Download Five District Partnership

Five District Partnership 1
Grade 6 Math Year-Long Plan Overview
Standards
Shorthand Description
6.RP.1
Understand ratios to describe relationships
X
6.RP.2
Understand unit rates
X
R
6.RP.3a
Ratios (tables and graphs)
X
R
6.RP.3b
X
R
X
R
6.RP.3d
Solve unit rate problems
Solve for missing quantity in percent
problem
Convert units with ratios
MA 6.RP.3e
Relate mass and volume of an object
6.NS.1
Divide fractions
X
6.NS.2
Divide multi-digit whole numbers
X
6.NS.3
Computing with decimals
Greatest common factor and distributive
property
Prime factorization and prime numbers
Contextual positive and negative rational
numbers
Opposites
X
6.RP.3c
6.NS.4
MA 6.NS.4a
6.NS.5
6.NS.6a
6.NS.6b
6.NS.6c
6.NS.7a
6.NS.7b
6.NS.7c
Sept-Oct
Signs of numbers and ordered pairs
Rational numbers on number lines and
coordinate pairs
Rational number inequalities and number
lines
Order rational numbers in real world
contexts
Absolute value
Nov-Dec
Jan-Feb
Mar-Apr
May-June
X
X
R
X
X
X
X
X
X
X
X
X
6.EE.2b
Absolute value comparison
Graph and find distance between
coordinate points
Write and evaluate numerical expressions
involving whole-number exponents.
Write word expressions with variables in
numerical form
Name parts of expressions
6.EE.2c
Evaluate algebraic expressions
X
R
6.EE.3
Generate equivalent expressions
X
R
6.EE.4
Identify equivalent expressions
Solve equations and inequalities by
substitution from a set
Use variables
Solve problems by writing and solving 1step equations
Inequalities
Relationships between independent and
dependent variables in equations, graphs,
and tables
Area of polygons by composition and
decomposition
Area and circumference of circles-solve
real world and mathematical problems
with circles
Volume of rectangular prisms with
fractional edge lengths
X
6.NS.7d
6.NS.8
6.EE.1
6.EE.2a
6.EE.5
6.EE.6
6.EE.7
6.EE.8
6.EE.9
6.G.1
MA 6.G.1ab
6.G.2
X
X
X
The Five District Partnership
R
X
R
X
X
R
X
X
R
X
X
R
X
X
X
Grade 6 Math
Five District Partnership 2
6.G.3
Polygons in the coordinate plane
X
6.G.4
Nets and surface area
X
6.SP.1
X
6.SP.4
Recognize statistical questions
Descriptions of data sets: center, spread,
shape
Describe numerical data: center and
variation
Dot plots, histograms, and box plots
MA.6.SP.4a
Read and interpret circle graphs
X
6.SP.5a
Number of observations
X
6.SP.5b
Attributes measured
X
6.SP.5c
Center, variability, patterns, and outliers
X
6.SP.5d
Choose measures of center and variability
X
6.SP.2
6.SP.3
X
X
X
Grade 6 Math 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.

Compute fluently with multi-digit numbers and find common
factors and multiples.

Apply and extend previous understandings of numbers to the
system of rational numbers.
STANDARDS FOR
MATHEMATICAL PRACTICE
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.
1. Make sense of problems and persevere in solving
them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the
reasoning of others.
4. Model with mathematics.
Geometry
5. Use appropriate tools strategically.

6. Attend to precision.
Solve real-world and mathematical problems involving area,
surface area, and volume.
Statistics and Probability

Develop understanding of statistical variability.

Summarize and describe distributions.
7. Look for and make use of structure.
8. Look for an express regularity in repeated
reasoning.
The Five District Partnership
Grade 6 Math
Five District Partnership 3
Grade 6 Math
Sept-Oct
28 teaching days
Standards Covered:
6.NS.1: Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g.,
by using visual fraction models and equations to represent the problem.
6.NS.2: Fluently divide multi-digit numbers using the standard algorithm.
6.NS.3: Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
6.NS.5: Understand that positive and negative numbers are used together to describe quantities having opposite directions or
values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge);
use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.
6.NS.7c: Understand ordering and absolute value of rational numbers. Understand the absolute value of a rational number as
its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world
situation
6.NS.7d: Understand ordering and absolute value of rational numbers. Distinguish comparisons of absolute value from
statements about order.
6.EE.1: Write and evaluate numerical expressions involving whole-number exponents.
Unit Name
Time Frame
Unit 1
9 Days
Unit 2
10 Days
Unit 3
6 Days
A1: 10/15-10/17
PARCC emphasis:
Major
Assessed on A1?
