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 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
[email protected]
Robin Barbour Middle Grades Mathematics Consultant 919-807-3841
[email protected]
Carmella Fair High School Mathematics Consultant 919-807-3840
[email protected]
Johannah Maynor High School Mathematics Consultant 919-807-3842
[email protected]
Barbara Bissell K-12 Mathematics Section Chief 919-807-3838
[email protected]
Susan Hart Program Assistant 919-807-3846
[email protected]
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