ROCKY FORD CURRICULUM GUIDE
SUBJECT: Math
TIMELINE: 2nd Quarter
GRADE: 6
Grade Level
Expectation
Evidence Outcome
Student-Friendly
Learning Objective
Level of
Thinking
Resource Correlation
Academic
Vocabulary
Concepts and skills
students master: 2.
Formulate, represent,
and use algorithms with
positive rational numbers
with flexibility,
accuracy, and efficiency
b. Fluently add, subtract, multiply,
and divide multidigit
decimals using standard algorithms
for each operation. C
We will fluently add,
subtract, multiply, and
divide multidigit (3 by 2)
decimals in a mixed format
using standard algorithms
for each operation.
Appl
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Evaluate
Compute
Regrouping
Addition
Addends
Sum
Plus
Subtraction
Minuend
Subtraend
difference
Minus
Multiplication
Factors
Product
Times
Powers of Ten
Division
Dividend
Divisor
Quotient
Remainder
Annex
Decimals
Repeating
Terminating
Inverse operations
Digits
Concepts and skills
students master: 3. In
the real number system,
rational numbers have a
unique location on the
number line and in
space
a. Explain why positive and
negative numbers are used
together to describe quantities
having opposite directions or
values.
i. Use positive and negative
numbers to represent quantities in
real-world contexts, explaining the
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We will use positive and
negative numbers to
represent quantities in realworld contexts, explaining
the meaning of 0 in each
situation.
Comp
Examples:
Temp. above/below 0
Elev. above/below sea level
Integers
Whole numbers
Opposites
Negative
Positive
Absolute value
Signed
numbers vs.
Page 1
ROCKY FORD CURRICULUM GUIDE
SUBJECT: Math
Grade Level
Expectation
TIMELINE: 2nd Quarter
GRADE: 6
Evidence Outcome
Student-Friendly
Learning Objective
Level of
Thinking
meaning of 0 in each situation. I
Concepts and skills
students master: 3. In
the real number system,
rational numbers have a
unique location on the
number line and in
space
Concepts and skills
students master: 3. In
Appl
b. Use number line diagrams and
coordinate axes to represent points
on the line and in the plane with
negative number coordinates.
i. Describe a rational number as a
point on the number line. I
We will give the definition of
rational numbers and give
examples of them.
Comp
ii. Use opposite signs of numbers to
indicate locations on opposite sides
of 0 on the number line. I
We will place negative and
positive numbers on a
number line.
Comp
iii. Identify that the opposite of the
opposite of a number is the number
itself. I
We will evaluate
expressions that use
multiple negative signs
and/or signed numbers.
Comp
iv. Explain when two ordered pairs
differ only by signs, the locations of
the points are related by reflections
across one or both axes. I
We will graph ordered pairs
and their reflections on a
coordinate graph.
Appl
v. Find and position integers and
other rational numbers on a
horizontal or vertical number line
diagram. I
We will find and position
integers and other rational
numbers on a horizontal or
vertical number line
diagram.
Appl
vi. Find and position pairs of
integers and other rational numbers
on a coordinate plane. I
We will find and position
pairs of integers and other
rational numbers on a
coordinate plane.
Appl
c. Order and find absolute value of
rational numbers.
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Resource Correlation
Academic
Vocabulary
Credits/debits
Pos./neg. electrical charge
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unsigned
numbers
Evaluate
Integers
Whole numbers
Opposites
Negative
Positive
Absolute value
Plane
Rational Numbers
Irrational Numbers
Signed numbers vs.
Unsigned numbers
Coordinate Axes
Orderd pairs
Coordinates
Horizontal
Vertical
Reflections
Position
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Example:
The expression: - (-(2))
Is the same as
2
Integers
Whole numbers
Page 2
ROCKY FORD CURRICULUM GUIDE
SUBJECT: Math
TIMELINE: 2nd Quarter
GRADE: 6
Grade Level
Expectation
Evidence Outcome
Student-Friendly
Learning Objective
Level of
Thinking
the real number system,
rational numbers have a
unique location on the
number line and in
space
i. Interpret statements of inequality
as statements about the relative
position of two numbers on a
number line diagram. I
We will interpret statements
of inequality of two
numbers and plot their
relative positions on a
number line.
Appl
ii. Write, interpret, and explain
statements of order for rational
numbers in realworld
contexts. I
We will give real life
applications of order for
rational numbers and
explain the value of those
applications.
Comp
iii. Define the absolute value of a
rational number as its distance from
0 on the number line and interpret
absolute value as magnitude for a
positive or negative quantity in a
real-world situation. I
We will define absolute
value, and give examples of
it in a real world situation.
Comp
iv. Distinguish comparisons of
absolute value from statements
about order. I
Concepts and skills
students master: 3. In
the real number system,
rational numbers have a
unique location on the
number line and in
d. Solve real-world and
mathematical problems by graphing
points in all four quadrants of the
coordinate plane including the use
of coordinates and absolute value
to find distances between points
© Learning Keys, 800.927.0478, www.learningkeys.org
Given a point on a number
line, we will give its value,
the opposite of its value,
and its absolute value.