Yes
Additional
Additional
Major
Yes
Yes
Yes
Major
Yes
Major
Yes
Major
Notes
Yes
Start Unit 4 with 3 remaining days
Resources
Applications of Integers
Factors and Multiples
Fractions
Introduction to Integers
Whole Numbers and Decimals
EngageNY module 2
EngageNY module 3
Established Goals/Standards
6.NS.7
6.NS.4, 6.MA.4.a
6.NS.1, 6.NS.6, 6.NS.7, SMP.1, SMP.2, SMP.3, SMP.4, SMP.5, SMP.6
6.NS.5, 6.NS.6, SMP.1, SMP.2, SMP.4, SMP.6, SMP.7, SMP.8
6.NS.2, 6.NS.3, 6.EE.1, SMP.1, SMP.2, SMP.3, SMP.4, SMP.5, SMP.6, SMP.7, SMP.8
6.NS.1, 6.NS.2, 6.NS.3, 6.NS.4
6.NS.5, 6.NS.6, 6.NS.7, 6.NS.8
The Five District Partnership
Grade 6 Math
Unit of Study 1
Grade 6
Approximate Time Frame: 9 Days
Topic: Decimal/Whole Number Operations
Standard:
Focus
SMP's
Objectives:
I can:
6.EE.1 Write and evaluate numerical expressions involving - identify and use exponents
whole-number exponents.
-evaluate expressions involving whole-number exponents
-write expressions involving whole-number exponents
I can:
6.NS.2 Fluently divide multi-digit numbers using the
-divide multi-digit numbers using the standard algorithm
standard algorithm.
-solve division problem that result in a solution that is a terminating decimal, for example 1/4 = 0.25
6.NS.3 Fluently add, subtract, multiply, and divide multidigit decimals using the standard algorithm for each
operation.
I can:
-add multi-digit decimals using the standard algorithm
-subtract multi-digit decimals using the standard algorithm
-multiply multi-digit decimals using the standard algorithm
-divide multi-digit decimals using the standard algorithm
Vocabulary:
base, cubed, digits, evaluate, exponents, expressions, GEMS, grouping symbols, Order of Operations, PEMDAS, squared, to the "nth" power, value
Standards for Mathematical Practice:
1.
2.
3.
4.
ANET: A1
*pretest recommended to determine time needed, if any, on each objective
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
5.
6.
7.
8.
Use appropriate tool strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
Additional Resources:
Five District Partnership UbD Units
Unit Name:
Established Goals/Standards
Whole Numbers and Decimals
EngageNY module 2
6.NS.2, 6.NS.3, 6.EE.1, SMP.1, SMP.2, SMP.3, SMP.4, SMP.5, SMP.6, SMP.7, SMP.8
6.NS.1, 6.NS.2, 6.NS.3, 6.NS.4
PARCC Content
Emphasis by
Cluster
6, 7
Major
6, 7
Additional
6, 7
Additional
Unit of Study 2
Grade 6
Approximate Time Frame: 10 Days
ANET: A1
Topic: Division of Fractions - Conceptual, Algorithmic, and Visual Approaches
PARCC Content
Emphasis by
Focus SMP's
Cluster
Standard:
Objectives:
6.NS.1 Interpret and compute quotients of fractions, and solve word
problems involving division of fractions by fractions, e.g., by using
visual fraction models and equations to represent the problem. For
example, create a story context for (2/3) ÷ (3/4) and use a visual
fraction model to show the quotient; use the relationship between
multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because
3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc .) How much
chocolate will each person get if 3 people share 1/2 lb of chocolate
equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt?
How wide is a rectangular strip of land with length 3/4 mi and area
1/2 square mi?
I can:
-find the reciprocal of a fraction
-multiply two fractions
-divide two fractions
-use cross simplification to make fraction operations more efficient
-show my answers in simplest form
-solve word problems involving fractions divided by fractions
-use visual models to solve word problems involving division of two fractions
-use equations to solve word problems involving division of two fractions
-create a story context to match a division problem involving two fractions
-create a visual model to show the quotient of the story problem
-extend the concept of multiplication/division fact families to problems involving two
fractions, i.e. explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3.
Vocabulary:
dividend, equation, equivalent fractions, improper fraction, mixed number, multiplicative inverse, quotient, reciprocal, reduce, simplest form, simplify
Standards for Mathematical Practice:
1.
2.
3.
4.
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
5.
6.
7.
8.
Use appropriate tool strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
Additional Resources:
Five District Partenership UbD Units
Unit Name:
Fractions
EngageNY module 2
Established Goals/Standards
6.NS.1, 6.NS.6, 6.NS.7, SMP.1, SMP.2, SMP.3, SMP.4, SMP.5, SMP.6
6.NS.1, 6.NS.2, 6.NS.3, 6.NS.4
2, 3, 4, 5, 6
Major
Unit of Study 3
Grade 6
Approximate Time Frame: 6 Days
ANET: A1
Topic: Apply and extend previous understandings of numbers to the system of rational numbers.
Standard:
Objectives:
I can:
6.NS.5 Understand that positive and negative numbers are used together to describe
quantities having opposite directions or values (e.g., temperature above/below zero, elevation -understand that positive and negative values are opposites and can also represent opposite directions
-use signed numbers to represent real-word situations
above/below sea level, credits/debits, positive/negative electric charge); use positive and
negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in -understand the meaning of zero in context of various real-life situations
each situation.
I can:
6.NS.7c. Understand the absolute value of a rational number as its distance from 0 on the
number line; interpret absolute value as magnitude for a positive or negative quantity in a real- -recognize absolute value as distance from zero on the number line
- interpret absolute value as magnitude for a positive or negative quantity in a real-world situation
world situation. For example, for an account balance of –30 dollars, write |–30| = 30 to
describe the size of the debt in dollars.
d. Distinguish comparisons of absolute value from statements about order. For example,
recognize that an account balance less than –30 dollars represents a debt greater than 30
dollars.
