Download Sixth Grade Unit documents-12 - GCS Haiku

Standard(s)
Priority Standards are in bold.
Unit
Unit 1
(4 wks)
6.EE.1
6.EE.2a EE.2b EE.2c
6.EE.3
6.EE.4
Unit 2
(4 wks)
6.NS.1
6.NS.2
6.NS.3
6.NS.4
Unit 3
(5 wks)
6.NS.5
6.NS.6a NS.6b NS.6c
6.NS.7a NS.7b NS.7c NS.7d
6.NS.8
6.EE.5
6.EE.6
6.EE.7
6.EE.8
6.EE.9
Unit 4
(4 wks)
Unit Title

Apply and extend previous understandings of arithmetic to
algebraic expressions.

Operating with Positive
Rational Numbers
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.
Understanding Positive and
Negative Numbers
 Apply and extend previous understandings of numbers to the
system of rational numbers.
Using Equations and
Expressions

Algebraic Reasoning
Unit 5
(7 wks)
6.RP.1
6.RP.2
6.RP.3a RP.3b RP.3c RP.3d
Ratios and Proportions
Unit 6
(5 wks)
6.G.1
6.G.2
6.G.3
6.G.4
Geometry
Unit 7
(4 wks)
6.SP.1
6.SP.2
6.SP.3
6.SP.4
6.SP.5a SP.5b SP.5c SP.5d
Cumulative
Review
(3 weeks)
All

Common Unit Assessment :
CLASSSCAPE

Benchmarks
Big Ideas and Understandings

Reason about and solve one-variable equations and
inequalities.
Represent and analyze quantitative relationships between
dependent and independent variables.

Understand ratio concepts and use ratio reasoning to solve
problems.

Solve real-world and mathematical problems involving area,
surface area and volume.
Statistics and Probability


Develop understanding of statistical variability.
Summarize and describe distributions.
Cumulative Review
 Prepare for State Test

Unit Test
Total Weeks
36
UNIT INFORMATION
Unit Title:
Subject/Topic:
Unit 1. Equations and Expressions
Grade Level:
6
Equations and Expressions
Length (in weeks / days):
4 weeks
% of Formal Assessment
27 – 32%
WHAT’S THE BIG IDEA(s)?
Apply and extend previous understandings of arithmetic to algebraic expressions.
STANDARDS
EE.1 Write and evaluate numerical expressions involving
whole-number exponents.
ENDURING UNDERSTANDINGS
To meet the standards, students will need to:

EE.2 Write, read, and evaluate expressions in which letters
stand for numbers.
a. Write expressions that record operations with numbers
and with letters standing for numbers. For example, express the
calculation “Subtract y from 5” as 5 – y. Write, read, and
evaluate expressions in which letters stand for
numbers.
b. 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.
c. 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 = 6
s2 to find the volume and surface area of a cube with sides of
length s = 1/2.






Write and evaluate numerical
expressions involving wholenumber exponents.
Write, read and evaluate
expressions in which letters stand
for numbers.
Write expressions that record
operations with numbers and with
letters standing for numbers.
Identify parts of an expression
using mathematical terms.
Evaluate expressions at specific
values of their variables.
Apply properties of equations to
generate equivalent expressions.
Identify when two expressions are
equivalent.
MATHEMATICAL PRACTICES

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.

Use appropriate tools strategically.

Attend to precision.

Look for and make use of
structure.

Look for and express regularity in
repeated reasoning.
EE.3 Apply the properties of operations to generate
equivalent expressions. For 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 expression 6 (4x + 3y); apply properties of
operations to y + y + y to produce the equivalent expression
3y.
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.
Essential Vocabulary:
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

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
Exponents
Base
Numerical expressions
Algebraic expressions
Evaluate
Sum
Term
Product
Factor
Quantity
Quotient
Coefficient
Constant
Like terms
Equivalent expressions
Variables
21st Century Learning Skills
Artisan “Must Big Six”






Clear Learning Goals
Congruency
Task Analysis
Diagnosis
Overt Responses
Mid Course Connections








Teamwork and Collaboration
Initiative and Leadership
Curiosity and Imagination
Innovation and Creativity
Critical Thinking and Problem
Solving
Flexibility and Adaptability
Effective Oral and Written
Communication
Accessing and Analyzing
Information
Suggested Resources:


