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Kitty Rutherford, Elementary Mathematics Consultant
Robin Barbour, Secondary Mathematics Consultant
Not Just a New Name
CCSA Conference April, 2011
Year Standards To Be TaughtStandards To Be
Assessed
2010 – 2011 2003 NCSCOS 2003 NCSCOS
2011 – 2012 2003 NCSCOS 2003 NCSCOS
2012 – 2013 CCSS CCSS
Common Core State Standards Adopted June, 2010
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
1. Make sense of problems and persevere in solving them2. Reason abstractly and quantitatively3. Construct viable arguments and critique the reasoning
of others4. Model with mathematics5. Use appropriate tools strategically6. Attend to precision7. Look for and make use of structure8. Look for and express regularity in repeated reasoning
Standards for Mathematical Practices
Format of the
Common Core
State Standards
Critical Areas
Critical AreaCritical Area
Focal PointsFocal Points
04/10/23 • page 10
Mathematical Mathematical PracticesPractices
Grade Level
Overview
K – 8 Domains
04/10/23 • page 11
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
Reading the Grade Level Standards
Grade Grade LevelLevel
DomainDomain Standards
High School Themes
• Number and Quantity
• Algebra
• Functions
• Modeling
• Geometry
• Statistics and Probability
Overviewof
Themes
Mathematical Mathematical PracticesPractices
Overviewof
Themes
StandardsDomainDomain
ClusterCluster
ConceptuaConceptual l
CategoriesCategories
StandardsStandards
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
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04/10/23 • page 24
Traditional PathwayOverview
Course Critical Areas
04/10/23 • page 25
04/10/23 • page 26
Unit Planning
04/10/23 • page 27
Integrated PathwayOverview
High School Courses in Middle School
Accelerated Traditional Pathway
04/10/23 • page 29
Accelerated Integrated Pathway
04/10/23 • page 30
High School Courses in Middle SchoolGetting Students Ready
Grade Option 1 Option 2 Option 3
6
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
1. Make sense of problems and persevere in solving them2. Reason abstractly and quantitatively3. Construct viable arguments and critique the reasoning
of others4. Model with mathematics5. Use appropriate tools strategically6. Attend to precision7. Look for and make use of structure8. Look for and express regularity in repeated reasoning
Standards for Mathematical Practices
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 StandardsGrade 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.
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.
Common Core State Standards
“Beyond One Right Answer”
Positive Changes
• Increased use of manipulatives and technology
• Increased use of personal strategies
• Increased classroom discussion
Marian Small Educational Leadership, September 2010
“Beyond One Right Answer”
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
Marian Small Educational Leadership, September 2010
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
Year Standards To Be TaughtStandards To Be
Assessed
2010 – 2011 2003 NCSCOS 2003 NCSCOS
2011 – 2012 2003 NCSCOS 2003 NCSCOS
2012 – 2013 CCSS CCSS
Common Core State Standards Adopted June, 2010
QUESTIONS
COMMENTS
Mathematics Section Contact Information
49
Kitty RutherfordElementary Mathematics [email protected]
Robin Barbour Middle Grades Mathematics Consultant 919-807-3841 [email protected]
Carmella FairHigh School Mathematics [email protected]
Johannah MaynorHigh School Mathematics [email protected]
Barbara BissellK-12 Mathematics Section [email protected]
Susan HartProgram [email protected]