I can:
- distinguish comparisons of absolute value from statements about order. For example, recognize that an
account balance less than –30 dollars represents a debt greater than 30 dollars.
Vocabulary:
absolute value, coordinates, inequality (symbols included), magnitude, negative, opposites, ordered pair, positive, quadrants, rational numbers, signed numbers, x-axis, y-axis, origin
Standards for Mathematical Practice:
1.
2.
3.
4.
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
5.
6.
7.
8.
Use appropriate tool strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
Additional Resources:
Unit Name:
Five District Partnership UbD Units
Established Goals/Standards
Whole Numbers and Decimals
6.NS.2, 6.NS.3, 6.EE.1, SMP.1, SMP.2, SMP.3, SMP.4, SMP.5, SMP.6, SMP.7, SMP.8
Introduction to Integers
EngageNY module 3
6.NS.5, 6.NS.6, SMP.1, SMP.2, SMP.4, SMP.6, SMP.7, SMP.8
6.NS.5, 6.NS.6, 6.NS.7, 6.NS.8
Focus SMP's
PARCC Content
Emphasis by
Cluster
2, 5
Major
2, 5
Major
2, 5
Major
Five District Partnership 4
Grade 6 Math
Nov-Dec
30 Teaching days
A2: 12/9-12/12
Standards Covered:
PARCC emphasis:
6.RP.1: Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.
Major
Major
6.RP.2: Understand the concept of a unit rate a/b associated with a ratio a:b with b  0, and use rate language in the context of a
ratio relationship.
6.RP.3a: Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of
Major
equivalent ratios, tape diagrams, double number line diagrams, or equations. 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.3b: Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of
Major
equivalent ratios, tape diagrams, double number line diagrams, or equations. Solve unit rate problems, including those involving
unit pricing and constant speed.
6.RP.3c: Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of
Major
equivalent ratios, tape diagrams, double number line diagrams, or equations. Find a percent of a quantity as a rate per 100 (e.g.,
30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.
MA.6.RP.3e:
6.RP.3d
6.NS.6a: Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar
Major
from previous grades to represent points on the line and in the plane with negative number coordinates. 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, e.g., –(–3) = 3, and that 0 is its own opposite.
6.NS.6b: Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar
Major
from previous grades to represent points on the line and in the plane with negative number coordinates. 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.6c: Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar
Major
from previous grades to represent points on the line and in the plane with negative number coordinates. 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.7a: Understand ordering and absolute value of rational numbers. Interpret statements of inequality as statements about the Major
relative positions of two numbers on a number line diagram.
6.NS.7b: Understand ordering and absolute value of rational numbers. Write, interpret, and explain statements of order for
Major
rational numbers in real-world contexts.
Unit Name
Unit 4
Unit 5
ANet Review Standards
Resources
Time Frame
9 days
24 Days
6.NS.1, 6.NS.2, 6.NS.3
Established Goals/Standards
The Five District Partnership
Notes
Notes
Grade 6 Math
Assessed on A2?
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Five District Partnership 5
Ratios and Rates (Chelsea)
Ratios and Rates (RTTT)
EngageNY module 3
EngageNY module 1
6.RP.1, 6.RP.2, 6.RP.3
6.RP.1, 6.RP.2, 6.RP.3, SMP1, SMP.2, SMP.3, SMP.4, SMP.7
6.NS.5, 6.NS.6, 6.NS.7, 6.NS.8
6.RP.1, 6.RP.2, 6.RP.3
The Five District Partnership
Grade 6 Math
Unit of Study 4
Grade 6
Approximate Time Frame: 9 Days
ANET: A2
Topic: Apply and extend previous understandings of numbers to the system of rational numbers.
Standard:
Objectives:
I can:
6.NS.6 Understand a rational number as a point on the number line. Extend number line
diagrams and coordinate axes familiar from previous grades to represent points on the line and -understand positive and negative rational numbers as points on horizontal and vertical number
lines, including the coordinate grid
in the plane with negative number coordinates.
I can:
6.NS.6a. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on -recognize that opposite numbers on the number line are on opposites sides of and equidistant
the number line; recognize that the opposite of the opposite of a number is the number itself, from zero
-recognize that -(-x) = x
e.g., –(–3) = 3, and that 0 is its own opposite.
-explain that 0 is its own opposite
I can:
6.NS.6b. Understand signs of numbers in ordered pairs as indicating locations in quadrants of -graph coordinates in all quadrants
the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations -understand that when ordered pairs differ only by signs, then location of the points are related
as reflections over one or both axes (reflections of points across the x-axis or
of the points are related by reflections across one or both axes.
y-axis must be explicitly taught)
6.NS.6c. 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.7 Understand ordering and absolute value of rational numbers.
I can:
- locate and position integers on vertical and horizontal number line diagrams
- locate and position rational numbers on vertical and horizontal number line diagrams
- find and position order pairs on the coordinate plane whose values are integers and other
rational numbers, for example, "Graph the ordered pair (-5, 2.75) on the coordinate plane."
