Prentice Hall
Grade 6
Connected Mathematics 2, Grade 6 Module Bundle
with West Virginia Additional Lessons © 2010
C O R R E L A T E D
T O
West Virginia 21st Century Mathematics
Content Standards and Objectives for Grade 6
PUBLISHER:
SUBJECT:
SPECIFIC GRADE:
COURSE:
TITLE:
COPYRIGHT DATE:
SE ISBN:
TE ISBN:
Pearson Education, Inc., publishing as Prentice Hall
Mathematics
6
Sixth Grade Mathematics
Prentice Hall Connected Mathematics 2, Grade 6 Module Bundle with West Virginia Additional Lessons
2010
0133731413
0133686132
GENERIC EVALUATION CRITERIA
2010-2015
Sixth Grade Mathematics
Yes
x
x
R-E-S-P-O-N-S-E
No
N/A
CRITERIA
NOTES
I. INTER-ETHNIC
The instructional material meets the
requirements of inter-ethnic: concepts, content
and illustrations, as set by West Virginia Board of
Education Policy (Adopted December 1970).
II. EQUAL OPPORTUNITY
The instructional material meets the
requirements of equal opportunity: concept,
content, illustration, heritage, roles contributions,
experiences and achievements of males and
females in American and other cultures, as set
by West Virginia Board of Education Policy
(Adopted May 1975).
1
INSTRUCTIONAL MATERIALS ADOPTION: 21st CENTURY LEARNING EVALUATION CRITERIA
GENERAL EVALUATION CRITERIA
2010-2015
Sixth Grade Mathematics
(Vendor/Publisher)
SPECIFIC LOCATION OF
CONTENT WITHIN PRODUCT
(IMR Committee) Responses
I=In-depth
A=Adequate
M=Minimal
N=Nonexistent
I
A
M
N
In addition to alignment of Content Standards and Objectives (CSOs), materials must also clearly connect to
Learning for the 21st Century which includes opportunities for students to develop
A.
This criteria is
addressed throughout
the program. Sample
citations follow:
SE: Prime Time
Investigation 2: WholeNumber Patterns and
Relationships (26–29,
31, 34), Investigation
3: Choosing Common
Multiples or Common
Factors (44); Bits and
Pieces I Investigation
2: Sharing and
Comparing with
Fractions (23–24),
Investigation 3:
Moving From
Fractions to Decimals
(41–42); Bits and
Pieces II Investigation
Learning Skills
•
Thinking and Problem-Solving Skills/ Rigor and Depth of Content
Content is presented in a way that deepens student understanding
through engagement in meaningful, challenging mathematics that
builds on prior knowledge and promotes connections among
mathematical concepts.
•
Thinking and Problem-Solving Skills /Development of Conceptual
Understanding
Learning opportunities require students to develop their own viable
mathematical understandings and help them build connections
between mathematical ideas.
•
Information and Communication Skills/Mathematical Language
Appropriately introduce and reinforce in multiple ways all necessary
terms and symbols.
•
Personal and Work Place Productivity Skills
2
3: Multiplying With
Fractions (32–37);
Covering and
Surrounding
Investigation 2:
Changing Area,
Changing Perimeter
(20–21, 24)
TG: Prime Time
Investigation 2: WholeNumber Patterns and
Relationships (45–48,
50, 51), Investigation
3: Choosing Common
Multiples or Common
Factors (72); Bits and
Pieces I Investigation
2: Sharing and
Comparing with
Fractions (57–62),
Investigation 3:
Moving From
Fractions to Decimals
(91–96); Bits and
Pieces II Investigation
3: Multiplying With
Fractions (60–74);
Covering and
Surrounding
Investigation 2:
Changing Area,
Changing Perimeter
(38–42, 47–50),
3
B.
Problem-solving
tools
This criteria is
addressed throughout
the program. Sample
citations follow:
SE: Shapes and
Designs Investigation
2: Polygons and
Angles (32–37, 44,
49), Investigation 3:
Polygon Properties
and Tiling (56–57);
Covering and
Surrounding
Investigation 1:
Designing Bumper
Cars (5–8)
TG: Shapes and
Designs Investigation
2: Polygons and
Angles (45–52, 58,
59), Investigation 3:
Polygon Properties
and Tiling (67–70);
Covering and
Surrounding
Investigation 1:
Designing Bumper
Cars (18–26)
21st Century Tools
•
Problem-solving tools (such as spreadsheets, decision support, design
tools)
•
Communication, information processing and research tools (such as word
processing, e-mail, groupware, presentation, Web development, Internet
search tools)
•
Personal development and productivity tools (such as e-learning, time
management/calendar, collaboration tools)
4
INSTRUCTIONAL MATERIALS ADOPTION: 21st Century Learning EVALUATION CRITERIA
The general evaluation criteria apply to each grade level and are to be evaluated for each grade level unless otherwise specified. These criteria consist of
information critical to the development of all grade levels. In reading the general evaluation criteria and subsequent specific grade level criteria, e.g. means
“examples of” and i.e. means that “each of” those items must be addressed. Eighty percent of the combined general and specific criteria must be met with I
(In-depth) or A (Adequate) in order to be recommended.
2010-2015
Sixth Grade Mathematics
(Vendor/Publisher)
SPECIFIC LOCATION OF
CONTENT WITHIN PRODUCT
(IMR Committee) Responses
I=In-depth
A=Adequate
M=Minimal
N=Nonexistent
I
A
M
N
For student mastery of content standards and objectives, the instructional materials will provide students with the opportunity to
4. Multimedia
Student Interactivity CD-ROM
1. offer appropriate multimedia (e.g., software, audio, visual, internet
access) materials.
on-line www.PHSchool.com
2. provide a website which provides links to relevant sites as well as
lesson plans, student activities and parent resources.
5
TG: Data About Us (12)
3. Integrate technology seamlessly when appropriate to model
mathematical situations, analyze data, calculate results, and solve
problems.