Glencoe Series : Skills Practice Workbooks, Problem Solving Workbooks, Study Guide and Intervention workbooks
Textbook: Glencoe Series – Applications and Concepts – Courses 1,2 and 3
o
Course 1 – Expressions and Equations pages: 18 – 19; 28- 29; 24 – 25; 332- 335,
o
Course 2 – pages: 8; 18; 14, 30
o
Course 3 pages: 98 – 101, 11-13; 469 - 497

Navigation through Problem Solving and Reasoning Grade 6
Navigating through Numbers and Operations

Navigating through Algebra
Common Core Unpacked Documents
Websites : www.symbaloo.com ( search concepts in gallery link)
Navigating through Mathematical Connections in Grades 6 - 8
o
www.brainpop.com
o
www.math.com
o
www.learn4good.com
o
www.amathsdictionaryforkids.com
o
www.discoveryed.com
o
www.illustrativemathematics.com
o
http://illuminations.nctm.org
o
www.readwritethink.org
UNIT INFORMATION
Unit Title:
Grade Level:
6
Unit 2. Rational Numbers
Subject/Topic:
The Number System
Length (in weeks / days):
4 weeks
% of Formal Assessment
27 – 32 %
WHAT’S THE BIG IDEA(s)?
Compute quotients of fractions by fractions. Fluently add, subtract multiply and divide decimals. Find the GCF and LCM of two numbers. Use the
distributive property in factoring numbers.
STANDARDS
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?
NS.2 Fluently divide multi-digit numbers using the standard
algorithm.
NS.3 Fluently add, subtract, multiply, and divide multi-digit
decimals using the standard algorithm for each operation.
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).
ENDURING
UNDERSTANDINGS
To meet the standards, students will need
to:

Interpret and compute quotients
of fractions and solve word
problems involving division of
fractions by fractions.

Fluently divide multi-digit
numbers using the standard
algorithm.

Fluently add, subtract, multiply
and divide multi-digit decimals
using the standard algorithm.

Find the greatest common factor
of two whole numbers les 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.
Essential Vocabulary:


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



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
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


Reciprocal
Multiplicative inverse
Visual fraction model
Multi-digit
Greatest common factor
Least common multiple
Prime numbers
Composite numbers
Relatively prime
Factors
Multiples
Distributive property
Prime factorization
MATHEMATICAL PRACTICES















Clear learning goals
Congruency
Task Analysis
Diagnosis
Overt Responses
Mid Course Connections
Glencoe Series: Skills Practice Workbooks, Problem Solving Workbooks, Study Guide and Intervention Workbooks
Textbook: Glencoe Series – Applications and Concepts – Courses 1,2 and 3
o
Course 1 –pages: Chapter 7, pp 121- 124; 177,178, 194, 195, 135, 155
o
Course 2 – pages; 254 – 266, 203, 204
Navigation through Problem Solving and Reasoning Grade 6
Navigating through Numbers and Operations in Grades 6 – 8
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.
Use appropriate tools
strategically.
Attend to precision.
Look for and make use of
structure.
Look for and express regularity
in repeated reasoning.
21st Century Learning Skills
Artisan “Big Six”
Suggested Resources:











Teamwork and Collaboration
Initiative and Leadership
Curiosity and Imagination
Innovation and Creativity
Critical Thinking and Problem
Solving
Flexibility and Adaptability
Effective Oral and Written
Communication
Accessing and Analyzing
Information

Navigating through Mathematical Connections in Grades 6 - 8
Websites : www.symbaloo.com ( search concepts in gallery link)
o
www.brainpop.com
o
www.math.com
o
www.learn4good.com
o
www.amathsdictionaryforkids.com
o
www.discoveryed.com
o
www.readwritethink.org
o
www.illustrativemathematics.com
o
http://illuminations.nctm.org
UNIT INFORMATION
Unit Title:
Subject/Topic:
Unit 3. Positive and Negative Numbers
Grade Level:
6
Rational Numbers/ The Number System
Length (in weeks / days):
5 weeks
% of Formal Assessment
27 – 32 %
WHAT’S THE BIG IDEA(s)?
Use the number line to identify positive, negative and rational numbers as a point on the line Understand the concept of opposites. Graph points in all
four quadrants of the coordinate plane.
MATHEMATICAL
STANDARDS
ENDURING UNDERSTANDINGS
PRACTICES
NS.5 Understand that positive and negative numbers are used
To meet the standards, students will need to:

Make sense of problems
together to describe quantities having opposite directions or values
and persevere in solving
 Understand that positive and negative
(e.g., temperature above/below zero, elevation above/below sea
them.
numbers are used together to describe
level, credits/debits, positive/negative electric charge); use positive

Reason abstractly and
quantities having opposite directions or
and negative numbers to represent quantities in real-world contexts,
quantitatively.
values.
explaining the meaning of 0 in each situation.