We will distinguish
comparisons of absolute
value from statements
about order.
We will solve real-world and
mathematical problems by
graphing points in all four
quadrants of the coordinate
plane.
know
Appl
Resource Correlation
Example:
Thermometers use order for
rational numbers with temps
in or closer to the positive
being warmer than those in or
closer to the negative. Write: 3oC>-7oC to express the fact
that -3oC is warmer than 7oC.
Example:
For an account balance of
-30 dollars, write l-30l = 30 to
describe the size of the debt
in dollars.
Academic
Vocabulary
Opposites
Negative
Positive
Absolute value
Magnitude
Plane
Quadrant
Rational Numbers
Irrational Numbers
Signed numbers vs.
unsigned numbers
Coordinate Axes
Orderd pairs
Coordinates
Horizontal
Vertical
Reflections
Position
Context
Distinguish
Example:
Recognize that an account
balance less than -30 dollars
represents a debt greater
than 30 dollars.
Example:
Make maps
Integers
Whole numbers
Opposites
Negative
Positive
Absolute value
Page 3
ROCKY FORD CURRICULUM GUIDE
SUBJECT: Math
TIMELINE: 2nd Quarter
GRADE: 6
Grade Level
Expectation
Evidence Outcome
Student-Friendly
Learning Objective
Level of
Thinking
Resource Correlation
Academic
Vocabulary
space
with the same first coordinate or the
same second coordinate. I
We will use absolute value
to find distances between
points with the same first
coordinate or the same
second coordinate.
Appl
If they’re in different
quadrants, you add the
absolute values; but if they’re
in the same quadrant, you’d
subtract the absolute
values?????
Plane
Quadrant
Rational Numbers
Irrational Numbers
Signed numbers vs.
Unsigned numbers
Coordinate Axes
Orderd pairs
Coordinates
Horizontal
Vertical
Reflections
Position
Context
Concepts and skills
students master:
1. Algebraic expressions
can be used to
generalize properties of
arithmetic
a. Write and evaluate numerical
expressions involving whole
number exponents. I
We will write and evaluate
numerical expressions
involving whole number
exponents.
Appl
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Concepts and skills
students master:
2. Variables are used to
represent unknown
quantities within
equations and
inequalities
c. Use variables to represent
numbers and write expressions
when solving a real-world or
mathematical problem. M
We will use variables to
represent numbers and
write expressions when
solving a real-world or
mathematical problem.
Appl
i. Recognize that a variable can
represent an unknown number, or,
depending on the purpose at hand,
any number in a specified set. M
b. Write, read, and evaluate
expressions in which letters stand
for numbers.
We will explain the purpose
of a variable and give
examples of when they
would be used.
Eval
Evaluate
Exponents
Repeating Factors
Powers
Base
Expression
Equation
Scientific Notation
Coefficient
Variables
Expressions
Evaluate
Equivalent
Inverse operations
Properties of
Equality
Equality
Inequality
Concepts and skills
students master:
1. Algebraic expressions
We will rewrite expressions
using scientific notation.
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Evaluate
Expression
Equation
Page 4
ROCKY FORD CURRICULUM GUIDE
SUBJECT: Math
TIMELINE: 2nd Quarter
GRADE: 6
Grade Level
Expectation
Evidence Outcome
Student-Friendly
Learning Objective
Level of
Thinking
Resource Correlation
Academic
Vocabulary
can be used to
generalize properties of
arithmetic
i. Write expressions that record
operations with numbers and with
letters standing for numbers. I
We will write expressions in
algebraic form.
Appl
Example:
Subtract a number from 5
5-y
ii. Identify parts of an expression
using mathematical terms (sum,
term, product, factor, quotient,
coefficient) and describe one or
more parts of an expression as a
single entity. I
We will identify parts of an
expression using
mathematical terms (sum,
term, product, factor,
quotient, coefficient) and
describe one or more parts
of an expression as a single
entity.
Comp
Example:
Describe the expression
2(8+7) as a product of two
factors; view (8+7) as both a
single entity and a sum of two
terms.
Variable
Sum
Term
Product
Factor
Quotient
Coefficient
Formula
Order of Operations
iii. Evaluate expressions at specific
values of their variables including
expressions that arise from
formulas used in real-world
problems. I
Concepts and skills
students master:
1. Objects in space and
their parts and attributes
can be measured and
analyzed
iv. Perform arithmetic operations,
including those involving
whole-number exponents, in the
conventional order when
there are no parentheses to specify
a particular order (Order
of Operations). C
a. Develop and apply formulas and
procedures for area of plane figures
i. Find the area of right triangles,
other triangles, special
quadrilaterals, and polygons by
composing into rectangles or
decomposing into triangles and
other shapes. I
ii. Apply these techniques in the
context of solving real-world and
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Free math worksheets
We will evaluate
expressions with the given
values of their variables
including expressions that
arise from formulas used in
real-world problems.
Appl
Example1:
If y = 5; if y = 7
6y
Example 2:
Use the formula A= ½ bh to
find the area of a triangle with
the base = 3, and the height
= 5.