I can:
-order rational numbers
-understand and use absolute value of rational numbers
6.NS.7a. Interpret statements of inequality as statements about the relative positions of two
numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is
located to the right of –7 on a number line oriented from left to right.
I can:
-recognize that inequalities are statements that describe the relative position of two numbers on
a number line diagram
-understand the connection between inequality statements and positioning on the number line,
i.e. -3>-7 indicates that -3 is further to the right on the number line
6.NS.7b. Write, interpret, and explain statements of order for rational numbers in real-world
contexts. For example, write –3oC > –7oC to express the fact that –3oC is warmer than –7oC.
I can:
-write a correct inequality when given two rational numbers
-use a number line to explain/justify a given inequality
-use a number line to write a correct inequality
-write an inequality involving rational numbers to math a real-world situation
-interpret and explain inequality statements as they pertain to real-world situations
Vocabulary:
coordinates, inequality (symbols included),negative, opposites, ordered pair, positive, quadrants, rational numbers, reflections, signed numbers, x-axis, y-axis, origin
Standards for Mathematical Practice:
1.
2.
3.
4.
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
5.
6.
7.
8.
Use appropriate tool strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
Additional Resources:
Unit Name:
Five District Partnership UbD Units
Established Goals/Standards
Whole Numbers and Decimals
6.NS.2, 6.NS.3, 6.EE.1, SMP.1, SMP.2, SMP.3, SMP.4, SMP.5, SMP.6, SMP.7, SMP.8
Introduction to Integers
EngageNY module 3
6.NS.5, 6.NS.6, SMP.1, SMP.2, SMP.4, SMP.6, SMP.7, SMP.8
6.NS.5, 6.NS.6, 6.NS.7, 6.NS.8
Focus SMP's
PARCC Content
Emphasis by
Cluster
4, 5, 6
Major
3, 4, 5, 6, 8
Major
3, 4, 5, 6, 8
Major
3, 4, 5, 6
Major
3, 6
Major
2, 5
Major
2, 3, 5
Major
Unit of Study 5
Grade 6
Approximate Time Frame: 24 Days
ANET: A2
Topic: Understand ratio concepts
Standard:
Objectives:
I can:
-understand that ratios compare two quantities, including part to whole and part to part
6.RP.1 Understand the concept of a ratio and use ratio language to describe a ratio
comparisons
relationship between two quantities. For example, “The ratio of wings to beaks in
-simplify a ratio as needed for problem solving
the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.”
-show ratios using words, a semi-colon, or as a fraction
“For every vote candidate A received, candidate C received nearly three votes.”
-use ratio language to describe a ratio relationship between two quantities
-recognize that a ratio can compare two quantities measured in different units
6.RP.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b
≠ 0, and use rate language in the context of a ratio relationship. For example, “This
recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is ¾ cup of flour for
each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per
hamburger.”
6.RP.3. Use ratio and rate reasoning to solve real-world and mathematical
problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams,
double number line diagrams, or equations.
I can:
-understand the concept of a unit rate (non-zero denominator)
-describe unit rates in words, with a semi-colon, and as a fraction
-use rate language in the context of a ratio relationship
I can:
-Use tape diagrams, double number line diagrams, and equations to solve ratio and unit rate
problems in real world contexts
I can:
-create tables of equivalent ratios relating quantities with whole-number measurements
a. 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 -find missing values in tables of equivalent ratios
-plot pairs of values on the coordinate plane
coordinate plane. Use tables to compare ratios.
-use tables to compare ratios
I can:
b. Solve unit rate problems, including those involving unit pricing and constant
-solve unit rate problems applied to a variety of real-world contexts, including those with unit
speed. For example, if it took 7 hours to mow 4 lawns, then, at that rate, how many
pricing and constant speed
lawns could be mowed in 35 hours? At what rate were lawns being mowed?
Focus
SMP's
PARCC Content
Emphasis by
Cluster
2
Major
2
Major
1, 2, 4, 5,
7
Major
2, 4, 5, 7,
8
Major
2, 3, 5
Major
c. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means
30/100 times the quantity); solve problems involving finding the whole, given a
part and the percent.
I can:
-recognize percent as "rate per 100"
-find percent of a number using "rate per 100"
-solve problems involving finding the whole, given a part and a percent
2, 5, 7, 8
Major
d. Use ratio reasoning to convert measurement units; manipulate and transform
units appropriately when multiplying or dividing quantities.
I can:
-use ratio reasoning to convert measurement units
-manipulate and transform units appropriately when multiplying or dividing quantities
2, 5, 6, 7,
8
Major
1, 4, 5
Major
MA.6.RP.3.e Solve problems that relate the mass of an object to its volume.
I can:
-Solve problems relating the mass of an object to its volume (include graphing results on the
coordinate plane)
Vocabulary:
constant speed, coordinate plane, coordinate system, customary measurement, double number line diagram, equation, equivalent ratio, metric system, ordered pair, origin, percent, plot, proportion, quadrants, quantity, rate, ratio, tape diagram,
unit rate, value, x-axis, y-axis
Standards for Mathematical Practice:
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5.
6.
7.
8.
