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STRATEGY MEETING

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Math Tools for Unpacking & Addressing the West Virginia Next Generation Math Standards Elementary School Version West Virginia RESAs 3 and 7 Charleston and Morgantown, WV – PowerPoint PPT presentation

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Title: STRATEGY MEETING


1
Math Tools for Unpacking Addressing the West
Virginia
Next Generation Math Standards
Elementary School Version
West Virginia RESAs 3 and 7Charleston and
Morgantown, WV
April, 2013
1
2
Essential Workshop Questions
  1. What is the relationship between the Common Core
    Standards an the Next Generation Math Standards,
    and why were they developed?
  2. How are the Next Generation Math Standards
    organized?
  3. What are the Six Instructional Shifts and the
    Eight Mathematical Practices What are their role
    in the Next Generation Standards?
  4. What processes are useful for unpacking the
    standards?
  5. What are the implications of the Standards on the
    way we approach the teaching and learning of
    mathematics?

2
3
VKR Math Vocabulary Activity
  • Assess your Vocabulary Knowledge Rating (VKR) of
    personal knowledge of these important workshop
    words.
  • Consider each word and check the appropriate
    column. Check 4 column, if you could explain and
    teach others. Check 3 column if you know the
    term well, but would not want to teach others.
    Check 2 column if you have heard of the term.
    Check 1 column if the word is new to you.

CCSS WV Institute 4 3 2 1
VKR
Standards for Mathematical Practices
Content Standards
etc.
4
VKR Math Vocabulary Activity
1 2 3 4
Common Core StandardsNext Generation
StandardsStandardClusterObjectiveTeaching
StrategyStudent Engagement ActivityFive Stages
of TL MathSix Instructional Shifts Eight
Mathematical Practices
5
Whats the connection between the Common Core
Standards and the Next Generation Standards, and
why were these standards developed?
5
6
What are the Common Core Standards?
The Common Core Standards are a product of a U.S.
education initiative that seeks to bring diverse
state curricula into alignment with each other by
following the principles of standards-based
education reform. The initiative is sponsored by
the National Governors Association (NGA) and the
Council of Chief State School Officers (CCSSO).
At this time, 45 U.S. States are committed to
implementing the Common Core Standards.
7
What are the Next Generation Standards?
The Next Generation Standards are West Virginias
education standards. These standards parallel
the Common Core Standards, and contain
modifications that meet the specific needs of
West Virginia. The Next Generation Standards
represent the next logical step in the
progression of the statewide movement called
EducateWV Enhancing Learning. For Now. For the
Future.
8
Why were the new Standards developed?
  • The Next Generation Standards were developed
    to provide a consistent, clear understanding
    of what students are expected to learn, so
    teachers and parents know what they need to
    do to help them. be robust and relevant to
    the real world reflect the knowledge and
    skills that our young people need for success
    in college and careers

9
Why were the new Standards developed?
  • The Next Generation Standards were developed
    to be sure that American students are fully
    prepared for success in the global economy
  • help teachers zero in on the most important
    knowledge and skills
  • establish shared goals among students,
    parents, and teachers

10
Why were the new Standards developed?
  • The Next Generation Standards were developed
    to help states and districts assess the
    effectiveness of schools and classrooms and
    give all students an equal opportunity for
    high achievement
  • help solve the problem of discrepancies
    between States test results and
    International test results
  • replace the discrepant array of curriculums
    that existed across the country

11
How are the Next Generation Standards organized?
11
12
Common Core and Next Generation Organization
Terminology
Common Core Standards (CCS)
Next Generation Standards (NGS)
Domain (CCS only)
Standards (CCS and NGS)
Cluster (CCS and NGS)
Objective (NGS only)
13
Common Core Organization/Terminology
In the Common Core Standards, the terms domain,
standard, and cluster have the following
meanings. domain used for the broad math
strand or category name standard
more specific math category name (next
level beyond domain) cluster group of
specific learning objectives that
connect with the standard
14
Common Core Standards for MathExample of how
they are organized
  • Grade 5 Standard Operations and Algebraic
    Thinking
  • Write and interpret numerical
    expressionsM.5.OA.1 Use parentheses, brackets
    or braces in numerical expressions, and evaluate
    expressions with these symbols.
  • M.5.OA.2 Write simple expressions that record
    calculations with numbers.