B. Scientifically-Based Research Strategies
This criteria is addressed
throughout the program. Sample
citations follow:
SE: Bits and Pieces II
Investigation 4: Preparing Food
(48–50);
TG: Bits and Pieces II
Investigation 4: Preparing Food
(92–96);
This criteria is addressed
throughout the program. Sample
citations follow:
Mathematical Reflections are
found at the end of each
Investigation; Looking Back and
Looking Ahead at the end of
each Unit
This criteria is addressed
throughout the program. Sample
citations follow:
SE: Bits and Pieces I
Investigation 3: Moving From
Fractions to Decimals (41–42);
TG: Bits and Pieces I
Investigation 3: Moving From
Fractions to Decimals (91–96)
1. Consistently require students to link prior knowledge to new
information to construct their own viable understandings of
mathematical ideas.
2. Consistently provide opportunities for students to solve complex
problems that have multiple entry points and the possibility of multiple
solution processes.
3. Consistently provide opportunities for students to communicate their
mathematical thinking processes to others orally, in writing, or
pictorially.
6
This criteria is addressed
throughout the program. Sample
citations follow:
SE: Bits and Pieces III
Investigation 5: More About
Percents (62–64);
TG: Bits and Pieces III
Investigation 5: More About
Percents (101–108)
This criteria is addressed
throughout the program. Sample
citations follow:
SE: Covering and Surrounding
Investigation 2: Changing Area,
Changing Perimeter (20–21, 24),
Investigation 5: Measuring
Irregular Shapes and Circles (70–
75, 77)
TG: Covering and Surrounding
Investigation 2: Changing Area,
Changing Perimeter (38–42, 47–
50), Investigation 5: Measuring
Irregular Shapes and Circles
(110–128)
This criteria is addressed
throughout the program. Sample
citations follow:
SE: Bits and Pieces II
Investigation 3: Multiplying With
Fractions (32–37)
TG: Bits and Pieces II
Investigation 3: Multiplying With
Fractions (60–74)
4. Routinely require students to develop and defend mathematical
conjectures, arguments, reasoning and proof.
5. Provide opportunities for the students to be involved in investigations
that enable them to make connections among mathematical ideas.
6. Expect students to develop multiple representations of the
mathematics in order to depict reasoning used to explain real world
phenomena or solutions to relevant problems and move fluently
between those representations.
7
SE: Bits and Pieces II
Investigation 1: Estimating With
Fractions (6–7), Investigation 3:
Multiplying With Fractions (32–37)
TG: Bits and Pieces II
Investigation 1: Estimating With
Fractions (20–24), Investigation 3:
Multiplying With Fractions (60–74)
7. Present varied teaching models with emphasis on differentiated
instruction in content, process, and product.
8
C. Critical Thinking
This criteria is addressed
throughout the program. Sample
citations follow:
SE: Covering and Surrounding
Investigation 3: Measuring
Triangles (38–43)
TG: Covering and Surrounding
Investigation 3: Measuring
Triangles (61–82)
This criteria is addressed
throughout the program. Sample
citations follow:
SE: Bits and Pieces II
Investigation 1: Estimating With
Fractions (6–7), Investigation 3
Multiplying With Fractions (37–38)
TG: Bits and Pieces II
Investigation 1: Estimating With
Fractions (20–24), Investigation 3
Multiplying With Fractions (75–80)
This criteria is addressed
throughout the program. Sample
citations follow:
SE: Covering and Surrounding
Investigation 1: Designing Bumper
Cars (5–10), Investigation 4:
Measuring Parallelograms (58–
59)
TG: Covering and Surrounding
Investigation 1: Designing Bumper
Cars (18–32), Investigation 4:
Measuring Parallelograms (101–
104)
1. emphasize questioning models to promote higher order thinking skills
based on depth of knowledge.
2. Consistently require students to discuss mathematics with each
other and with the teacher, make arguments, conjecture and
reason, and justify/clarify their ideas in writing and orally in
precise mathematical symbols and language.
3. Present real world application that is current, engaging, integrated
throughout the instruction, and promotes and develops critical
thinking.
9
D. Life Skills
This criteria is addressed
throughout the program. Sample
citations follow:
SE: Bits and Pieces III
Investigation 4: Using Percents
(51–53)
TG: Bits and Pieces III
Investigation 4: Using Percents
(89–92)
This criteria is addressed
throughout the program. Sample
citations follow:
SE: Prime Time Investigation 1:
Factors and Products (7–10)
TG: Prime Time Investigation 1:
Factors and Products (16–24)
1. address life skills (e.g., reading road maps, using reference tools,
researching, reading a newspaper, using want ads, completing an
application, applying the interview process and goal setting).
2. address habits of mind activities (e.g., literacy skills, interpersonal
communications, problem solving and self-directional skills).
E. Classroom Management
This criteria is addressed
throughout the program. Sample
citations follow:
SE: Bits and Pieces II
Investigation 1: Estimating With
Fractions (6–7)
TG: Bits and Pieces II
Investigation 1: Estimating With
Fractions (20–24)
1. include opportunities for large group, small group, and independent
learning.
10
This criteria is addressed
throughout the program. Sample
citations follow:
SE: Prime Time Investigation 1:
Factors and Products (7–11, 11–
13); Covering and Surrounding
Investigation 3: Measuring
Triangles (38–43), Investigation 4:
Measuring Parallelograms (56–
57, 67); Bits and Pieces III
Investigation 4: Using Percents
(51–53)
TG: Prime Time Investigation 1:
Factors and Products (17–24, 25–
30); Covering and Surrounding
Investigation 3: Measuring
Triangles (68–82), Investigation 4:
Measuring Parallelograms (101–
104, 107); Bits and Pieces III
Investigation 4: Using Percents
(89–92)
This criteria is addressed
throughout the program. Sample
citations follow:
SE: Prime Time Investigation 1:
Factors and Products (12),
Investigation 3: Common
Multiples and Common Factors
(43); Shapes and Designs
Investigation 3: Common
Multiples and Common Factors
(43); How Likely Is It?
Investigation 1: A First Look at
Chance (13)
2. Consistently require students to explore mathematical ideas,
individually and collaboratively, while integrating the process
standards (see Section I of this rubric).
3. provide suggestions for differentiated instruction (e.g., practice
activities, learning stations, assessment, lesson plans).