Construct viable arguments
 Understand a rational number as a point
and critique the reasoning
on the number line.
NS.6 Understand a rational number as a point on the number
of others.

Extend
number
line
diagrams
and
line. Extend number line diagrams and coordinate axes familiar

Model with mathematics.
coordinate axes familiar from previous
from previous grades to represent points on the line and in the

Use appropriate tools
grades to represent points on the line
plane with negative number coordinates.
strategically.
and in the plane with negative number
a. Recognize opposite signs of numbers as indicating

Attend to precision.
coordinates.
locations on opposite sides of 0 on the number line; recognize

Look for and make use of
 Recognize opposite signs of numbers as
that the opposite of the opposite of a number is the number
structure.
indicating locations on opposite sides of
itself, e.g., –(–3) = 3, and that 0 is its own opposite.

Look for and express
0 on the number line.
b. Understand signs of numbers in ordered pairs as
regularity in repeated

Recognize
that
the
opposite
of
the
indicating locations in quadrants of the coordinate plane;
reasoning.
opposite of a number is the number itself
recognize that when two ordered pairs differ only by signs,
and that 0 is its own opposite.
the locations of the points are related by reflections across
one or both axes.
 Understand signs of numbers in ordered
pairs as indicating locations in quadrants
c. Find and position integers and other rational
of the coordinate plane.
numbers on a horizontal or vertical number line diagram;
find and position pairs of integers and other rational
 Recognize that when two ordered pairs
numbers on a coordinate plane.
differ only by signs, the locations of the
points are related by reflections across
NS.7 7. Understand ordering and absolute value of rational
one or both axes.
numbers.
 Find and position integers and other
a. Interpret statements of inequality as statements about the
rational numbers on a horizontal or
relative position of two numbers on a number line diagram. For
vertical number line diagram.
example, interpret –3 > –7 as a statement that –3 is located to the
 Find and position pairs of integers and
right of –7 on a number line oriented from left to right.
other rational numbers on a coordinate
b. Write, interpret, and explain statements of order for
plane.
rational numbers in real-world contexts. For example, write –3
 Understand ordering and absolute value
oC > –7 oC to express the fact that –3 oC is warmer than –7 oC.
of rational numbers.
c. Understand the absolute value of a rational number as its

Interpret statements of inequality as
distance from 0 on the number line; interpret absolute value as
statements about the relative position of
magnitude for a positive or negative quantity in a real-world
two numbers on a number line diagram.
situation. For example, for an account balance of –30 dollars, write
 Write, interpret, and explain statements
|–30| = 30 to describe the size of the debt in dollars.
of order for rational numbers in real
d. Distinguish comparisons of absolute value from
world contexts.
statements about order. For example, recognize that an account
 Understand the absolute value of a
balance less than –30 dollars represents a debt greater than 30
rational number as its distance from 0 on
dollars.
the number line.
NS.8 Solve real-world and mathematical problems by graphing 
Interpret absolute value as magnitude for
points in all four quadrants of the coordinate plane. Include use
a positive or negative quantity in a realof coordinates and absolute value to find distances between
world situation.
points with the same first coordinate or the same second
 Distinguish comparisons of absolute
coordinate.
value from statements about order.
 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.
Essential Vocabulary:

Rational Numbers

Opposites

Absolute value

Greater than >

Less than <

Greater than or equal to 

Less than or equal to 

Origin

Quadrants

Coordinate plane

Ordered pairs

X – axis

Y- axis

Coordinates

Suggested Resources:
Artisan “Big Six”

Clear learning goals

Congruency

Task Analysis

Diagnosis

Overt Responses
 Mid Course Connections


Glencoe Series: Skills Practice Workbooks, Problem Solving Workbooks, Study Guide and Intervention workbooks
Textbook: Glencoe Series – Applications and Concepts – Courses 1,2 and 3
o
Course 1 –pages: 294- 297; 320-325, 298
o
Course 2 – pages; 107