Domain
Standard
Cluster
15
Next Generation Organization/Terminology
In the Next Generation Standards, the terms
standard, cluster, and objective have the
following meanings. standard used for the
broad math strand or category name
(replaces the CC word domain) cluster more
specific math category name (next
level beyond standard, replaces the CC
word standard) objectives specific things
that students should learn and be able
to do (listed in each cluster)
16
How are the Next GenerationMath Standards
organized?
  • Grade 5 Standard Operations and Algebraic
    Thinking
  • Write and interpret numerical
    expressionsM.5.OA.1 Use parentheses, brackets
    or braces in numerical expressions, and evaluate
    expressions with these symbols.
  • M.5.OA.2 Write simple expressions that record
    calculations with numbers.

Standard
Cluster
Objectives
17
The Next Generation Math Standards for Grades K-5
  • The next five slides show the standards (broad
    math categories or strands) for grades K-5. Note
    the similarities and differences among the grade
    levels.

18
The Next Generation Math Standards for Grades K-5
  • Kindergarten Standards
  • Counting and CardinalityQuestions and Algebraic
    ThinkingNumbers and Operations in Base
    TenMeasurement and DataGeometry

19
The Next Generation Math Standards for Grades K-5
  • First Grade Standards
  • Operations and Algebraic ThinkingNumbers and
    Operations in Base TenMeasurement and
    DataGeometry

20
The Next Generation Math Standards for Grades K-5
  • Second Grade Standards
  • Operations and Algebraic ThinkingNumbers and
    Operations in Base TenMeasurement and
    DataGeometry

21
The Next Generation Math Standards for Grades K-5
  • Third Grade Standards
  • Operations and Algebraic ThinkingNumbers and
    Operations in Base TenNumbers and Operations
    with FractionsMeasurement and DataGeometry

22
The Next Generation Math Standards for Grades K-5
  • Fourth Grade Standards
  • Operations and Algebraic ThinkingNumbers and
    Operations in Base TenNumbers and Operations
    with FractionsMeasurement and DataGeometry

23
The Next Generation Math Standards for Grades K-5
  • Fifth Grade Standards
  • Operations and Algebraic ThinkingNumbers and
    Operations in Base TenNumbers and Operations
    with FractionsMeasurement and DataGeometry

24
The Next Generation Math Standards for Grades K-5
  • The next five slides show the breakdown of the
    common Operations and Algebraic Thinking
    (Questions and Algebraic Thinking for
    Kindergarten) standard for grades K-5. Each
    slide shows the clusters for the standard, and
    the number of objectives associated with each
    cluster.

25
The Next Generation Math Standards for Grades K-5
  • Take note of the standard, cluster, and number of
    objectives for each cluster. Work with a partner
    from your grade level, and see if you can guess
    what the objectives are for your grade-level
    clusters.

26
How are the Next Generation Math Standards
organized?
  • Kindergarten Standard and Cluster
  • Questions and Algebraic Thinking Understand
    addition as putting together and adding to, and
    understand subtraction as taking apart and taking
    from (5 objectives)

27
How are the Next Generation Math Standards
organized?
  • First Grade Standard and Cluster
  • Operations and Algebraic ThinkingRepresent and
    Solve Problems Involving Addition and
    Subtraction- (2 objectives) Understand and
    Apply Properties of Operations and the
    Relationship between Addition and
    Subtraction- (2 objectives) Add and Subtract
    within 20- (2 objectives) Work with Addition
    and Subtraction Equations- (2 objectives)