11
F. Instructional Materials
This criteria is addressed
throughout the program. Sample
citations follow:
SE: Prime Time Investigation 1:
Factors and Products (7–11, 11–
13)
TG: Prime Time Investigation 1:
Factors and Products (17–30),
This criteria is addressed
throughout the program. Sample
citations follow:
SE: Prime Time Investigation 1:
Factors and Products (7–10);
Bits and Pieces I Investigation 3:
Moving From Fractions to
Decimals (41–42); Bits and
Pieces II Investigation 1:
Estimating With Fractions (8–9),
Investigation 3 Multiplying With
Fractions (37–38); Bits and
Pieces III Investigation 4: Using
Percents (51–53)
TG: Prime Time Investigation 1:
Factors and Products (16–24);
Bits and Pieces I Investigation 3:
Moving From Fractions to
Decimals (91–96); Bits and
Pieces II Investigation 1:
Estimating With Fractions (25–
30), Investigation 3 Multiplying
With Fractions (75–80); Bits and
Pieces III Investigation 4: Using
Percents (89–92)
1. Are organized according to WV content standards or other increments
that allow students to investigate and explore major mathematical
ideas; provide a variety of lessons, activities, and projects from which
to choose; and emphasize connections between mathematical ideas.
2. Consistently integrate tasks that engage students and invite them to
speculate and hypothesize, are open-ended, and require them to
determine appropriate strategies.
12
TG: Every Problem in each
Investigation provides questions
to develop understanding
ExamView ™ , Teacher
Express™ CD-ROM, LessonLab
Online Courses
ExamView ™ , Teacher
Express™ CD-ROM, LessonLab
Online Courses
Differentiated Instruction provided
in every section of ACE Answers
for all Investigations; Special
Needs Handbook
Differentiated Instruction provided
in every section of ACE Answers
for all Investigations; Special
Needs Handbook
ExamView ™ , Teacher
Express™ CD-ROM, LessonLab
Online Courses
TG: Prime Time (4–9); Bit and
Pieces I (4–8); Shapes and
Designs (4–10); Bit and Pieces II
(4–12); Covering and
Surrounding (4–9); Bit and
Pieces III (4–8); How Likely Is it?
(3–7); Data About Us (4–8)
LessonLab Online Courses
SE: Bits and Pieces I
Investigation 3: Moving From
Fractions to Decimals (41–42);
Bits and Pieces III Investigation
1: Decimals—More or Less! (6–7),
TG: Bits and Pieces I
Investigation 3: Moving From
Fractions to Decimals (91–96);
Bits and Pieces III Investigation
1: Decimals—More or Less! (16–
20)
3. Provide teachers with guiding questions to aid students’ development
of mathematical discourse to further mathematical understanding.
4. Provide additional resources that are organized in a way that is easy
to access and use.
5. Include various instructional models to address varied learning styles
of students.
6. Provide extensive and varied opportunities to differentiate individual
needs for skill-building.
7. Provide supplemental materials for intervention and enrichment.
8. Provide teachers with support to properly integrate the process
standards using the available resources.
9. Include a teacher resource that builds content knowledge for the
teacher.
10. Spiral previously taught skills and strategies with new content.
13
G. Assessment
TG: Prime Time (14); Bit and
Pieces I (13); Shapes and
Designs (15); Bit and Pieces II
(17); Covering and Surrounding
(15); Bit and Pieces III (13); How
Likely Is it? (12); Data About Us
(15)
TG: Prime Time (13–14); Bit and
Pieces I (12–13); Shapes and
Designs (14–15); Bit and Pieces
II (16–17); Covering and
Surrounding (13–15); Bit and
Pieces III (12–13); How Likely Is
it? (11–12); Data About Us (15)
TG: Prime Time (11); Bit and
Pieces I (10); Shapes and
Designs (12); Bit and Pieces II
(14); Covering and Surrounding
(11); Bit and Pieces III (10); How
Likely Is it? (9); Data About Us
(10–11)
Covering and Surrounding Unit
Project (89–90); Bit and Pieces
III Unit Project (74–75)
TG: Prime Time (13); Bit and
Pieces I (12); Shapes and
Designs (14); Bit and Pieces II
(16); Covering and Surrounding
(12–13); Bit and Pieces III (12);
How Likely Is it? (11); Data
About Us (12–13)
1. provide assessment formats commensurate with WV assessment
programs (e.g., WESTEST, NAEP, State Writing Assessment,
informal assessments, PLAN, EXPLORE, ACT and SAT).
2. provide opportunities for assessment based on performance-based
measures, open-ended questioning, portfolio evaluation, rubrics and
multimedia simulations.
3. provide benchmark and ongoing progress monitoring.
4. provide rubric-based differentiated assessment.
5. provide an electronic system for managing assessment data to
facilitate the implementation of tiered instruction
14
TG: Prime Time (13); Bit and
Pieces I (12); Shapes and
Designs (14); Bit and Pieces II
(16); Covering and Surrounding
(13); Bit and Pieces III (12); How
Likely Is it? (11); Data About Us
(12–13)
TG: Prime Time (13–14); Bit and
Pieces I (12–13); Shapes and
Designs (14–15); Bit and Pieces
II (16–17); Covering and
Surrounding (13–15); Bit and
Pieces III (12–13); How Likely Is
it? (11–12); Data About Us (15)
TG: Prime Time (13); Bit and
Pieces I (12); Shapes and
Designs (14); Bit and Pieces II
(16); Covering and Surrounding
(13); Bit and Pieces III (12); How
Likely Is it? (11); Data About Us
(12–13)
6. integrate student self-assessment for and of learning by providing
tools and organizers that are linked to clearly identified learning goals.
7. Integrate formal and informal means of assessment in the materials
for diagnostic, formative, and summative purposes.
8. include various types of assessments: performance tasks, multiple
choice, short answer, and free response.
15
H. Process Standards
Mathematical Reflections are
found at the end of each
Investigation
1. Problem Solving: Provide frequent opportunities for students to
formulate, grapple with, and solve complex problems that require a
significant amount of effort and have multiple viable solution paths.
SE: Prime Time Unit Project (70)
2. Communication: Routinely challenge students to communicate their
thinking to others orally, in writing, and/or pictorially, using precise
mathematical language.