Navigating through Problem Solving and Reasoning Grade 6
Navigating through Numbers and Operations in Grades 6 - 8
Common Core Unpacked Documents
Websites : www.symbaloo.com ( search concepts in gallery link)
o
www.brainpop.com
o
www.math.com
o
www.learn4good.com
o
www.amathsdictionaryforkids.com
o
www.discoveryed.com
o
www.readwritethink.org
o
www.illustrativemathematics.com
o
http://illuminations.nctm.org
21st Century Learning Skills








Teamwork and
Collaboration
Initiative and Leadership
Curiosity and Imagination
Innovation and Creativity
Critical Thinking and
Problem Solving
Flexibility and Adaptability
Effective Oral and Written
Communication
Accessing and Analyzing
Information
UNIT INFORMATION
Unit Title:
Subject/Topic:
Unit 4: Algebraic Reasoning
Grade Level:
6
Expressions and Equations
Length (in weeks / days):
5 weeks
% of Formal Assessment
27 – 32%
WHAT’S THE BIG IDEA(s)?
Reason about and solve one-variable equations and inequalities.
STANDARDS
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.
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.
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.
MATHEMATICAL
PRACTICES
ENDURING UNDERSTANDINGS
To meet the standards, students will need to:

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.

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.

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.








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.
Use appropriate tools
strategically.
Attend to precision.
Look for and make use of
structure.
Look for and express
regularity in repeated
reasoning
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.
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.
Essential Vocabulary:








Inequalities
Equations
Greater than >
Less than <
Greater than or equal to 
Less than or equal to 
Profit
exceed
Artisan “Must Haves”






Clear learning goals
Congruency
Task Analysis
Diagnosis
Overt Responses
Mid Course Connections
21st Century Learning Skills








Teamwork and
Collaboration
Initiative and Leadership
Curiosity and Imagination
Innovation and Creativity
Critical Thinking and
Problem Solving
Flexibility and Adaptability
Effective Oral and Written
Communication
Accessing and Analyzing
Information
Suggested Resources:






Glencoe Series: Skills Practice Workbooks, Problem Solving
Workbooks, Study Guide and Intervention Workbooks
Textbook: Glencoe Series – Applications and Concepts – Courses 1,2
and 3
o
Course 1 –pages: 338 – 351, 6 – 8, 339 – 340, 344 -345,
350 -351,
o
Course 2 – pages: 156- 157, 172 – 173, 6 - 7, 150 – 151,
156, 172 – 173,
o
Course 3- pages: 492 – 493, 496 – 497, 6 – 8, 45 – 46, 548
– 549, 517- 518
Navigation through Problem Solving and Reasoning Grade 6
Navigating through Numbers and Operations
Navigating through Algebra in grades 6 – 8
Common Core Unpacked Documents
Websites : www.symbaloo.com ( search concepts in gallery link)
o
www.brainpop.com
o
http://illuminations.nctm.org
o
www.math.com
o
www.learn4good.com
o
www.amathsdictionaryforkids.com
o
www.discoveryed.com
o
www.readwritethink.org
o
www.illustrativemathematics.com
o
www.ixl.com
o
www.khanacademy.org
UNIT INFORMATION
Unit Title:
Subject/Topic:
Unit 5. Ratios and Proportions
Grade Level:
6
Ratio and Proportional Relationships
Length (in weeks / days):
4 weeks
% of Formal Assessment
12 – 17%
WHAT’S THE BIG IDEA(s)?
Understand concept of a ratio and use ratios to solve problems.
STANDARDS
ENDURING UNDERSTANDINGS
RP.1. Understand the concept of a ratio and use ratio language
to describe a ratio relationship between two quantities. For
example, “The ratio of wings to beaks in the bird house at the
zoo was 2:1, because for every 2 wings there was 1 beak.” “For
every vote candidate A received, candidate C received nearly
three votes.”
To meet the standards, students will need to:
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 3/4 cup of flour for
each cup of sugar.” “We paid $75 for 15 hamburgers, which is
a rate of $5 per hamburger.”1
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.
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 coordinate
plane. Use tables to compare ratios.
b. Solve unit rate problems including those involving
unit pricing and constant speed. For example, if it took 7
hours to mow 4 lawns, then at that rate, how many lawns
could be mowed in 35 hours? At what rate were lawns being
mowed?
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.
d. Use ratio reasoning to convert measurement units;
manipulate and transform units appropriately when
multiplying or dividing quantities.
Essential Vocabulary:








Ratio
Equivalent ratios
Tape diagram
Unit rate
Part-to-part
Part-to- whole
Percent
MATHEMATICAL PRACTICES



Understand the concept of a ratio.