28
How are the Next Generation Math Standards
organized?
  • Second Grade Standard and Cluster
  • Operations and Algebraic Thinking Represent and
    Solve Problems Involving Addition and
    Subtraction- (1 objective) Add and Subtract
    within 20- (1 objective) Work with Equal
    Groups of Objects to Gain Foundations for
    Multiplication- (2 objectives)

29
How are the Next Generation Math Standards
organized?
  • Third Grade Standard and Cluster
  • Operations and Algebraic Thinking Represent and
    Solve Problems Involving Multiplication and
    Division- (4 objectives) Understand
    Properties of Multiplication and the Relationship
    between Multiplication and Division- (2
    objectives) Multiply and Divide within 100- (1
    objective) Solve Problems Involving the Four
    Operations and Identify and Explain Patterns
    in Arithmetic- (2 objectives)

30
How are the Next Generation Math Standards
organized?
  • Fourth Grade Standard and Cluster
  • Operations and Algebraic Thinking Use the Four
    Operations with Whole Numbers to Solve Problems-
    (3 objectives) Gain Familiarity with Factors
    and Multiples- (1 objective) Generate and
    Analyze- (1 objective)

31
How are the Next Generation Math Standards
organized?
  • Fifth Grade Standard and Cluster
  • Operations and Algebraic Thinking Write and
    Interpret Numerical Expressions- (2
    objectives) Analyze Patterns and Relationships-
    (1 objective)

32
The Next Generation Math Standards for Grades K-5
  • After guessing what the objectives are for each
    cluster, work in grade-level teams and read the
    objectives for each cluster identified in this
    activity. For each objective, work together to
    create a math problem that captures the essence
    of the objective. The standard, clusters,
    objectives and sample problems will be share with
    the entire group to provide a K-5 vertical view
    of the teaching and learning progressions
    associated with the K-5 math program.

33
Six Instructional Shifts Associated with West
Virginias Next Generation Math Standards
33
34
Six Instructional Shifts in Math
Focus
Coherence
Fluency
Understanding
Applications
Dual Intensity
New Points of Emphasis for Teaching the Next
Generation Standards
35
Instructional Shifts
  • Instructional Shifts within the common core are
    needed for students to attain the standards.

Kelly L. Watts, RESA 3
36
6 Shifts in Mathematics
  • Focus
  • Coherence
  • Fluency
  • Deep Understanding
  • Applications
  • Dual Intensity

Kelly L. Watts, RESA 3
37
Focus
  • In reference to the TIMMS study, there is power
    of the eraser and a gift of time. The Core is
    asking us to prioritize student and teacher time,
    to excise out much of what is currently being
    taught so that we can put an end to the mile
    wide, inch deep phenomenon that is American Math
    education and create opportunities for students
    to dive deeply into the central and critical math
    concepts. We are asking teachers to focus their
    time and energy so that the students are able to
    do the same.

Kelly L. Watts, RESA 3
38
Focus
  • Teachers
  • Make conscious decisions about what to excise
    from the curriculum and what to focus on
  • Pay more attention to high leverage content and
    invest the appropriate time for all students to
    learn before moving onto the next topic
  • Think about how the concepts connect to one
    another
  • Build knowledge, fluency, and understanding of
    why and how we do certain math concepts.
  • Students
  • Spend more time thinking and working on fewer
    concepts
  • Being able to understand concepts as well as
    processes. (algorithms)

Kelly L. Watts, RESA 3
39
Coherence
  • We need to ask ourselves
  • How does the work Im doing affect work at the
    next grade level?
  • Coherence is about the scope and sequence of
    those priority standards across grade bands.
  • How does multiplication get addressed across
    grades 3-5?
  • How do linear equations get handled between 8 and
    9?
  • What must students know when they arrive, what
    will they know when they leave a certain grade
    level?