SE: Prime Time Investigation 2:
Whole-Number Patterns and
Relationships (24–26);
TG: Prime Time Investigation 2:
Whole-Number Patterns and
Relationships (41–44);
SE: Covering and Surrounding
Investigation 2: Changing Area,
Changing Perimeter (20–21, 24),
Investigation 5: Measuring
Irregular Shapes and Circles (70–
75);
TG: Covering and Surrounding
Investigation 2: Changing Area,
Changing Perimeter (38–42, 47–
50), Investigation 5: Measuring
Irregular Shapes and Circles
(110–122);
SE: Covering and Surrounding
Investigation 3: Measuring
Triangles (42–43)
TG: Covering and Surrounding
Investigation 3: Measuring
Triangles (75–82)
3. Reasoning and Proof: Provide frequent opportunities for students to
complete mathematical investigations with and without technology;
develop conjectures, mathematical arguments and proofs to confirm
those conjectures.
4. Connections with Mathematics: Consistently establish connections,
and provide opportunities for students to establish connections,
among mathematical concepts and their real-world applications.
5. Representations: Provide frequent opportunities for students to
develop multiple representations of the mathematics in order to depict
reasoning used to explain real world phenomena or solutions to
relevant problems and move fluently between those representations.
16
SPECIFIC EVALUATION CRITERIA
Sixth Grade Mathematics
Sixth grade objectives place continued emphasis on the study of whole numbers, decimals and fractions (primary focus on
multiplication and division of fractions and mixed numbers). Introductory work with integers includes understanding why the rules for
adding, subtracting, multiplying and dividing integers work. Opportunities to apply these skills to real world situations help to make
sense of the mathematics. Calculators, computers and manipulatives may be used to solve problems. Probability, Statistics, Geometry,
and Pre-Algebra will be stressed. Concepts of using ratios to compare data sets, making geometric constructions of three-dimensional
figures and solving problems involving circles, volume and surface area are emphasized. The West Virginia Standards for 21st Century
Learning include the following components: 21st Century Content Standards and Objectives and 21st Century Learning Skills and
Technology Tools. All West Virginia teachers are responsible for classroom instruction that integrates learning skills, technology tools
and content standards and objectives.
Standard 1: Number and Operations
Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the
field of mathematics, students will
• demonstrate understanding of numbers, ways of representing numbers, and relationships among numbers and number
systems,
• demonstrate meanings of operations and how they relate to one another, and
• compute fluently and make reasonable estimates.
Standard 2: Algebra
Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the
field of mathematics, students will
• demonstrate understanding of patterns, relations and functions,
• represent and analyze mathematical situations and structures using algebraic symbols,
• use mathematical models to represent and understand quantitative relationships, and
• analyze change in various contexts.
17
Standard 3: Geometry
Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the
field of mathematics, students will
• analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical
arguments about geometric relationships,
• specify locations and describe spatial relationships using coordinate geometry and other representational systems,
• apply transformations and use symmetry to analyze mathematical situations, and
• solve problems using visualization, spatial reasoning, and geometric modeling.
Standard 4: Measurement
Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the
field of mathematics, students will
• demonstrate understanding of measurable attributes of objects and the units, systems, and processes of
measurement, and
• apply appropriate techniques, tools and formulas to determine measurements.
Standard 5: Data Analysis and Probability
Through communication, representation, reasoning and proof, problem solving, and making connections within and beyond the
field of mathematics, students will
• formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them,
• select and use appropriate statistical methods to analyze data,
• develop and evaluate inferences and predictions that are based on models, and
• apply and demonstrate an understanding of basic concepts of probability.
18
(Vendor/Publisher)
SPECIFIC LOCATION OF
CONTENT WITHIN PRODUCT
(IMR Committee) Responses
I=In-depth
A=Adequate
M=Minimal
N=Nonexistent
I
A
M
N
For student mastery of content standards and objectives, the instructional materials will…
A. Number and Operations
SE: WV Additional Lessons
Grade 6 Topic 1:
Exponential Form
SE: Prime Time Investigation 2
Whole-Number Patterns and
Relationships (26–29, 31,
34), Investigation 3:
Choosing Common
Multiples or Common
Factors (37–38, 39–40, 40–
41, 41), Investigation 4:
Factorizations: Searching for
Factor Strings (50–55),
Investigation 5: Putting It All
Together (61–64); Bits and
Pieces I Investigation 2:
Sharing and Comparing with
Fractions (32); Shapes and
Designs Investigation 2:
Polygons and Angles (47)
TG: Prime Time
Investigation 2: WholeNumber Patterns and
1. provide a variety of examples and exercises to
demonstrate an understanding of large numbers by
converting and comparing numbers in scientific notation
and standard notation (with and without technology).
2. provide a variety of examples and exercises to determine
the greatest common factor and least common multiple
using multiple strategies to solve real-world problems; find
prime factorization of a number.
19
Relationships (45–48, 50,
51), Investigation 3:
Common Multiples and
Common Factors (54–58,
59–62, 63–66, 67–70),
Investigation 4:
Factorizations: Searching for
Factor Strings (75–92),
Investigation 5: Putting It All
Together (96–100); Bits
and Pieces I Investigation
2: Sharing and Comparing
with Fractions (75); Shapes
and Designs Investigation
2: Polygons and Angles (59)
SE: Bits and Pieces II
Investigation 2: Adding and
Subtracting Fractions (30);
Bits and Pieces III
Investigation 1: Decimals—
More or Less! (19),
Investigation 2: Decimal
Times (34); West Virginia
Additional Lessons Grade
6 Topic 2: Understanding
Integers (3-4)
TG: Bits and Pieces II
Investigation 2: Adding and
Subtracting Fractions (57);
Bits and Pieces III
Investigation 1: Decimals—
More or Less! (32),
Investigation 2: Decimal
Times (56–57); West
Virginia Teacher’s
Resource Guide Grade 6
Topic 2: Understanding
Integers (3-4)
3. provide a variety of examples and exercises to compare
and order integers using multiple strategies (e.g.,
symbols, manipulatives, number line).
