Not Just a New Name
CCSA Conference April, 2011
Kitty Rutherford, Elementary Mathematics Consultant
Robin Barbour, Secondary Mathematics Consultant
www.corestandards.org
Timeline
Common Core Mathematics
Implementation
Common Core State Standards Adopted June, 2010
Year
Standards To Be Taught Standards To Be Assessed
2010 – 2011
2003 NCSCOS
2003 NCSCOS
2011 – 2012
2003 NCSCOS
2003 NCSCOS
2012 – 2013
CCSS
CCSS
Common Core Attributes
• Focus and coherence
–
–
Focus on key topics at each grade level
Coherent progression across grade level
• Balance of concepts and skills
–
Content standards require both conceptual understanding and
procedural fluency
• Mathematical practices
–
Fosters reasoning and sense-making in mathematics
• College and career readiness
–
Level is ambitious but achievable
Standards for 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
Format of the
Common Core
State Standards
Critical Areas
Focal Points
Critical Area
Grade
Level
Overview
Mathematical
Practices
4/13/2015 • page 10
K – 8 Domains
Domains
K
1
2
3
4
5
6
7
8
Counting and Cardinality
Operations and Algebraic Thinking
Number and Operations in Base Ten
Measurement and Data
Geometry
Number and Operations - Fractions
Ratios and Proportional Relationships
The Number System
Expressions and Equations
Statistics and Probability
Functions
4/13/2015 • page 11
Reading the Grade Level Standards
Domain
Standards
Grade Level
High School Themes
•
•
•
•
•
•
Number and Quantity
Algebra
Functions
Modeling
Geometry
Statistics and Probability
Overview
of
Themes
Overview
of
Themes
Mathematical
Practices
Domain
Standards
Conceptual
Categories
Cluster
Standards
High School Standards Notation
Perform operations on matrices and use matrices in applications.
6. (+) Use matrices to represent and manipulate data, e.g., to represent
payoffs of incidence relationship in a network.
11. Explain why the x-coordinates of the points where the graphs of the
equations y = f(x) and y =g(x intersect are the solutions of the equations f(x)
= g(x); find the solutions approximately, e.g., using technology to graph the
functions, make tables of values, or find successive approximations. Include
cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value,
exponential, and logarithmic functions.★
Common Core Resources
• Glossary
• Operations and Properties
Information Tables
Table 1. Common addition and subtraction situations
Table 3. The properties of operations
Other Common Core Resources
• Appendix A
- High School Pathways
- Compacted Middle School Courses
Pathways
4/13/2015 • page 23
Traditional
Pathway
Overview
4/13/2015 • page 24
Course Critical Areas
4/13/2015 • page 25
Unit Planning
4/13/2015 • page 26
Integrated
Pathway
Overview
4/13/2015 • page 27
High School Courses in Middle School
Accelerated Traditional Pathway
4/13/2015 • page 29
Accelerated Integrated Pathway
4/13/2015 • page 30
High School Courses in Middle School
Getting Students Ready
Grade
Option 1
Option 2
100% 6th grade
content
100% 6th grade
content
100% 6th grade
content; 50% 7th
grade content
7
100% 7th grade
content; 50% 8th
grade content
100% 7th grade
content; 50% 8th
grade content
50% 7th grade
content; 100% 8th
grade content
8
50% 8th grade
content; 100%
Algebra I
50% 8th grade
content; 100%
Integrated
Mathematics
Algebra I or CC
Integrated
Mathematics
6
Option 3
Standards for 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
Jigsaw
Now Let’s Do Some Math!
Task 1: Fractions of a Square
Instructions
Discuss the following at your table
– What thinking and learning occurred as
you completed the task?
– What mathematical practices were used?
– What are the instructional implications?
Common Core State Standards
Grade 4
Number and Operations – Fractions
Extend understanding of fraction equivalence and ordering.
1.Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by
using visual fraction models, with attention to how the number and
size of the parts differ even though the two fractions themselves are
the same size. Use this principle to recognize and generate
equivalent fractions.
2.Compare two fractions with different numerators and different
denominators, e.g., by creating common denominators or
numerators, or by comparing to a benchmark fraction such as 1/2.
Recognize that comparisons are valid only when the two fractions
refer to the same whole. Record the results of comparisons with
symbols >, =, or <, and justify the conclusions, e.g., by using a visual
fraction model.
Common Core State Standards
Grade 4
Number and Operations – Fractions
Build fractions from unit fractions by applying and extending previous
understandings of operations on whole numbers.
3. Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
a. Understand addition and subtraction of fractions as joining and
separating parts referring to the same whole.
b. Decompose a fraction into a sum of fractions with the same denominator
in more than one way, recording each decomposition by an equation.
Justify decompositions, e.g., by using a visual fraction model.
Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 =
8/8 + 8/8 + 1/8.
“Beyond One Right Answer”
Marian Small
Educational Leadership, September 2010
Positive Changes
• Increased use of manipulatives and
technology
• Increased use of personal strategies
• Increased classroom discussion
“Beyond One Right Answer”
Marian Small
Educational Leadership, September 2010
Two Beliefs That Need to Change
• All students in a mathematics classroom
work on the same problem at the same
time
• Each math question should have a single
answer
Open Questions
Broad enough to meet the needs of a wide
range of students while still engaging
each one in meaningful mathematics.
Example 1:
If someone asked you to name two numbers to
multiply, which numbers would you choose and why?
Strategies to Create Open Questions
1. Start with the answer.
1. Ask for similarities and differences.
1. Allow choice in the data provided.
1. Ask students to create a sentence.
Creating Parallel Tasks
1. Let students choose between two
problems.
1. Pose common questions for all students
to answer
Your Turn…
5
10
What is the area of this rectangle?
What is the perimeter of this
rectangle?
Possible Open Question
The area of the rectangle is 50 square
inches. What might be its length and
width?
Common Core Math Resources
http://www.ncpublicschools.org/acre
/standards/support-tools/
• Crosswalks
• Unpacking
Timeline
Common Core Mathematics
Implementation
Common Core State Standards Adopted June, 2010
Year
Standards To Be Taught Standards To Be Assessed
2010 – 2011
2003 NCSCOS
2003 NCSCOS
2011 – 2012
2003 NCSCOS
2003 NCSCOS
2012 – 2013
CCSS
CCSS
QUESTIONS
COMMENTS
Mathematics Section Contact Information
Kitty Rutherford
Elementary Mathematics Consultant
919-807-3934
krutherford@dpi.state.nc.us
Robin Barbour
Middle Grades Mathematics
Consultant
919-807-3841
rbarbour@dpi.state.nc.us
Carmella Fair
High School Mathematics Consultant
919-807-3840
cfair@dpi.state.nc.us
Johannah Maynor
High School Mathematics Consultant
919-807-3842
jmaynor@dpi.state.nc.us
Barbara Bissell
K-12 Mathematics Section Chief
919-807-3838
bbissell@dpi.state.nc.us
Susan Hart
Program Assistant
919-807-3846
shart@dpi.state.nc.us
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