Kelly L. Watts, RESA 3
40
Coherence
  • Students
  • Build on knowledge from year to year, in a
    coherent learning progression
  • Teachers
  • Connect the threads of math focus areas across
    grade levels
  • Think deeply about what youre focusing on and
    the ways in which those focus areas connect to
    the way it was taught the year before and the
    years after

Kelly L. Watts, RESA 3
41
Fluency
  • Fluency is the quick mathematical content what
    you should quickly know. It should be recalled
    very quickly. It allows students to get to
    application much faster and get to deeper
    understanding. We need to create contests in our
    schools around these fluencies. This can be a
    fun project. Deeper understanding is a result of
    fluency. Students are able to articulate their
    mathematical reasoning, they are able to access
    their answers through a couple of different
    vantage points its not just getting the answer
    but knowing why. Students and teachers need to
    have a very deep understanding of the priority
    math concepts in order to manipulate them,
    articulate them, and come at them from different
    directions.

Kelly L. Watts, RESA 3
42
Fluency
  • Students
  • Spend time practicing, with intensity, skills (in
    high volume)
  • Teacher
  • Push students to know basic skills at a greater
    level of fluency
  • Focus on the listed fluencies by grade level
  • Create high quality worksheets, problem sets, in
    high volume

Kelly L. Watts, RESA 3
43
Deep Understanding
  • The Common Core is built on the assumption that
    only through deep conceptual understanding can
    students build their math skills over time and
    arrive at college and career readiness by the
    time they leave high school. The assumption here
    is that students who have deep conceptual
    understanding can
  • Find answers through a number of different
    routes
  • Articulate their mathematical reasoning
  • Be fluent in the necessary baseline functions in
    math, so that they are able to spend their
    thinking and processing time unpacking
    mathematical facts and make meaning out of them.
  • Rely on their teachers deep conceptual
    understanding and intimacy with the math concepts

Kelly L. Watts, RESA 3
44
Deep Understanding
  • Students
  • Show, through numerous ways, mastery of material
    at a deep level
  • Use mathematical practices to demonstrate
    understanding of different material and concepts
  • Teacher
  • Ask yourself what mastery/proficiency really
    looks like and means
  • Plan for progressions of levels of understanding
  • Spend the time to gain the depth of the
    understanding
  • Become flexible and comfortable in own depth of
    content knowledge

Kelly L. Watts, RESA 3
45
Applications
  • The Common Core demands that all students engage
    in real world application of math concepts.
    Through applications, teachers teach and measure
    students ability to determine which math is
    appropriate and how their reasoning should be
    used to solve complex problems. In college and
    career, students will need to solve math problems
    on a regular basis without being prompted to do
    so.

Kelly L. Watts, RESA 3
46
Applications
  • Students
  • Apply math in other content areas and situations,
    as relevant
  • Choose the right math concept to solve a problem
    when not necessarily prompted to do so
  • Teachers
  • Apply math in areas where its not directly
    required (i.e. science)
  • Provide students with real world experiences and
    opportunities to apply what they have learned

Kelly L. Watts, RESA 3
47
Dual Intensity
  • This is an end to the false dichotomy of the
    math wars. It is really about dual intensity
    the need to be able to practice and do the
    application. Both things are critical.

Kelly L. Watts, RESA 3
48
Dual Intensity
  • Students
  • Practice math skills with a intensity that
    results in fluency
  • Practice math concepts with an intensity that
    forces application in novel situations
  • Teacher
  • Find the dual intensity between understanding and
    practice within different periods or different
    units
  • Be ambitious in demands for fluency and
    practices, as well as the range of application

Kelly L. Watts, RESA 3
49
The Next Generation Math Standards for Grades K-5
  • The next six slides show the six instructional
    shifts and short instructional scenarios that
    each connect with one of the shifts. Read each
    scenario and determine the instructional shift
    that it represents.