20
SE: Bits and Pieces I
Investigation 4: Working
With Percents (56–57); Bits
and Pieces II Investigation
1: Estimating With Fractions
(5–9), Investigation 3:
Multiplying With Fractions
(32–38); Investigation 4:
Dividing With Fractions (49–
53); Bits and Pieces III
Investigation 1: Decimals—
More or Less! (6–12),
Investigation 2: Decimal
Times (21–23, 24–25, 29–
30, 33), Investigation 3: The
Decimal Divide (36–37)
West Virginia Additional
Lessons Grade 6 Topic 5:
Integer Operations (9-10)
TG: Bits and Pieces I
Investigation 4: Working
With Percents (113–126);
Bits and Pieces II
Investigation 1: Estimating
With Fractions (20–30),
Investigation 3: Multiplying
With Fractions (71–80),
Investigation 4: Dividing
With Fractions (92–108);
Bits and Pieces III
Investigation 1: Decimals—
More or Less! (16–32),
Investigation 2: Decimal
Times (37–42, 47–50, 57–
59), Investigation 3: The
Decimal Divide (62–64)
4. provide a variety of examples and exercises to analyze
and solve real-world problems involving addition,
subtraction , multiplication and division of
ƒ whole numbers,
ƒ fractions, mixed numbers,
ƒ decimals
ƒ integers
and justify the reasonableness by estimation.
21
SE: Prime Time Investigation 3:
Common Multiples and
Common Factors (46); Bits
and Pieces II Investigation
3: Multiplying With Fractions
(37–38, 40), Investigation 4:
Dividing With Fractions (59);
Covering and Surrounding
Investigation 1: Designing
Bumper Cars (15); West
Virginia Additional
Lessons Grade 6 Topic 14:
Number Properties (33-34)
TG: Prime Time Investigation 3:
Common Multiples and
Common Factors (72); Bits
and Pieces II Investigation
3: Multiplying With Fractions
(75–80, 86), Investigation 4:
Dividing With Fractions
(117); Covering and
Surrounding Investigation
1: Designing Bumper Cars
(35); West Virginia
Teacher’s Resource Guide
Grade 6 Topic 14: Number
Properties (29-30)
SE: Bits and Pieces I
Investigation 2: Sharing and
Comparing with Fractions
(25–27), Investigation 3:
Moving Between Fractions
and Decimals (36–39, 43–
44), Investigation 4: Working
With Percent (55–60);
Shapes and Designs
Investigation 1: Bees and
Polygons (20), Investigation
2: Polygons and Angles
(47), Investigation 4:
5. provide a variety of examples and exercises to apply the
distributive, commutative, associative and identity
properties to numeric expressions and use to prove
equivalency.
6. provide a variety of examples and exercises to convert
between fractions/ratios, mixed numbers, decimals and
percents in appropriate real-world problems.
22
Building Polygons (78); Bits
and Pieces II Investigation
1: Estimating With Fractions
(12), Investigation 3:
Multiplying With Fractions
(37–38, 46), Investigation 4:
Dividing With Fractions (50–
53); Bits and Pieces III
Investigation 1: Decimals—
More or Less! (10–11),
Investigation 2: Decimal
Times (21–23)
TG: Bits and Pieces I
Investigation 2: Sharing and
Comparing with Fractions
(67–72), Investigation 3:
Moving Between Fractions
and Decimals (79–84, 97–
100), Investigation 4:
Working With Percent (113–
132); Shapes and Designs
Investigation 1: Bees and
Polygons (33), Investigation
2: Polygons and Angles
(59), Investigation 4:
Building Polygons (96); Bits
and Pieces II Investigation
1: Estimating With Fractions
(32–33), Investigation 3:
Multiplying With Fractions
(75–80, 87), Investigation 4:
Dividing With Fractions (97–
108); Bits and Pieces III
Investigation 1: Decimals—
More or Less! (25–28),
Investigation 2: Decimal
Times (37–42)
23
SE: Bits and Pieces I
Investigation 4: Working
With Percents (56–57, 60);
Bits and Pieces III
Investigation 4: Using
Percents (50–54),
Investigation 5: More About
Percents (62–64, 72); Data
About Us Investigation 2:
Using Graphs to Explore
Data (44)
TG: Bits and Pieces I
Investigation 4: Working
With Percents (113–126,
129–132); Bits and Pieces
III Investigation 4: Using
Percents (81–96),
Investigation 5: More About
Percents (101–108, 115);
Data About Us
Investigation 2: Using
Graphs to Explore Data (69)
7. provide a variety of examples and exercises to compute
the percent of a number to solve application problems and
justify the reasonableness by estimation.
24
SE: Prime Time Investigation 2:
Whole-Number Patterns and
Relationships (24–26),
Investigation 3: Common
Multiples and Common
Factors (46); Bits and
Pieces II Investigation 3:
Multiplying With Fractions
(37–39,40), Investigation 4:
Dividing With Fractions (49–
50, 53–54, 59); Bits and
Pieces III Investigation 3:
The Decimal Divide (40)
TG: Prime Time Investigation 2:
Whole-Number Patterns and
Relationships (41–44),
Investigation 3: Common
Multiples and Common
Factors (72); Bits and
Pieces II Investigation 3:
Multiplying With Fractions
(75–84, 86), Investigation 4:
Dividing With Fractions (92–
96, 117); Bits and Pieces III
Investigation 3: The Decimal
Divide (71–74)
8. provide a variety of examples and exercises to
demonstrate an understanding of the effect of multiplying
and dividing, whole numbers, fractions and decimals by
numbers including 0, 1 and values between 0 and 1.
25
SE: West Virginia Additional
Lessons Grade 6 Topic 5:
Integer Operations (9-10)
TG: West Virginia Teacher’s
Resource Guide Grade 6
Topic 5: Integer Operations
(9-10)
9. provide a variety of examples and exercises to develop
and test hypotheses to derive the rules for addition,
subtraction, multiplication and division of integers, justify
by using real-world examples and use them to solve
problems.
B. Algebra
SE: Prime Time Investigation 2:
Whole-Number Patterns and
Relationships (24–26);
Covering and Surrounding
Investigation 5: Measuring
Irregular Shapes and Circles
(86); West Virginia
Additional Lessons Grade
6 Topic 9: Evaluating
Expressions Using Order of
Operations (19-20)
TG: Prime Time Investigation 2:
Whole-Number Patterns and
Relationships (41–44);
Covering and Surrounding
Investigation 5: Measuring
Irregular Shapes and Circles
(131); West Virginia
Teacher’s Resource Guide
Grade 6 Topic 9: Evaluating
Expressions Using Order of
Operations (19-20)
1. provide examples and exercises to simplify numerical
expressions and evaluate algebraic expressions using
order of operations.
