% b equals c for
any one of the
variables a, b, or c