Use appropriate tool strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
Additional Resources:
Unit Name:
Ratios and Rates (Chelsea)
Ratios and Rates (RTTT)
EngageNY Module 1
Five District Partnership UbD Units
Established Goals/Standards
6.RP.1, 6.RP.2, 6.RP.3
6.RP.1, 6.RP.2, 6.RP.3, SMP1, SMP.2, SMP.3, SMP.4, SMP.7
6.RP.1, 6.RP.2, 6.RP.3
Five District Partnership 6
Grade 6 Math
Jan-Feb
32 Teaching Days
A3: 2/10-2/13
Standards Covered:
PARCC emphasis:
6.NS.4a: Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two
Additional
whole numbers less than or equal to 12. 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. Apply number theory concepts, including
prime factorization and relatively prime numbers, to the solution of problems.
6.NS.8: Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use
Major
of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.
6.EE.2a: Write, read, and evaluate expressions in which letters stand for numbers. Write expressions that record operations with
Major
numbers and with letters standing for numbers.
6.EE.2b: Write, read, and evaluate expressions in which letters stand for numbers. Identify parts of an expression using
Major
mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity.
6.EE.2c: Write, read, and evaluate expressions in which letters stand for numbers. Evaluate expressions at specific values of their
Major
variables. Include expressions that arise from formulas used in real-world problems. 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).
6.EE.3: Apply the properties of operations to generate equivalent expressions.
Major
6.EE.4: Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which
Major
value is substituted into them).
6.EE.5: Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if
Major
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.6: 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.7: Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in
Major
which p, q, and x are all nonnegative rational numbers.
6.EE.8: Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical
Major
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.9: Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an
Major
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 independent variables using graphs and tables, and
relate these to the equation.
Unit Name
Unit 6
Unit 7
Unit 8
ANet Review Standards
Time Frame
9 Days
14 Days
9 Days
6.RP.3.b, 6.RP.3.c
The Five District Partnership
Notes
Grade 6 Math
Assessed on A3?
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Five District Partnership 7
Resources
EngageNY module 2
EngageNY module 3
EngageNY module 4
Established Goals/Standards
6.NS.1, 6.NS.2, 6.NS.3, 6.NS.4
6.NS.5, 6.NS.6, 6.NS.7, 6.NS.8
6.EE.1, 6.EE.2, 6.EE.3, 6.EE.4, 6.EE.5, 6.EE.6, 6.EE.7, 6.EE.8, 6.EE.9
The Five District Partnership
Notes
Grade 6 Math
Unit of Study 6
Grade 6
Topic: Write, read, and evaluate expressions in which letters stand for numbers.
Approximate Time Frame: 9 Days
ANET: A3
**start unit 6 before A2 testing to finish A3 in time
PARCC Content
Emphasis by
Focus SMP's
Cluster
Standard:
Objectives:
6.EE.2 Write, read, and evaluate expressions in which letters stand for numbers.
I can:
-write expressions in which letters stand for numbers
-read expressions in which letters stand for numbers
-evaluate expression in which letters stand for numbers
I can:
6.EE.2a Write expressions that record operations with numbers and with letters
-explain what an algebraic expression is
standing for numbers. For example, express the calculation “Subtract y from 5” as 5 -understand the role of a variable in an algebraic expression
– y.
-translate verbal phrases into algebraic expressions containing variables and numbers
6.EE.2b. 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. For 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.
6.EE.2c Evaluate expressions at specific values of their variables. Include
expressions that arise from formulas used in real-world problems. 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). For example, use the formulas V = s3 and A = 6s2 to find the
volume and surface area of a cube with sides of length s = ½ .
I can:
-identify parts of an expression using appropriate mathematical terminology
-recognize that expressions of the form a(b + c) are composed of two separate entities and represent
a product of two factors
-view one or more parts of an expression as a single entity (extends beyond distributive property)
I can:
-evaluate an expression at a given value
-apply evaluating expressions to formulas used for real-world problem solving
-correctly apply the Order of Operations to expressions with and without parenthesis that contain
whole number exponents and arithmetic operations
I can:
6.EE.3 Apply the properties of operations to generate equivalent expressions. For -apply the distributive property to generate an equivalent expression in factored form
example, apply the distributive property to the expression 3 (2 + x) to produce the -apply the distributive property to factor out a common factor from an algebraic expression
equivalent expression 6 + 3x; apply the distributive property to the expression 24x + -use the properties of operations to combine like terms and generate equivalent expressions
18y to produce the equivalent expression 6(4x + 3y); apply properties of operations
to y + y + y to produce the equivalent expression 3y.
6.EE.4 Identify when two expressions are equivalent (i.e., when the two
expressions name the same number regardless of which value is substituted into
them). For example, the expressions y + y + y and 3y are equivalent because they
name the same number regardless of which number y stands for.
6.NS.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 1–100
with a common factor as a multiple of a sum of two whole numbers with no
common factor. For example, express 36 + 8 as 4(9 + 2).
MA.6.NS.4.a Apply number theory concepts, including prime factorization and
relatively prime numbers, to the solution of problems.
