Transcript Medford Refresher

The Common Core State
Standards for Mathematics
Transitioning to the
Common Core
K-8 Content Standards
Grade
Domain
Cluster
Standard
K-8 Grade Level Overview
Critical Areas –
similar to
NCTM’s
Curriculum
Focal Points
Format of K-8 Standards
Grade Level
Domain
Format of K-8 Standards
Cluster
Standard
Cluster
Standard
Domains
Domain
Counting and Cardinality (CC)
Operations and Algebraic Thinking
(OA)
Number and Operations in Base Ten
(NBT)
Measurement and Data (MD)
Geometry (G)
Numbers and Operations- Fractions
(NF)
K
1
2
3
4
5
Domains
Domain
Ratios and Proportional Relationships
(RP)
The Number System (NS)
Expressions and Equations (EE)
Geometry (G)
Statistics and Probability (SP)
Functions (F)
6
7
8
High School
Conceptual Categories
• The big ideas that connect mathematics across
high school – such as Functions or Probability
and Statistics
• A progression of increasing complexity
• Description of mathematical content to be
learned elaborated through domains, clusters,
and standards
High School Conceptual Categories
•
•
•
•
•
•
Number and Quantity
Algebra
Functions
Geometry
Statistics and Probability
Modeling
Pathways
• Four model pathways:
– Traditional Pathway (Algebra 1, Geometry,
Algebra 2)
– Integrated Pathway
– Compacted Traditional Pathway*
– Compacted Integrated Pathway*
*7th, 8th, and Algebra 1 standards covered in 2 years
See CCSSM APPENDIX A
for course descriptions for both pathways.
8 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.
SMARTER Balanced Assessment
Consortium System Highlights
Assessment Design
The Consortium will provide the following by
the 2014-15 school year:
3. Formative tools and resources
4. Responsible flexibility
5. Distributed summative assessment
a. Content clusters throughout a course
b. Most appropriate time for each student
c. Scores rolled up
Smarter Balanced Assessment Consortium
Link to Practice Standards
Four Claims Used in Draft 2 Test Specifications
Claim 1 ≈ 40% of assessment
Claim 2 ≈ 20% of assessment
Claim 3 ≈ 20% of assessment
Claim 4 ≈ 20% of assessment
SHIFT #1: Focus
Similar to the Oregon standards in Mathematics, the
intent of the CCSSM is to narrowly and deeply focus
the time and energy spent in the math classroom.
The CCSSM emphasizes concepts prioritized in the
standards so that students reach strong foundational
knowledge and deep conceptual understanding and
are able to transfer mathematical skills and
understanding across concepts and grades.
The Three-Legged Stool
In order to focus on
content, you must teach to
address all three legs of
mathematical learning:
• Conceptual
Understanding
• Computational Fluency
• Problem-Solving
Draft Emphases (Sample – Grade 6)
Ratios and Proportional Relationships
[m] Understand ratio concepts and use ratio reasoning to solve problems.
The Number System
[m] Apply and extend previous understandings of multiplication and division to divide
fractions by fractions.
[a] Compute fluently with multi-digit numbers and find common factors and multiples.
[m] Apply and extend previous understandings of numbers to the system of rational
numbers.
Expressions and Equations
[m] Apply and extend previous understandings of arithmetic to algebraic expressions.
[m] Reason about and solve one-variable equations and inequalities.
[m] Represent and analyze quantitative relationships between dependent and independent
variables
Geometry
[s] Solve real-world and mathematical problems involving area, surface area, and volume.
Statistics and Probability
[a] Develop understanding of statistical variability.
[a] Summarize and describe distributions.
Activity: Focus
(find a partner or small group at your grade level)
Grades K-2
• Read through the
Critical Areas page of
your standards
• Discuss with a partner
how you could better
address all three legs of
the “mathematics”
stool in these areas
Grades 3-HS
• Pick up the appropriate
Emphases page from
the front
• Look at the “m” clusters
and discuss how you
could better address all
three legs of the
“mathematics” stool in
these areas
SHIFT #2: Coherence
Deep conceptual understanding of core
content at each grade is critical for
student success in subsequent years.
Each standard is not a new event, but an
extension of previous learning. For
example, fractions and multiplication
build across grade levels and students
can scaffold new understanding onto
foundations built in previous years.
Activity: Coherence
(with same partner or small group at your grade level)
Grades K-2
• Look at the standards not
in your critical areas (may
fall in the same domain
but be listed at the end)
• How are these connecting
to your grade level while
introducing or reinforcing
other grade level skills?
Grades 3-8
• Look at the “s” and “a”
clusters. How are these
connecting to your
grade level while
introducing or
reinforcing other grade
level skills?
Activity: Coherence (Cont)
(with same partner or small group at your grade level)
High School
• Only your major emphases are listed on the Emphases
handout.
• Coherence may come from connecting and reinforcing
previous grade level standards.
• How do the additional and supporting (non-major)
standards fit into your program(s)?
Shift #4: Modeling
Modeling links classroom mathematics and statistics to
everyday life, work, and decision-making
– Choose and use appropriate mathematics to analyze
situations
– Better understanding real-world scenarios involving math
Teachers at all grade levels should identify
opportunities for students to apply math concepts
in “real world” situations.
Activity: Modeling
1. Locate your goldenrod stations activity template.
2. Visit between 4-6 stations.
 Pink Cards = Elementary Content
 Blue Cards = Middle/High School Content
3. While visiting stations, have others sign off on the
correctness of your answer. Nobody can sign your
paper more than twice.
4. When finished, return to your seat and answer the
two questions at the bottom of the page.
Performance Task
Choose a new partner or small group:
Elementary or Secondary
1. Pick up the appropriate performance task
up front.
Options: Elementary (4th Grade) or High School
2. Understand purpose and placement of
task in classroom instruction and
assessment.
3. Read/Attempt the task.
4. Discuss implications for classroom
instruction.
Contact Information
Shannon McCaw, SMc Curriculum
www.SMcCurriculum.com
[email protected]
503-550-4298