Transcript Day 5 Math PLC final

Mapping to the Core
Professional Learning
Community
Day 5 Math
We do not want
anyone to be a
casualty of the
standards.
1 CCSS, 2010, p. 5
2 PARCC – Draft Content Framework - 2011
Math PLC Norms
Practice the “P” word (Perseverance)
Think, Talk, and Write about mathematics
Manage your electronic devices respectfully
Track your progress toward learning targets
Big/Ideas for this course
Day 1-Laying the Foundation- Phase 1
Day 2-Consensus Mapping using Comparatives-Phase 2
Day 3- Draft Unit/Lesson Plan Development and align
assessments- Phase 3
Day 4-Training on Mapping Software and entering
units/plans in the system.
Day 5-Read-throughs for SMP’s, Critical Areas of Focus
and upgrading with web 2.0 tools-Phase 4
Day 5
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Phase 4 of Curriculum Mapping
What are 21st Century Skills?
Investigate web 2.0 tools to use with K-2 for Math
Lunch11:30-12:30
What about Assessments?
Team time to work further on plans
Track your progress toward learning goals for this
training
• Evaluation
Check for understanding
Back to Back Partner 3 min
What are the 8 Standards of Mathematical Practices?
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Write them on an index card
When cued, get with a back to back partner, turn and share.
Add to your card
When cued, get with another back to back partner, turn and share.
Add to your card
CCSS Mathematical Practices
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 tools strategically
6. Attend to precision
7. Look for and make use of structure
8. Look for and express regularity in repeated reasoning
Change of Emphasis K- Grade 5
K-2
• Greater development of how numbers work
• Data analysis is just a tool for working with
numbers and shapes
Grades 3-5
• Fractions then decimals
• Multiplication with inverse division
• Operation strategies and relationships
developed BEFORE algorithm procedures
What does literacy look like in the
mathematics classroom?
• Learning to read mathematical text
• Communicating using correct mathematical terminology
• Reading, discussing and applying the mathematics
found in literature
• Researching mathematics topics or related problems
• Reading appropriate text providing explanations for
mathematical concepts, reasoning or procedures
• Applying readings as citing for mathematical reasoning
• Listening and critiquing peer explanations
• Justifying orally and in writing mathematical reasoning
• Representing and interpreting data
CCSS Domain Progression
K
1
2
3
4
5
6
7
8
HS
Counting &
Cardinality
Number and Operations in Base Ten
Number and Operations –
Fractions
Ratios and Proportional
Relationships
The Number System
Expressions and Equations
Number &
Quantity
Algebra
Operations and Algebraic Thinking
Functions
Geometry
Measurement and Data
Functions
Geometry
Statistics and Probability
Statistics &
Probability
Standards Progression:
Number and Operations in Base Ten
Use Place Value Understanding
Grade 1
Grade 2
Grade 3
Use place value understanding
and properties of operations to
add and subtract.
4. Add within 100, including adding a
two-digit number and a one-digit
number, and adding a two-digit
number and a multiple of 10, using
concrete models or drawings and
strategies based on place value,
properties of operations, and/or the
relationship between addition and
subtraction; relate the strategy to a
written method and explain the
reasoning used.
Understand that in adding two-digit
numbers, one adds tens and tens,
ones and ones; and sometimes it is
necessary to compose a ten.
5. Given a two-digit number, mentally
find 10 more or 10 less than the
number, without having to count;
explain the reasoning used.
6. Subtract multiples of 10 in the
range 10-90 from multiples of 10 in
the range 10-90 (positive or zero
differences), using concrete models
or drawings and strategies based on
place value, properties of operations,
Use place value understanding
and properties of operations to
add and subtract.
5. Fluently add and subtract within
100 using strategies based on place
value, properties of operations,
and/or the relationship between
addition and subtraction.
6. Add up to four two-digit numbers
using strategies based on place
value and properties of operations.
7. Add and subtract within 1000,
using concrete models or drawings
and strategies based on place value,
properties of operations, and/or the
relationship between addition and
subtraction; relate the strategy to a
written method. Understand that in
adding or subtracting three digit
numbers, one adds or subtracts
hundreds and hundreds, tens and
tens, ones and ones; and sometimes
it is necessary to compose or
decompose tens or hundreds.
8. Mentally add 10 or 100 to a given
number 100–900, and mentally
subtract 10 or 100 from a given
number 100–900.
Use place value understanding
and properties of operations to
perform multi-digit arithmetic.
1. Use place value understanding to
round whole numbers to the nearest
10 or 100.
2. Fluently add and subtract within
1000 using strategies and algorithms
based on place value, properties of
operations, and/or the relationship
between addition and subtraction.
3. Multiply one-digit whole numbers
by multiples of 10 in the range 10–90
(e.g., 9 × 80, 5 × 60) using strategies
based on place value and properties
of operations.
Grade Level Comparative Analysis
Content that is new to Grade 8
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The Number System Know that
there are numbers that are not
rational, and approximate them by
rational numbers. (8.NS.1-2)
Functions Define, evaluate, and
compare functions. (8.F.1-3)
Functions Use functions to model
relationships between quantities.
(8.F.4-5)
Geometry Understand congruence
and similarity using physical
models, transparencies, or
geometry software.[initial
introduction] (8.G.1-2)
Geometry Understand and apply
the Pythagorean Theorem. [initial
introduction] (8.G.6-8)
Statistics and Probability
Investigate patterns of association
in bivariate data. (8.SP.4)
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Content that is still included at Grade 8, but
may be modified or at a greater depth
Expressions and Equations Work with
radicals and integer exponents.
(8.EE.1-4)
Expressions and Equations Understand
the connections between proportional
relationships, lines, and linear equations.