50
Six Instructional Shifts in Math
Fluency
Mrs. Johnson, a fifth-grade teacher, delivered
two informational lessons on the concept of
parentheses, brackets, braces, and numeric
expressions. After two days of paper/pencil
practice, she decided to teach her students the
550 Game (demonstrated in the Corwin/Silver
Strong workshop) and to let them compete in
pairs. Her goal was to help her 5th graders to
sharpen their proficiency with numeric
expressions and math symbols, and to mentally
process numbers faster.
51
Six Instructional Shifts in Math
Focus
In planning a unit on Place Value, Mrs. Smith
used the Five Stages planning tool (demonstrated
in the Corwin/Silver Strong workshop) to ensure
that she would design lessons and student
engagement activities that would help her
students to develop a strong knowledge base,
understanding of concepts, proficiency of skills,
and the ability to solve a variety of related
problems.
52
Six Instructional Shifts in Math
Dual Intensity
Principal Joe visited several math classes and
noticed that the lessons all emphasized
procedures, skills, and practice. Joe met with
the teachers and complimented them on their
thorough approach to skill development. Joe also
encouraged them to work together and to devise a
plan to show students how those math skills are
used in the real world. The goal would be to
continue to strengthen students skills, and to
teach students how to use those skills in problem
solving.
53
Six Instructional Shifts in Math
Coherence
Several math teachers and administrators from
participated in a joint exercise where they
investigated several Next Generation math
objectives from grades levels K-5. The
participants developed sample math problems that
aligned with the K-5 objectives and shared their
work with each other, so they could all
understand how the curriculum pieces fit
together.
54
Six Instructional Shifts in Math
Understanding
Prior to learning the rules associated with
operations on fractions and mixed numbers,
students participated in the Fraction Paper
Cutting Activity (demonstrated in the
Corwin/Silver Strong workshop). The
student-centered activity allowed students to cut
paper, form fraction pieces, and use their paper
pieces to model and investigate a variety of
fraction problems.
55
Six Instructional Shifts in Math
Applications
Mr. Williams noticed that his fourth-grade
science curriculum presented a number of
opportunities to integrate math into several
science lessons, and vice versa. Mr. Williams
decided to create a simple correlation of science
concepts with math concepts that featured common
math concepts and skills, so they can be taught
together.
56
The Six Instructional Shifts
  • Can you remember the Six Instructional Shifts?
    The Great Coverup Strategy, shown on the next
    slide, will challenge you to see how many shifts
    you can recall and recite.

57
Six Instructional Shifts
Focus
Coherence
Fluency
Understanding
Application
Dual Intensity
57
58
Standards for the Eight Mathematical Practices
58
59
Making a case . . .
Work individually and investigate the result of
adding two even whole numbers. Is the sum always,
sometimes, or never even? Create a sensible rule
for adding two even whole numbers and the
expected result. Explain why your rule
works. Continue to work individually and
investigate the result of adding two odd whole
numbers. Is the sum always, sometimes, or never
odd? Create a sensible rule for adding two odd
whole numbers and the expected result. Explain
why your rule works.
Share your findings, rules, and explanations with
a learning partner. Will your rules always work?
Be sure to critique your partners argument.
60
Making a case . . .
In the preceding activity, participants had
opportunities to think about math, investigate
math, draw conclusions, communicate their
findings to other participants, and critique each
others thinking. This kind of math engagement
satisfies one of the 8 Mathematical Practices
shown below.
Mathematical Practice 3 Construct viable
arguments and critique the reasoning of others
The Eight Mathematical Practice are shown on the
next slide.
61
The 8 Mathematical Practices
Building insights about meaning, and learning how
to communicate those insights
  • 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. Use appropriate tool strategically.
  • 6. Attend to precision.
  • 7. Look for and make use of structure.
  • 8. Look for and express regularity in repeated
    reasoning.

62
Eight Mathematical Practices Applied to a Real
Standard
Review the list of Eight Mathematical Practices.
How can they be applied to the standard and
objectives below?
  • Grade 5 Standard Operations and Algebraic
    Thinking
  • Cluster Write and interpret numerical
    expressionsM.5.OA.1 Use parentheses, brackets or
    braces in numerical expressions, and evaluate
    expressions with these symbols.
  • M.5.OA.2 Write simple expressions that record
    calculations with numbers.