I can:
-find a number's prime factorization
-apply number theory concepts to problem solving
Vocabulary:
coefficient, distributive property, equivalent expressions, expression, factor, product sum, term, composite, distributive property, factor, GCF, LCM, multiple, prime, prime factorization, product of primes, relatively prime
Standards for Mathematical Practice: (not limited to but must include)
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Major
7, 8
Major
7
Major
7
Major
3, 6, 7
Major
3, 6, 7
Major
7
Additional
1, 6, 7
Additional
I can:
-show that two expressions are equivalent by substituting the same value into each expression and
evaluating to reach a common value
I can:
-classify a numbers as prime or composite
-classify a pair of numbers as relatively prime
-find the greatest common factor for two whole number less than or equal to 100
-find the least common multiple for two numbers less than or equal to 12
-describe and provide examples of the distributive property applied to numeric expressions
-use the distributive property to factor numeric expressions represented as the sum of two whole
number less than or equal to 100 where the terms have a common factor, i.e. "pulling out the
common factor", to create a new expression that whose terms are relatively prime
1.
2.
3.
4.
7
5.
6.
7.
8.
Use appropriate tool strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
Additional Resources:
Unit Name:
Five District Partnership UbD Units
Established Goals/Standards
Factors and Multiples
EngageNY module 2
EngageNY module 4
6.NS.4, MA.6.NS.4.a
6.NS.1, 6.NS.2, 6.NS.3, 6.NS.4
6.EE.1, 6.EE.2, 6.EE.3, 6.EE.4, 6.EE.5, 6.EE.6, 6.EE.7, 6.EE.8, 6.EE.9
Unit of Study 7
Grade 6
Approximate Time Frame: 14 Days
ANET: A3
Topic: Reason about and solve one-variable equations and inequalities.
Standard:
6.EE.5 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? Use substitution to determine whether a given
number in a specified set makes an equation or inequality
true.
Objectives:
I can:
-explain the difference between an expression and an equation
-articulate that equations ask the question, "Which values from a specified set, if any, make the equation
true?"
-substitute a value into an equation to see if it makes a true statement
-articulate that inequalities ask the question, "Which values from a specified set, if any, make the equation
true?"
-substitute a value into an inequality to see if it makes a true statement
6.EE.6 Use variables to represent numbers and write
I can:
expressions when solving a real-world or mathematical
-use variable to write and solve equations that represent real-world problems
problem; understand that a variable can represent an
-understand that a variable can represent an unknown number, or depending on the case at hand, any
unknown number, or, depending on the purpose at hand, member of a specified set
any number in a specified set.
6.EE.7 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.
I can:
-solve equations of the form x + p = q and px = q when p and q are positive rational numbers (should include
fraction division)
-solve equations of the form x + p = q and px = q when p and q are positive rational numbers (should include
fraction division)
6.EE.8 Write an inequality of the form x > c or x < c to
represent a constraint or condition in a real-world 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.
I can:
-write inequalities of the form x>c or x<c
-apply inequalities of the form x>c or x<c to a real-world or mathematical problem
-identify that inequalities of the form x>c or x<c have infinitely many solutions
-display inequalities of the form x>c or x<c on a number line diagram
Vocabulary:
constraint, equation, greater than, greater than or equal to, inequality, infinite, less than or equal to, set of values, solution
Standards for Mathematical Practice: (not limited to but must include)
1.
2.
3.
4.
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
5.
6.
7.
8.
Use appropriate tool strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
Additional Resources:
Unit Name:
EngageNY module 4
Five District Partnership UbD Units
Established Goals/Standards
6.EE.1, 6.EE.2, 6.EE.3, 6.EE.4, 6.EE.5, 6.EE.6, 6.EE.7, 6.EE.8, 6.EE.9
PARCC Content
Emphasis by
Focus SMP's
Cluster
2, 5
Major
2, 6, 7
Major
1, 2, 6, 7
Major
2, 6, 7
Major
Unit of Study 8
Grade 6
Approximate Time Frame: 9 Days
ANET: A3
Topic: Represent and analyze quantitative relationships between dependent and independent variables.
Standard:
Objectives:
I can:
-identify the four quadrants
6.NS.8 Solve real-world and mathematical problems by graphing
-plot and label points on the coordinate plane
points in all four quadrants of the coordinate plane. Include use of
-find the horizontal distance between two points on the coordinate plane when they share the same y-value
coordinates and absolute value to find distances between points with
-find the vertical distance between two points on the coordinate plane when they share the same x-value
the same first coordinate or the same second coordinate.
-Use absolute value to find horizontal/vertical distance between two points
6.EE.9 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 independent
variables using graphs and tables, and relate these to the equation.
For example, in a problem involving motion at constant speed, list and
graph ordered pairs of distances and times, and write the equation d =
65t to represent the relationship between distance and time.
I can:
-understand why some equations require more than one variable
-use variables to represent two different quantities in a real-world problem
-identify the dependent and independent variable in an equation
-write equations that describe an independent variable in terms of a dependent variable
-analyze the relationship between an independent and dependent variable using graphs
-analyze the relationship between an independent and dependent variable using tables
-relate graphs and tables to the corresponding equation
Vocabulary:
coordinate, dependent variable, horizontal, "in terms of", independent variable, linear, mass, ordered pair, scale, solution, vertical, volume, x-axis, y-axis
Standards for Mathematical Practice: (not limited to but must include)
1.
2.
3.
4.
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
5.
6.
7.
8.