26
SE: Prime Time Investigation 2:
Whole-Number Patterns and
Relationships (33),
Investigation 3: Common
Multiples and Common
Factors (46, 47); Bits and
Pieces I Investigation 3:
Moving Between Fractions
and Decimals (39–40, 49);
Shapes and Designs
Investigation 3: Polygon
Properties and Tiling (67);
Bits and Pieces III
Investigation 3: The Decimal
Divide (47); West Virginia
Additional Lessons Grade
6 Topic 3: Inductive
Reasoning (5-6)
TG: Prime Time Investigation 2:
Whole-Number Patterns and
Relationships (51),
Investigation 3: Common
Multiples and Common
Factors (72); Bits and
Pieces I Investigation 3:
Moving Between Fractions
and Decimals (85–90, 109);
Shapes and Designs
Investigation 3: Polygon
Properties and Tiling (80);
Bits and Pieces III
Investigation 3: The Decimal
Divide (81); West Virginia
Teacher’s Resource Guide
Grade 6 Topic 3: Inductive
Reasoning (5-6)
2. provide opportunities to use inductive reasoning to extend
patterns to predict the nth term (e.g., powers and
triangular numbers).
27
SE: Covering and Surrounding
Investigation 1: Designing
Bumper Cars (8–9),
Investigation 4: Measuring
Parallelograms (54–57, 67);
West Virginia Additional
Lessons Grade 6 Topic 15:
Algebraic Expressions (3536)
TG: Covering and Surrounding
Investigation 1: Designing
Bumper Cars (27–32),
Investigation 4: Measuring
Parallelograms (88–100,
107); West Virginia
Additional Lessons Grade
6 Topic 15: Algebraic
Expressions (31-32)
SE: Covering and Surrounding
Investigation 1: Designing
Bumper Cars (8–9),
Investigation 4: Measuring
Parallelograms (56–57, 67);
West Virginia Additional
Lessons Grade 6 Topic 16:
Tables and Functions (3738)
TG: Covering and Surrounding
Investigation 1: Designing
Bumper Cars (27–32),
Investigation 4: Measuring
Parallelograms (101–104,
107); West Virginia
Teacher’s Resource Guide
Grade 6 Topic 16: Tables
and Functions (33-34)
3. provide opportunities to create algebraic expressions that
correspond to real-world situations; use the expressions
to solve problems.
4. provide examples and exercises to determine the rule,
output or input; given an input/output model using one
operation, write an algebraic expression for the rule and
use to identify other input/output values.
28
SE: Prime Time Investigation 3:
Common Multiples and
Common Factors (44); Bits
and Pieces I Investigation
4: Working With Percents
(61–63); Bits and Pieces II
Investigation 2: Adding and
Subtracting Fractions (28–
29), Investigation 3:
Multiplying With Fractions
(44); How Likely Is It?
Investigation 1: A First Look
at Chance (6–10),
Investigation 2:
Experimental and
Theoretical Probability (21–
26), Investigation 3: Making
Decisions With Probability
(39–43), Investigation 4:
Probability, Genetics, and
Games (55–61); Data
About Us Investigation 2:
Using Graphs to Explore
Data (44); West Virginia
Additional Lessons Grade
6 Topic 12: Proportional
Relationships (25-26)
TG: Prime Time Investigation 3:
Common Multiples and
Common Factors (72); Bits
and Pieces I Investigation
4: Working With Percents
(133–134); Bits and Pieces
II Investigation 2: Adding
and Subtracting Fractions
(57), Investigation 3:
Multiplying With Fractions
(87); SE: How Likely Is It?
Investigation 1: A First Look
at Chance (15–32),
5. provide examples and exercises to solve real-world
proportion problems involving rates, probability and
measurements using multiple strategies, justify selection
of strategies.
29
Investigation 2:
Experimental and
Theoretical Probability (37–
48), Investigation 3: Making
Decisions With Probability
(59–70), Investigation 4:
Probability, Genetics, and
Games (76–86); Data
About Us Investigation 2:
Using Graphs to Explore
Data (69); West Virginia
Teacher’s Resource Guide
Grade 6 Topic 12:
Proportional Relationships
(25-26)
30
SE: Bits and Pieces II
Investigation 2: Adding and
Subtracting Fractions (18–
21, 24); Bits and Pieces III
Investigation 2: Decimal
Times (30), Investigation 3:
The Decimal Divide (40);
West Virginia Additional
Lessons Grade 6 Topic 8:
Solving One-Step Equations
(17-18)
TG: Bits and Pieces II
Investigation 2: Adding and
Subtracting Fractions (35–
46, 55); Bits and Pieces III
Investigation 2: Decimal
Times (58), Investigation 3:
The Decimal Divide (71–74);
West Virginia Teacher’s
Resource Guide Grade 6
Topic 8: Solving One-Step
Equations (17-18)
6. provide examples and exercises to write and solve onestep equations using number sense, properties of
operations and the idea of maintaining equality to
represent and solve real-world problems.
C. Geometry
SE: Shapes and Designs
Investigation 1: Bees and
Polygons (8–16),
Investigation 2: Polygons
and Angles (24–29, 38-39,
45, 46), Investigation 3:
Polygon Properties and
Tiling (54–57, 60–61, 66–
67), Investigation 4: Building
Polygons (70–75); Covering
and Surrounding
Investigation 3: Measuring
Triangles (38–43); Bits and
1. provide opportunities to analyze characteristics using
defining properties of
• lines,
• angles,
• polygons,
• triangles, and
compare these geometric figures.
31
Pieces III Investigation 1:
Decimals – More or Less!