[derive y=mx] (8.EE.5-6)
Expressions and Equations Analyze and
solve linear equations and pairs of
simultaneous linear equations.
(8.EE.7-8)
Geometry Understand congruence and
similarity using physical models,
transparencies, or geometry software.
(8.G.3-5)
Geometry Solve real-world and
mathematical problems involving volume
of cylinders, cones, and spheres. (8.G.9)
Statistics and Probability Draw informal
comparative inferences about two
populations. (7.SP.3-4)
Statistics and Probability Investigate
patterns of association in bivariate data.
(8.SP.1-3)
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Content that is no longer a focus at
Grade 8
Number, Number Sense and
Operations Ratio, proportion percent
problems (See Grade 7.RP)
Measurement Order and conversion
of units of measure (See Grade 6.G)
Measurement Rates (See Grade
7.RP)
Geometry Geometric figures on
coordinate plane (See Grades 6-7.G)
Geometry Nets (See 6.G.4)
Patterns, Functions and Algebra
Algebraic expressions
(See Grades 6-7.EE)
Patterns, Functions and Algebra
Grade 8 learning is limited to linear
equations
Patterns, Functions and Algebra
Quadratic equations (See HS)
Data Analysis Graphical
representation analysis
(See Grade 6.SP)
Data Analysis Measures of center
and spread; sampling
(See Grade 7.SP)
Probability (See Grade 7.SP)
MP + CAF + Standards = Instruction
In order to design instruction that meets the
rigor and expectations of the CCSSM,
understanding the Mathematical Practices
and Critical Areas of Focus are essential.
Activity 1:
K-2 Critical Areas of Focus
• Read your grade level’s
Critical Areas of Focus
–What are the concepts?
–What are the skills and
procedures?
–What relationships are
students to make?
Concepts, Skills and Procedures
Concepts
• Big ideas
• Understandings or meanings
• Strategies
• Relationships
Understanding concepts underlies the development and
usage of skills and procedures and leads to connections
and transfer.
Skills and Procedures
• Rules
• Routines
• Algorithms
Skills and procedures evolve from the understanding and
usage of concepts.
Concepts, Skills and Procedures
Grade 4 Number and Operations in Base Ten
Generalize place value understanding for multi-digit whole
numbers.
• Recognize that in a multi-digit whole number, a digit
in one place represents ten times what it represents
in the place to its right. For example, recognize that
700  70 = 10 by applying concepts of place value
and division.
• Read and write multi-digit whole numbers using
base-ten numerals, number names, and expanded
form. Compare two multi-digit numbers based on
meanings of the digits in each place, using >, =,
and < symbols to record the results of comparisons.
• Use place value understanding to round multi-digit
whole numbers to any place.
What Makes a Problem Rich?
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Significant mathematics
Mathematical Practices
Multiple layers of complexity
Multiple entry points
Multiple solutions and/or strategies
Leads to discussion or other questions
Students are the workers and the decision
makers
How will you embed Web 2.0 tools
in your Math Classroom?
1. Investigate resources listed on
wikispace 20 minutes
2. Get into Grade Level Groups
3. Frayer Model Define Web. 2.0
in Math Classroom at your
grade level
45 min
Break- 10 minutes
Wikispace…
Team Time
Use this time to continue with your Unit Plans, Daily Plans
How can you embed Web 2.0 tools and rich problems into your daily
plans?
Lunch-on your own
1 HOUR
Team Time
Use this time to continue with your Unit Plans, Daily Plans
How can you embed Web 2.0 tools and rich problems into your daily
plans?
Shift HAPPENS…
-NCTM
From
Toward
Assessing students knowledge of specific
facts and isolated skills
Assessing students full mathematical power
Developing assessments by oneself
Developing a shared vision of what to assess
Treating assessments as separate from
curriculum and instruction
Aligning assessments with curriculum and
instruction
Viewing students as objects of assessments
Viewing students as active participants in the
assessment process
Using assessments to filter students out of
select opportunities to learn math
Using assessments to ensure that all students
have the opportunity to achieve their potential
Regarding assessments as sporadic and
conclusive
Regarding assessment as continual and
recursive
Break- 10 minutes
How to teach Math as a Social Activity
How can you make this work in your classroom?
Rich Task Sources
Ohio Resource Center
• www.OhioRC.org
Inside Mathematics
• http://www.insidemathematics.org
Balanced Assessment (MARS tasks)
• http://balancedassessment.concord.org
NCTM Illuminations
• http://illuminations.nctm.org/
External Resources for CCSSM
• CCSSO
– www.ccsso.org/
• Achieve
– www.achieve.org
• NCTM
– www.Nctm.org
• Center for K-12 Assessment & Performance
Management at ETS
– www.k12center.org
• YouTube Video Vignettes explaining the CCSS
– http://www.Youtube.com/user/TheHuntInstitute#P/a
Learning Targets.. Track your
progress and turn in to me
I Can…
• Access the Common Core Standards, Model Curriculum,
Comparatives and Crosswalks online
• Review the Crosswalks and Comparative documents for Math
Common Core standards to identify the non-negotiables and
targeted levels of instruction
• Collaborate with peers to develop scaffolded curriculum
units/lessons that emphasize coherence, focus, and rigor
Next Steps
What Should Districts Do Now?
• Deepen your understanding of the CCSSM in
Professional Learning Communities through:
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the Standards for Mathematical Practice
the Critical Areas
the Model Curriculum
the Standards Progressions
the Comparative Analysis
• Begin focusing instruction around:
– the Mathematical Practices
– The Critical Areas
• Develop support structures for reaching all students
– Use previous mathematics in service of new ideas
– Provide all students access to the regular curriculum; RtI
Wikispace…
ODE Mathematics Consultants
• Brian Roget
[email protected]
• Ann Carlson
[email protected]
• Yelena Palayeva
[email protected]