Use appropriate tool strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
Additional Resources:
Unit Name:
EngageNY module 3
EngageNY module 4
Five District Partnership UbD Units
Established Goals/Standards
6.NS.5, 6.NS.6, 6.NS.7, 6.NS.8
6.EE.1, 6.EE.2, 6.EE.3, 6.EE.4, 6.EE.5, 6.EE.6, 6.EE.7, 6.EE.8, 6.EE.9
PARCC Content
Emphasis by
Focus SMP's
Cluster
1, 2, 5
Major
2, 3, 4, 6, 8
Major
Five District Partnership 8
Grade 6 Math
Standards Covered:
March-April
30 Teaching Days
A4: 4/13-4/17
PARCC emphasis:
Assessed on A4?
6.G.1a: Find the area of 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 and mathematical
problems. Use the relationships among radius, diameter, and center of a circle to find its circumference and area.
6.G.1b: Find the area of 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 and mathematical
problems. Solve real-world and mathematical problems involving the measurements of circles.
6.G.2: Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate
unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism.
Apply the formulas V = lwh and V = bh to find volumes of right rectangular prisms with fractional edge lengths in the context of
solving real-world and mathematical problems.
6.G.3: Draw polygons in the coordinate plane 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 realworld and mathematical problems.
6.G.4: Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface
areas of these figures. Apply these techniques in the context of solving real-world and mathematical problems.
6.SP.1: 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.2: 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.3: 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.4a: Display numerical data in plots on a number line, including dot plots, histograms, and box plots. Read and interpret circle
graphs. (MA 6.SP.4a)
6.SP.5a: Summarize numerical data sets in relation to their context, such as by reporting the number of observations.
6.SP.5b: Summarize numerical data sets in relation to their context, such as by describing the nature of the attribute under
investigation, including how it was measured and its units of measurement.
6.SP.5c: Summarize numerical data sets in relation to their context, such as 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 which the data were gathered.
6.SP.5d: Summarize numerical data sets in relation to their context, such as 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.
Supporting
Yes
Supporting
Yes
Supporting
Yes
Supporting
Yes
Supporting
Yes
Additional
Yes
Additional
Yes
Additional
Yes
Additional
Yes
Additional
Additional
Yes
Yes
Additional
Yes
Additional
Yes
Unit Name
Unit 9
Unit 10
ANet Review Standards
Resources
Notes
Time Frame
15 Days
15 Days
6.EE.2, 6.EE.7, 6.EE.9
Established Goals/Standards
The Five District Partnership
Notes
Grade 6 Math
Five District Partnership 9
Area, Volume, Surface
Statistics
EngageNY module 5
EngageNY module 6
6.G.1, 6.G.2, 6.G.3, 6.G.4, SMP.1, SMP.2, SMP.4, SMP.5, SMP.6
6.SP.1, 6.SP.2, 6.SP.3, 6.SP.4, 6.SP.5, MA.6.SP.4.a
6.G.1, 6.G.2, 6.G.3, 6.G.4
6.SP.1, 6.SP.2, 6.SP.3, 6.SP.4, 6.SP.5
The Five District Partnership
Grade 6 Math
Unit of Study 9
Grade 6
Approximate Time Frame: 15 Days
ANET: A4
Topic: Solve real-world and mathematical problems involving area and surface area.
Standard:
6.G.1 Find the area of 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 and mathematical
problems.
Objectives:
I can:
-find the area of triangles
-find the area of special quadrilaterals and polygons by composing into rectangles or decomposing into triangles
and other shapes
-apply composing and decomposing shapes to find their area in real-world and mathematical problem solving
6.G.3 Draw polygons in the coordinate plane 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 realworld and mathematical problems.
I can:
-draw polygons on the coordinate plane when given the coordinates for their vertices
-use coordinates to find side lengths of a polygon that are either horizontal or vertical (subtracting either the x or y
value depending on the situation)
-apply coordinate subtraction technique for finding side length to real-world and mathematical problems
6.G.4 Represent three-dimensional figures using nets made up
of rectangles and triangles, and use the nets to find the surface
areas of these figures. Apply these techniques in the context of
solving real-world and mathematical problems.
I can:
-create nets of prisms and pyramids containing only triangles and rectangles
-use nets of figures to find the total surface area of a shape
-use nets for real-world and mathematical problem solving
6.G.2 Find the volume of a right rectangular prism with
fractional edge lengths by packing it with unit cubes of the
appropriate unit fraction edge lengths, and show that the
volume is the same as would be found by multiplying the edge
lengths of the prism. Apply the formulas V = lwh and V = bh to
find volumes of right rectangular prisms with fractional edge
lengths in the context of solving real-world and mathematical
problems.
MA.6.G1.a Use the relationships among radius, diameter, and
center of a circle to find its circumference and area.
I can:
-find the volume of right rectangular prisms with fractional edge lengths by packing it with unit cubes of
appropriate unit fraction edge lengths
-show that filling a right rectangular prism to find its volume produces the same value as the formula V = l x w x h
MA.6.G.1.b Solve real-world and mathematical problems
involving the measurements of circles.
I can:
-find the circumference of a circle
-given the circumference of a circle, find its radius or diameter
-find the area of a circle
I can:
-solve real-world and mathematical problems involving the measurement of circles
Vocabulary:
center, circumference, coordinates, diameter, polygons, quadrilaterals, radius, triangles, unit cubes, volume, vertices
Standards for Mathematical Practice: (not limited to but must include)
1.