63
Unpacking the Standards
63
64
Unpacking the Standards
  • Many organization templates and tools exist and
    can be used to unpack math standards. One such
    tool is the Five Stages Unpacking Tool for Math
    Standards. This tool is aligned with the Five
    Stages of Teaching and Learning Mathematics. The
    next three slides provide an explanation of the
    Five Stages of Teaching and Learning Math.

65
Try this . . .
1. Write the numerical expression for the sum of
the interior angles of a polygon with n sides.
(n 2)180
2. Explain why this formula works.
3. Use the formula to calculate the sum of the
interior angles of an octagon.
(8 2)180 6(180) 600 480 1080 degrees
4. Knowing that 3 interior angles of home plate
are right angles, find the measures of the other
two.
66
Try this . . .
4. Knowing that 3 interior angles of home plate
are right angles, find the measures of the other
two.
(n 2)180
(5 2)180
(3)180
540
540 270 270
270 2 135o
67
Try this . . .
1. Write the numerical expression for the sum of
the interior angles of a polygon with n sides.
(n 2)180
Knowledge
2. Explain why this formula works.
Understanding
3. Use the formula to calculate the sum of the
interior angles of an octagon.
Proficiency of Skills
(8 2)180 1080 degrees
4. Knowing that 3 interior angles of home plate
are right angles, find the measures of the other
two.
Applications
Each angle 135 degrees
Retention
5. Now that you know how to solve this kind of
problem, what will help you to remember how to
solve the
problem for future applications?
68
The Five Stages of Teaching and Learning
Mathematics
  • Success or failure associated with solving an
    arbitrary math problem comes down to five
    questions. 1. Did the student know the math
    vocabulary, terms, formulas, and number facts
    associated with the problem?2. Did the student
    understand the math concepts, hidden questions,
    and math connections in the problem?3. Was the
    student fluent with respect to the math
    procedures and skills needed to solve the
    problem?4. Was the student able to apply the
    knowledge, understanding, and skills in relation
    to the real-world context of the problem?5. Was
    the student able to retain or remember important
    math facts, skills, and concepts needed to solve
    the problem?

69
The Five Stages of Teaching and Learning
Mathematics
  • The Five Stages of Teaching and Learning
    Mathematics is a helpful framework for planning,
    teaching, and assessing a math lesson or unit.
  • The Five Stages of Teaching and Learning
    Mathematics can also serve as a model for
    unpacking a math standard.

70
The Five Stages of Teaching and Learning Math
Knowledge
Understanding
Proficiency of Skills
Applications
Retention
Great Considerations for Unpacking a Math Standard
71
The Five Stages of Teaching and Learning
Mathematics
  • The next three slides provide an example of how
    the Five Stages of Teaching and Learning Math can
    be used to unpack a math objective. A sample
    objective is shown below.
  • Grade 4 M.4.NF4 Apply and extend previous
    understandings of multiplication to multiply a
    fraction by a whole number.

72
Unpacking Grade4 M.4.NF4
  • Grade 4 M.4.NF4 Apply and extend previous
    understandings of multiplication to multiply a
    fraction by a whole number.

Knowledge
Teaching Strategies
product- answer to multiplication
problem The fractional equivalent to a whole
number n is n/1. 1 times any number is the
number itself. 0 times any number is zero n x
a/b na/b how to simplify an improper fraction
Mental Math Strings that feature these
facts The Great Cover Up Convergence
Mastery Proceduralizing
Understanding
Teaching Strategies
For any fraction a/b, a is the number of
times that 1/b occurs If n gt1, then n x a/b is
greater than a/b. The concept of n x a/b
expresses the idea of bringing the amount a/b to
the table n times. improper fraction and proper
fraction equivalencies
The hands-on/multiplication component of the
Fraction Paper Cutting Activity
73
Unpacking Grade4 M.4.NF4
  • Grade 4 M.4.NF4 Apply and extend previous
    understandings of multiplication to multiply a
    fraction by a whole number.