Understand the concept of a unit rate
a/b associated with a ratio a:b with b 0.

Use rate language in the context or a
ratio relationship.

Use ratio and rate reasoning to solve
real-world and mathematical problems.

Make tables of equivalent ratios relating
quantities with whole-number
measurements.

Find missing values in tables and plot the
pairs of values on the coordinate plane.


Use tables to compare ratios.

Find a percent of a quantity as a rate per
100.

Solve problems involving finding the
whole given the part and the percent.

Use ratio reasoning to convert
measurement units.

Manipulate and transform units
appropriately when multiplying and
dividing quantities.
Use ratio language to describe a ratio
relationship between two quantities.




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Solve unit rate problems including those
involving unit pricing and constant
speed.
21st Century Learning Skills
Artisan “ Big Six”
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Clear learning goals
Congruency
Task Analysis
Diagnosis
Overt Responses
Mid Course Connections
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Suggested Resources:
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.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of
structure.
Look for and express regularity in
repeated reasoning
Teamwork and Collaboration
Initiative and Leadership
Curiosity and Imagination
Innovation and Creativity
Critical Thinking and Problem
Solving
Flexibility and Adaptability
Effective Oral and Written
Communication
Accessing and Analyzing
Information


Glencoe Series: Skills Practice Workbooks, Problem Solving Workbooks, Study Guide and Intervention Workbooks
Textbook: Glencoe Series – Applications and Concepts – Courses 1,2 and 3
o
Course 1 –pages: 364, 365, 380, 381, Chapter 12
o
Course 2 – pages; 292, 324, 407 – 411
o
Course 3- Chapter 5

Navigation through Problem Solving and Reasoning Grade 6

Navigating through Numbers and Operations
Navigating through Algebra in Grades 6 - 8

Common Core Unpacked Documents
Websites : www.symbaloo.com ( search concepts in gallery link)
o
www.brainpop.com
o
www.math.com
o
www.learn4good.com
o
www.amathsdictionaryforkids.com
o
www.discoveryed.com
o
www.readwritethink.org
o
o
www.illustrativemathematics.com
http://illuminations.nctm.org
UNIT INFORMATION
Unit Title:
Subject/Topic:
Unit 6. Geometry
Grade Level:
6
Geometry
Length (in weeks / days):
7 weeks
% of Formal Assessment
12 – 17%
WHAT’S THE BIG IDEA(s)?
Solve real world problems involving area, surface area and volume
STANDARDS
ENDURING UNDERSTANDINGS
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.
To meet the standards, students will need to:

Find the area of right 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.

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 = l w h and V=b h to
find volumes of right rectangular prisms with
fractional edge lengths in the context of
solving real-world and mathematical
problems.

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.

Represent three-dimensional figures using
nets made up of rectangles and triangles and
use the nets to find the surface area of these
figures. Apply these techniques in the
context of solving real-world and
mathematical problems.
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 = l w h and
V = b h to find volumes of right rectangular prisms with
fractional edge lengths in the context of solving real-world
and mathematical problems.
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 real-world and mathematical
problems.
G.4. Represent three-dimensional figures using nets made
up of rectangles and triangles, and use the nets to find the
surface area of these figures. Apply these techniques in the
context of solving real-world and mathematical problems.
Essential Vocabulary:
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Area
Surface area
Volume
Decomposing
Edges
Dimensions
Net
Vertices
Face
Base
Height
Trapezoid
Isosceles
Right triangle
Quadrilateral
Rectangles
Squares
Parallelograms
Rhombi
Kites
Artisan “Big Six”






Clear learning goals
Congruency
Task Analysis
Diagnosis
Overt Responses
Mid Course Connections
MATHEMATICAL
PRACTICES








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.
Use appropriate tools
strategically.
Attend to precision.
Look for and make use of
structure.
Look for and express
regularity in repeated
reasoning
21st Century Learning Skills








Teamwork and
Collaboration
Initiative and Leadership
Curiosity and Imagination
Innovation and Creativity
Critical Thinking and
Problem Solving
Flexibility and
Adaptability
Effective Oral and
Written Communication
Accessing and Analyzing
Information