2.
3.
4.
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
5.
6.
7.
8.
Use appropriate tool strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
Additional Resources:
Unit Name:
Five District Partnership UbD Units
Established Goals/Standards
Area, Volume, and Surface Area
EngageNY module 5
6.G.1, 6.G.2, 6.G.3, 6.G.4, SMP.1, SMP.2, SMP.4, SMP.5, SMP.6
6.G.1, 6.G.2, 6.G.3, 6.G.4
Focus SMP's
PARCC Content
Emphasis by
Cluster
1, 2, 5, 7
Supporting
1, 5
Supporting
1, 4, 5
Supporting
1, 4, 5
Supporting
1, 4, 5
Supporting
1, 4, 5
Supporting
Unit of Study 10
Grade 6
Approximate Time Frame: 15 Days
ANET: A4
Topic: Develop understanding of statistical variability. Summarize and describe distributions.
Focus SMP's
Standard:
Objectives:
6.SP.1 Recognize a statistical question as one that anticipates
variability in the data related to the question and accounts for it
in the answers. For example, “How old am I?” is not a statistical
question, but “How old are the students in my school?” is a
statistical question because one anticipates variability in
students’ ages.
I can:
-determine if a question is statistical in nature based on the way it is phrased and implication of variability in answers
6.SP.2 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.3 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.
N/A
Additional
I can:
-recognize that data collected to answer statistical questions has a distribution
-understand that a distribution can be described by its center, spread, and overall shape
4
Additional
I can:
-calculate the mean, median, mode, range, interquartile range, and mean absolute deviation of a data set
-define measure of center as a single value that summarizes an entire data set with a single number
-recognize and describe mean, median, and mode as measures of center
-define measure of variation as how a data set's values vary with a single number
4
Additional
2, 5
Additional
1, 4
Additional
4
Additional
6.SP.4 Display numerical data in plots on a number line, including I can:
dot plots, histograms, and box plots.
-display numerical data in plots on a number line, including dot plots, histograms, and box plots
MA.6.SP.4.a Read and interpret circle graphs.
I can:
Read and interpret circle graphs.
6.SP.5 Summarize numerical data sets in relation to their context,
such as by:
a. Reporting the number of observations.
b. Describing the nature of the attribute under investigation,
including how it was measured and its units of measurement.
c. 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 which the data were gathered.
d. 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.
I can:
-relate numerical data sets to their context
-summarize numerical data sets by reporting the number of observations
-describe the nature of the attribute under investigation, including how it was measured and its units of measure, i.e.
weight measured in pounds
-describe any overall patterns in the data
-describe any striking deviations from overall pattern of the data and consider the context in which the data was gathered,
i.e. when taking the average age of a sixth grade class, including the teachers age artificially inflates the mean and results in
an outlier
-choose the best measure of center and variability to match the shape of the data distribution and the context in which the
data was gathered
Vocabulary:
center, interquartile range, measure of center, mean absolute deviation, measure of variation, outlier, spread, statistics, variability
Standards for Mathematical Practice: (not limited to but must include)
1.
2.
3.
4.
PARCC Content
Emphasis by
Cluster
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
5.
6.
7.
8.
Use appropriate tool strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
Additional Resources:
Five District Partnership UbD Units
Unit Name:
Established Goals/Standards
Statistics
6.SP.1, 6.SP.2, 6.SP.3, 6.SP.4, 6.SP.5, MA.6.SP.4.a
EngageNY module 6
6.SP.1, 6.SP.2, 6.SP.3, 6.SP.4, 6.SP.5
Five District Partnership 10
Grade 6 Math
May-June - REVIEW
Standards Covered:
6.NS.3: Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
6.RP.2: Understand the concept of a unit rate a/b associated with a ratio a:b with b  0, and use rate language in the context of a
ratio relationship.
6.RP.3a: Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of
equivalent ratios, tape diagrams, double number line diagrams, or equations. 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.3b: Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of
equivalent ratios, tape diagrams, double number line diagrams, or equations. Solve unit rate problems, including those involving
unit pricing and constant speed.
6.RP.3c: Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of
equivalent ratios, tape diagrams, double number line diagrams, or equations. Find a percent of a quantity as a rate per 100 (e.g.,
30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.
6.EE.1: Write and evaluate numerical expressions involving whole-number exponents.
6.EE.2a: Write, read, and evaluate expressions in which letters stand for numbers. Write expressions that record operations with
numbers and with letters standing for numbers.
6.EE.2c: Write, read, and evaluate expressions in which letters stand for numbers. Evaluate expressions at specific values of their
variables. Include expressions that arise from formulas used in real-world problems. 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).
6.EE.3: Apply the properties of operations to generate equivalent expressions.
6.EE.5: 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? Use substitution to determine whether a given number in a specified set makes an
equation or inequality true.
6.EE.7: 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.9: 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 independent variables using graphs and tables, and
relate these to the equation.
Unit Name
Established Goals/Standards
The Five District Partnership
PARCC emphasis:
Additional
Major
Major
Major
Major
Major
Major
Major
Major
Major
Major
Major
Notes
Grade 6 Math