Proficiency of Skills
Teaching Strategies
Multiply any whole number n times any of
the common fractions a/b where b 1, 2, 3, 4, 5,
6, 8, 10, and 12. Simplify problems of the
type n x a/b n x a/b m and n x a/b
c/b
Mental Math Strings that feature these
facts The Great Cover Up Algebra War Games
(modified) Timed Challenges (for fractions)
Convergence Mastery
Applications
Teaching Strategies
Work with Tangram pieces Solve problems
involving fractional pieces of Hersheys
chocolate bars Solve two-step word problems
Solve problems involving fractional parts of time
and money
Task Rotation applied to problem solving
Graduated Difficulty Modeling and
Experimentation
74
Unpacking Grade4 M.4.NF4
  • Grade 4 M.4.NF4 Apply and extend previous
    understandings of multiplication to multiply a
    fraction by a whole number.

Retention
Teaching Strategies
General Math Facts Measurement
Equivalencies Properties of Fractions
Patterns
Review math facts using Timed Challenges
Incorporate measurement equivalencies in fraction
problems Create patterns based on whole numbers
x fractions
8 Math Practices that apply
1. Make sense of problems and persevere in
solving them. (All problems and experiences)2.
Reason abstractly and quantitatively. (Fraction
Paper Cutting Activity)3. Construct viable
arguments and critique the reasoning of others
(Is nxa/b always gt a/b?)4. Model with
mathematics. (Fraction Paper Cutting Activity,
Tangrams, Candy bars)5. Use appropriate tool
strategically.6. Attend to precision. (Computing
exact answers, not estimates)7. Look for and make
use of structure.8. Look for and express
regularity in repeated reasoning. (n x a/b always
equals na/b.)
75
The Five Stages of Teaching and Learning
Mathematics
  • The next two slides provide a sample objective
    for grades K-5. Work with a grade level partner.
    Unpack the objective using the Five Stages
    Unpacking Tool. Make connections between the
    Eight Mathematical Practices and the things that
    students will learn and experience as they learn
    the math associated with the objective.

76
Unpacking the Common Core Math Standards
The Five Stages of Teaching and Learning
Mathematics
Grade K Solve addition and subtraction word
problems, by adding and subtracting within 10, by
using objects or drawings Grade 1 Apply
properties of operations as strategies to add and
subtract within 20 Grade 2 Use addition and
subtraction within 100 to solve one and two-step
word problems
Knowledge
Understanding
Proficiency of Skills
Applications
Retention
Work with a partner, choose a standard, and
unpack the standard using the Five Stages tool.
77
Unpacking the Next Generation Math Standards
The Five Stages of Teaching and Learning
Mathematics
Grade 3 Fluently multiply and divide within 100,
using strategies such as the relationship between
multiplication and division Grade 4 Solve
multi-step word problems, posed with whole
numbers, using the four operations Grade 5 Use
parentheses, brackets, or braces in numerical
expressions, and evaluate expressions with these
symbols
Knowledge
Understanding
Proficiency of Skills
Applications
Retention
Work with a partner, choose a standard, and
unpack the standard using the Five Stages tool.
78
Instructional Considerations
The 3- 4- 5- Math Instructional Model
78
79
The 3- 4- 5- Math Instructional Model
RVD
3
Repetition, Variation of Context, Depth of Study
4
The Four Learning Styles and Task Rotation
5
The Five Stages of Teaching and Learning Math
80
Teaching math associated with the Next Generation
Standards Mathematics
  • The next slides provide important information
    about The RVD Instructional Model, The Four
    Learning Styles of students, and The Five
    Stages of Teaching and Learning Math
  • Each of these have important roles in the
    teaching and learning of mathematics.