Right rectangular prism
Suggested Resources


Glencoe Series: Skills Practice Workbooks, Problem Solving Workbooks, Study Guide and Intervention Workbooks
Textbook: Glencoe Series – Applications and Concepts – Courses 1,2 and 3
o
Course 1 –pages: 551- 552; 546 – 555; 570-571; 574 -576
o
Course 2 – pages: 270 – 271; 483, 489, 520, 530 - 532
o
Course 3- pages: 314 – 316; 335-336; 346

Navigation through Problem Solving and Reasoning Grade 6

Navigating through Numbers and Operations

Navigating through Geometry in grades 6 – 8

Common Core Unpacked Documents
Websites : www.symbaloo.com ( search concepts in gallery link)
o
www.brainpop.com
o
www.math.com
o
www.learn4good.com
o
www.amathsdictionaryforkids.com
o
www.discoveryed.com
o
www.readwritethink.org
o
www.illustrativemathematics.com
o
www.ixl.com
o
www.internet4classrooms.com/skills_6th_math_new.htm
o
http://illuminations.nctm.org
UNIT INFORMATION
Unit Title:
Subject/Topic:
Unit 7: Statistics and Probability
Grade Level:
6
Statistics and Probability
Length (in weeks / days):
4 Weeks
% of Formal Assessment
7 – 12%
WHAT’S THE BIG IDEA(s)?
Develop understanding of statistic variability.
STANDARDS
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.
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.
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.
SP.4. Display numerical data in plots on a number line,
including dot plots, histograms, and box plots.
ENDURING UNDERSTANDINGS
To meet the standards, students will need to:




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.
Essential Vocabulary:
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

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Statistics
Data
Variability
Distribution
Dot plot
Histograms
Box plots
Median
Mean
Frequency tables
Cluster
Peaks
Gap
Interquartile range
Measures of center
Measures of variability
Mean Absolute Deviation ( M.A.D.)
Quartiles
Lower quartiles
1st quartile or Q1
Upper quartile
Recognize a statistical question as
one that anticipates variability in
the data related to the question
and accounts for it in the answers.
Understand that a set of data
collected has a distribution, which
can be described by its center,
spread, and overall shape.
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.
Display numerical data in plots on a
number line, including dot plots,
histograms, and box plots.
MATHEMATICAL PRACTICES

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.

Use appropriate tools strategically.

Attend to precision.

Look for and make use of
structure.

Look for and express regularity in
repeated reasoning
21st Century Learning Skills
Artisan “Big Six”






Clear learning goals
Congruency
Task Analysis
Diagnosis
Overt Responses
Mid Course Connections








Teamwork and Collaboration
Initiative and Leadership
Curiosity and Imagination
Innovation and Creativity
Critical Thinking and Problem
Solving
Flexibility and Adaptability
Effective Oral and Written
Communication
Accessing and Analyzing
Information





3rd quartile or Q3
Symmetrical
Skewed
Summary statistics
Outlier
Suggested Resources:

Glencoe Series: Skills Practice Workbooks, Problem Solving
Workbooks, Study Guide and Intervention Workbooks

Textbook: Glencoe Series – Applications and Concepts – Courses 1,2
and 3
o
Course 1 –pages: 76- 90, 222, 438
o
Course 2 – pages: Chapter 2 pages 54-99
o
Course 3- pages: Chapter 9 pages 420 – 449.

Navigation through Problem Solving and Reasoning Grade 6

Navigating through Data Analysis Grades 6-8
Websites : www.symbaloo.com ( search concepts in gallery link)
o
www.brainpop.com
o
http://illuminations.nctm.org
o
www.math.com
o
www.learn4good.com
o
www.amathsdictionaryforkids.com
o
o
o
o
o
o
o
www.discoveryed.com
www.readwritethink.com
www.illustrativemathematics.com
www.ixl.com
www.internet4classrooms.com/skills_6th_math_new.htm
http://mathlearnnc.sharpschool.com (Instructional resources)
www.khanacademy.org
UNIT INFORMATION
Unit Title:
Grade Level:
Subject/Topic:
Length (in weeks / days):
% of Formal Assessment
WHAT’S THE BIG IDEA(s)?
STANDARDS
ENDURING UNDERSTANDINGS
To meet the standards, students will need to:
ESSENTIAL QUESTIONS
To understand, students will need to
consider such questions as:
I can
Essential Vocabulary:
Suggested Resources:
Month:
Grade/Subject:
Unit Number and Topic:
Total Days:
From:
To:
Monday
Tuesday
Wednesday
Thursday
Friday
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