(17); West Virginia
Additional Lessons Grade
6 Topic 4: Types of Lines (78) Topic 6: Polygon Vertices
(11-12) Topic 13: Similar
Figures and Scale Drawings
(27-28)
TG: Shapes and Designs
Investigation 1: Bees and
Polygons (18–30),
Investigation 2: Polygons
and Angles (36–40, 53–56,
58), Investigation 3: Polygon
Properties and Tiling (63–
70, 75–78, 80), Investigation
4: Building Polygons (83–
94); Covering and
Surrounding Investigation
3: Measuring Triangles (61–
82); Bits and Pieces III
Investigation 1: Decimals –
More or Less! (34); West
Virginia Teacher’s
Resource Guide Grade 6
Topic 4: Types of Lines (7-8)
Topic 6: Polygon Vertices
(11-12) Topic 13: Similar
Figures and Scale Drawings
(27-28)
SE: Shapes and Designs
Investigation 3: Polygon
Properties and Tiling (54–
57, 67)
TG: Shapes and Designs
Investigation 3: Polygon
Properties and Tiling (63–
70, 80)
2. provide examples and exercises to use inductive
reasoning with the measures of interior angles in polygons
and derive the formula to determine the sum of the
measures of the interior angles.
32
SE: Shapes and Designs
Investigation 2: Polygons
and Angles (35–39),
Investigation 4: Building
Polygons (79); West
Virginia Additional
Lessons Grade 6 Topic 4:
Types of Lines (7-8)
TG: Shapes and Designs
Investigation 2: Polygons
and Angles (49–56),
Investigation 4: Building
Polygons (96) ; West
Virginia Teacher’s
Resource Guide Grade 6
Topic 4: Types of Lines (7-8)
SE: Shapes and Designs
Investigation 1: Bees and
Polygons (12–16, 18–19),
Investigation 2: Polygons
and Angles (49),
Investigation 4: Building
Polygons (74–75, 80); West
Virginia Additional
Lessons Grade 6 Topic 7:
Symmetry (13-16)
TG: Shapes and Designs
Investigation 1: Bees and
Polygons (23–30),
Investigation 2: Polygons
and Angles (60),
Investigation 4: Building
Polygons (91–94, 96) ; West
Virginia Teacher’s
Resource Guide Grade 6
Topic 7: Symmetry (15-16)
3. provide examples and exercises to apply the concepts of
parallel, perpendicular, intersecting, and skew lines to
real-world situations (i.e. roads and routes).
4. provide examples and exercises to create designs using
line and rotational symmetry.
33
SE: Shapes and Designs
Investigation 1: Bees and
Polygons (12–13),
Investigation 2: Polygons
and Angles (48–50),
Investigation 4: Building
Polygons (80)
TG: Shapes and Designs
Investigation 1: Bees and
Polygons (23–26),
Investigation 2: Polygons
and Angles (60),
Investigation 4: Building
Polygons (91–94)
SE: Shapes and Designs
Investigation 3: Polygon
Properties and Tiling (54–
57); Covering and
Surrounding Investigation
1: Designing Bumper Cars
(5–9, 14–17), Investigation
2: Changing Area, Changing
Perimeter (19–21, 24, 31–
34), Investigation 4:
Measuring Parallelograms
(58–59), Investigation 5:
Measuring Irregular Shapes
and Circles (74–77, 81–82,
85, 87)
TG: Shapes and Designs
Investigation 3: Polygon
Properties and Tiling (63–
70); Covering and
Surrounding Investigation
1: Designing Bumper Cars
(18–32, 35–36),
Investigation 2: Changing
Area, Changing Perimeter
(38–42, 47–50),
5. provide examples and exercises to predict, describe, and
perform transformations on two-dimensional shapes
• translations
• rotations
• reflections
6. provide examples and exercises to use geometric
representations to solve real-world problems.
34
Investigation 4: Measuring
Parallelograms (101–104),
Investigation 5: Measuring
Irregular Shapes and Circles
(119–128, 130)
SE: Shapes and Designs
Investigation 2: Polygons
and Angles (49); West
Virginia Additional
Lessons Grade 6 Topic 6:
Polygon Vertices (11-12)
TG: Shapes and Designs
Investigation 2: Polygons
and Angles (60); West
Virginia Teacher’s
Resource Guide Grade 6
Topic 6: Polygon Vertices
(11-12)
7. provide examples and exercises to plot polygons on
coordinate grids, determine lengths and areas from the
graph.
D. Measurement
SE: Covering and Surrounding
Investigation 5: Measuring
Irregular Shapes and Circles
(72–77, 80–87); How Likely
Is It? Investigation 3:
Making Decisions With
Probability (52)
TG: Covering and Surrounding
Investigation 5: Measuring
Irregular Shapes and Circles
(115–122, 129–131); How
Likely Is It? Investigation 3:
Making Decisions With
Probability (73)
1. provide opportunities to determine an approximation for pi
using actual measurements.
35
SE: Covering and Surrounding
Investigation 1: Designing
Bumper Cars (8–9),
Investigation 2: Changing
Area, Changing Perimeter
(31–34), Investigation 3:
Measuring Triangles (38–40,
48–51), Investigation 4:
Measuring Parallelograms
(53–57), Investigation 5:
Measuring Irregular Shapes
and Circles (72–73, 77);
Bits and Pieces III
Investigation 1: Decimals—
More or Less! (16–17),
Investigation 2: Decimal
Times (32), Investigation 3:
The Decimal Divide (48)
West Virginia Additional
Lessons Grade 6 Topic 11:
Discovering Volume (23-24)
TG: Covering and Surrounding
Investigation 1: Designing
Bumper Cars (27–32),
Investigation 2: Changing
Area, Changing Perimeter
(58, 59), Investigation 3:
Measuring Triangles (61–68,
85–86), Investigation 4:
Measuring Parallelograms
(88–100), Investigation 5:
Measuring Irregular Shapes
and Circles (115–118); Bits
and Pieces III Investigation
1: Decimals—More or Less!
(34), Investigation 2:
Decimal Times (59),
Investigation 3: The Decimal
Divide (82) West Virginia
Teacher’s resource Guide
2. provide examples and exercises to develop and test
hypotheses to determine formulas for
• perimeter of polygons, including composite figures
• area of parallelograms
• area of triangles
• area of composite figures made of parallelograms
and triangles
• circumference of a circle
• area of a circle
• volume of a rectangular prism
36
Grade 6 Topic 11:
Discovering Volume (23-24)
37
SE: Covering and Surrounding
Investigation 3: Measuring
Triangles (50), Investigation
4: Measuring Parallelograms
(58–59); How Likely Is it?