We will apply the rules for
order of operation to
evaluate expressions.
Appl
Textbook: Order of
Operations
We will develop and apply
formulas to find the area of
triangles, quadrilaterals,
and polygons.
We will use the formulas
we’ve developed and other
problem solving strategies
to find the area in real-world
Analysis
& Synt
Appl
Find the area of right
triangles, other triangles,
special quadrilaterals, and
polygons by composing into
rectangles or decomposing
into triangles and other
shapes
Area
Square units
Plane figures
Polygons
Formulas
Quadrilaterals
Compose
Decompose
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Page 5
ROCKY FORD CURRICULUM GUIDE
SUBJECT: Math
Grade Level
Expectation
Concepts and skills
students master: 2.
Formulate, represent,
and use algorithms with
positive rational numbers
with flexibility,
accuracy, and efficiency
Concepts and skills
students master: 2.
Formulate, represent,
and use algorithms with
positive rational numbers
with flexibility,
accuracy, and efficiency
Concepts and skills
students master: 2.
Formulate, represent,
and use algorithms with
positive rational numbers
with flexibility,
accuracy, and efficiency
Concepts and skills
students master: 2.
Formulate, represent,
and use algorithms with
positive rational numbers
with flexibility,
accuracy, and efficiency
Concepts and skills
students master:
1. Algebraic expressions
can be used to
generalize properties of
arithmetic
TIMELINE: 2nd Quarter
GRADE: 6
Evidence Outcome
Student-Friendly
Learning Objective
mathematical problems. I
a. Fluently divide multi-digit
numbers using standard algorithms.
C
situations.
We will fluently divide multidigit numbers (4 by 2) using
standard algorithms.
c. Find the greatest common factor
of two whole numbers less than or
equal to 100. C
We will find the greatest
common factor of two
whole numbers less than or
equal to 100.
Appl
Book Shelf:
36 =2x2x3x3
42 = 2x3x 7
GCF= 2x3
=6
LCM= 2x2x3x3x7=252
Factor
Common Factor
GCF (greatest
common factor)
Prime factorization
Divisibility
d. Find the least common multiple
of two whole numbers less than or
equal to 12. C
We will find the least
common multiple of two
whole numbers less than or
equal to 12.
Appl
See above
Common multiple
LCM (least common
multiple)
Prime factorization
e. Use the distributive property to
express a sum of two whole
numbers 1–100 with a common
factor as a multiple of a sum of two
whole numbers with no common
factor. C
We will factor the sum of
two numbers.
Appl
Example:
4+8 = 4(1+2)
Distribute
Property
Distributive
Property
GCF
c. Apply the properties of operations
to generate equivalent
expressions. I
We will apply the properties
of operations to generate
equivalent expressions
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Level of
Thinking
Resource Correlation
Appl
Dividend
Divisor
Quotient
Remainder
Divisibilty
Algorithms
4+8
4(1) + 4(2)
4(1+2)
Appl
Academic
Vocabulary
Example:
Apply the distributive property
to the expression 3(2+x) to
produce the equivalent
expression 6+3x; apply the
distributive property to the
expression 24x + 18y to
produce the equivalent
Variables
Expressions
Evaluate
Equivalent
Inverse operations
Properties of
Equality
Equality
Page 6
ROCKY FORD CURRICULUM GUIDE
SUBJECT: Math
Grade Level
Expectation
TIMELINE: 2nd Quarter
GRADE: 6
Evidence Outcome
Student-Friendly
Learning Objective
Level of
Thinking
Resource Correlation
Academic
Vocabulary
expression 6(4x+3y); apply
properties of operations to
y+y+y to produce the
equivalent expression 3y.
Inequality
We will identify equivalent
expressions.
Comp
See above
f. Interpret and model quotients of
fractions through the creation of
story contexts. C
We will draw and describe
(annotate) a
model/diagram/picture that
represents a story problem
which uses quotients of
fractions
Synth
Concepts and skills
students master: 2.
Formulate, represent,
and use algorithms with
positive rational numbers
with flexibility,
accuracy, and efficiency
g. Compute quotients of fractions.
C
We will compute quotients
of fractions.
Appl
Concepts and skills
students master: 2.
Formulate, represent,
and use algorithms with
positive rational numbers
with flexibility,
accuracy, and efficiency
h. Solve word problems involving
division of fractions by fractions,
e.g., by using visual fraction
models and equations to
represent the problem. C
We can solve word
problems involving division
of fractions by fractions by
using both visual fraction
models and equations to
represent the problem.
Appl
Quotient
Dividend
Divisor
Reciprocal
Multiplicative
Inverse
Model
Diagram
Annotate
Compute
Quotient
Dividend
Divisor
Reciprocal
Multiplicative
Inverse
Model
Quotient
Dividend
Divisor
Reciprocal
Multiplicative
Inverse
Model
Concepts and skills
students master:
1. Algebraic expressions
can be used to
generalize properties of
arithmetic
Concepts and skills
students master: 2.
Formulate, represent,
and use algorithms with
positive rational numbers
with flexibility,
accuracy, and efficiency
d. Identify when two expressions
are equivalent. I
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