81
R - V - D
RVD provides teachers with three important ideas
that can be applied to the teaching and learning
process. Repetition reminds us that practice is
an essential tool for developing fluency and
proficiency with math skills and procedures.
Variation reminds us that students need to
experience math in more than one context.
Different instructional and application contexts
give students opportunities to make important
connections and deepen their understanding of
math. Depth reminds us that students need to
learn and experience all aspects of a math
concept and not superficially engage in exercises
that only scratch the surface.
82
Introduction to the Four Learning Styles
Interpersonal Learner
Mastery Learner
Understanding Learner
Self-Expressive Learner
83
Introduction to the Four Learning Styles
Mastery Learners
Want to learn practical information and
procedures
Like math problems that are algorithmic
Approach problem solving in a step by step
manner
Experience difficulty when math becomes abstract
Are not comfortable with non-routine problems
Want a math teacher who models new skills,
allows time for practice, and builds in feedback
and coaching sessions
84
Introduction to the Four Learning Styles
Interpersonal Learners
Want to learn math through dialogue and
collaboration
Like math problems that focus on real world
applications
Approach problem solving as an open discussion
among a community of problem solvers
Experience difficulty when instruction focuses
on independent seatwork
Want a math teacher who pays attention to their
successes and struggles in math
Want a math teacher who pays attention to their
successes and struggles in math
Want a math teacher who pays attention to their
successes and struggles in math
85
Introduction to the Four Learning Styles
Understanding Learners
Want to understand why the math they learn works
Like math problems that ask them to explain or
prove
Approach problem solving by looking for
patterns and identifying hidden questions
Experience difficulty when there is a focus on
the social environment of the classroom
Want a math teacher who challenges them to
think and who lets them explain their thinking
Want a math teacher who pays attention to their
successes and struggles in math
Want a math teacher who pays attention to their
successes and struggles in math
86
Introduction to the Four Learning Styles
Self-Expressive Learners
Want to use their imagination to explore math
Like math problems that are non-routine
Approach problem solving by visualizing the
problem, generating possible solutions and
explaining alternatives
Experience difficulty when instruction focuses
on drill and practice and rote problem solving
Want a math teacher who invites imagination and
creative problem solving into the math classroom
Want a math teacher who pays attention to their
successes and struggles in math
Want a math teacher who pays attention to their
successes and struggles in math
87
The Four Learning Styles
Research shows that student learn in different
ways. The Four Learning Styles provide the basis
for a teaching and learning framework that
addresses the different ways students learn. By
providing rich learning experiences that reflect
the different learning styles, teachers can lead
more students to success in math. The Task
Rotation Teaching Strategy provides four tasks,
one for each type of learner. Students who study
math through the contexts of different learning
styles will increase their levels of success in
math.
88
The Five Stages of Teaching and Learning Math
Knowledge
Understanding
Proficiency of Skills
Applications
Retention
Great Considerations for Planning, Teaching, and
Assessing a Math Lesson
89
The Five Stages of Teaching and Learning
Mathematics
  • Success or failure associated with solving a math
    problem comes down to five questions. 1. Did
    the student know the math terms, formulas, and
    number facts associated with the problem?2. Did
    the student understand the math concepts, hidden
    questions, and math connections in the
    problem?3. Was the student fluent with respect
    to the math procedures and skills needed to solve
    the problem?4. Was the student able to apply
    the knowledge, understanding, and skills in the
    context of the problem?5. Was the student able
    to retain or remember important math facts,
    skills, and concepts needed to solve the problem.

90
Cooperative Planning Activity
  • Work together and talk about how you will use the
    information and strategies, featured in this
    workshop, to improve math instruction and
    achievement in your classroom(s).

91
Workshop Reflections
Specific facts and ideas that I learned today
Things I learned that will really help me in my
classroom
Why the things I learned will help my students to
learn math
Creative modifications and extentions to the
things I learned today
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