Investigation 4: Probability,
Genetics, and Games (68);
West Virginia Additional
Lessons Grade 6 Topic 10:
Surface Area (21-22)
TG: Covering and Surrounding
Investigation 3: Measuring
Triangles (85), Investigation
4: Measuring Parallelograms
(101–104); How Likely Is
it? Investigation 4:
Probability, Genetics, and
Games (89) ; West Virginia
Teacher’s Resource Guide
Grade 6 Topic 10: Surface
Area (21-22)
SE: West Virginia Additional
Lessons Grade 6 Topic 11:
Discovering Volume (23-24)
TG: West Virginia Teacher’s
Resource Guide Grade 6
Topic 11: Discovering
Volume (23-24)
SE: Covering and Surrounding
Investigation 4: Measuring
Parallelograms (63) ); Bits
and Pieces II Investigation
3: Multiplying With Fractions
(44); Bits and Pieces III
Investigation 5: More About
Percents (72); West
Virginia Additional
Lessons Grade 6 Topic 13:
3. provide opportunities to investigate, model and describe
surface area of rectangular prisms and cylinders; develop
strategies to determine the surface area of rectangular
prisms.
4. provide opportunities to develop strategies to determine
volume of cylinders; solve real-world problems involving
volume of cylinders, justify the results.
5. provide opportunities to construct a scale drawing given
the scale factor of a two-dimensional polygon.
38
Similar Figures and Scale
Drawings (27-31)
TG: Covering and Surrounding
Investigation 4: Measuring
Parallelograms (106); Bits
and Pieces II Investigation
3: Multiplying With Fractions
(87); Bits and Pieces III
Investigation 5: More About
Percents (114); West
Virginia Teacher’s
Resource Guide Grade 6
Topic 13: Similar Figures
and Scale Drawings (27-28)
E. Data Analysis and Probability
SE: Prime Time Investigation 1:
Factors and Products (9–
10), Investigation 4:
Factorizations: Searching for
Factor Strings (51–55); Bits
and Pieces I Investigation
1: Fundraising Fractions
(16), Investigation 4:
Working With Percents (60);
Shapes and Designs
Investigation 3: Polygon
Properties and Tiling (54-55,
68); Covering and
Surrounding Investigation
1: Designing Bumper Cars
(5–7), Investigation 2:
Changing Area, Changing
Perimeter (20–21, 24),
Investigation 3: Measuring
Triangles (38–39),
Investigation 4: Measuring
Parallelograms (56–57, 67),
1. provide examples and exercises to collect, organize,
display, read, interpret and analyze real-world data using
appropriate graphs and tables (with and without
technology).
39
Investigation 5: Measuring
Irregular Shapes and Circles
(77); Bits and Pieces III
Investigation 5: More About
Percents (65–66); How
Likely Is it? Investigation 1:
A First Look at Chance (17,
18); Data About Us
Investigation 1: Looking at
Data (7–20), Investigation 2:
Using Graphs to Explore
Data (30–33, 36–38)
TG: Prime Time Investigation 1:
Factors and Products (21–
24), Investigation 4:
Factorizations: Searching for
Factor Strings (87–92); Bits
and Pieces I Investigation
1: Fundraising Fractions
(42), Investigation 4:
Working With Percents
(129–132); Shapes and
Designs Investigation 3:
Polygon Properties and
Tiling (63–68, 81); Covering
and Surrounding
Investigation 1: Designing
Bumper Cars (18–26),
Investigation 2: Changing
Area, Changing Perimeter
(38–42, 47–50),
Investigation 3: Measuring
Triangles (61–68),
Investigation 4: Measuring
Parallelograms (101–104,
107), Investigation 5:
Measuring Irregular Shapes
and Circles (123–128); Bits
and Pieces III Investigation
5: More About Percents
40
(109–112); How Likely Is
it? Investigation 1: A First
Look at Chance (34, 35);
Data About Us
Investigation 1: Looking at
Data (17–40), Investigation
2: Using Graphs to Explore
Data (47–52, 57–62)
SE: Bits and Pieces I
Investigation 3: Moving
From Fractions to Decimals
(39–40), Investigation 4:
Working With Percents (66,
67); Bits and Pieces III
Investigation 3: The Decimal
Divide (40); Data About Us
Investigation 1: Looking at
Data (9–20, 25),
Investigation 2: Using
Graphs to Explore Data (34–
35), Investigation 3: What
Do We Mean by Mean?
(50–55, 57)
TG: Bits and Pieces I
Investigation 3: Moving
From Fractions to Decimals
(85–90), Investigation 4:
Working With Percents (134,
135); Bits and Pieces III
Investigation 3: The Decimal
Divide (71–74); Data About
Us Investigation 1: Looking
at Data (21–40, 43),
Investigation 2: Using
Graphs to Explore Data (53–
56), Investigation 3: What
Do We Mean by Mean?
(74–90, 92 )
2. provide opportunities to identify a real life situation using
statistical measures (mean, median, mode, range,
outliers) overtime, make a hypothesis as to the outcome;
design and implement a method to collect, organize and
analyze data; analyze the results to make a conclusion;
evaluate the validity of the hypothesis based upon
collected data, design a mode of presentation using
words, graphs, models, and/or tables (with and without
technology).
41
SE: How Likely Is it?
Investigation 1: A First Look
at Chance (6–12, 16),
Investigation 2:
Experimental and
Theoretical Probability (22,
24–26), Investigation 3:
Making Decisions With
Probability (39–40, 43),
Investigation 4: Probability,
Genetics, and Games (55–
60)
TG: How Likely Is it?
Investigation 1: A First Look
at Chance (15–32, 34),
Investigation 2:
Experimental and
Theoretical Probability (37–
40, 45–48), Investigation 3:
Making Decisions With
Probability (59–62, 67–70),
Investigation 4: Probability,
Genetics, and Games (77–
86)
SE: West Virginia Additional
Lessons Grade 6 Topic 17:
Determining Combinations
and Permutations (39-40)
TG: West Virginia Teacher’s
Resource Guide Grade 6
Topic 17: Determining
Combinations and
Permutations (35-36)
3. provide opportunities to perform simple probability events
using manipulatives; predict the outcome given events
using experimental and theoretical probability; express
experimental and theoretical probability as a ratio, decimal
or percent.
4. provide opportunities to determine combinations and
permutations of given real-world situations by multiple
strategies, including creating lists.
42