Kitty Rutherford, Elementary Mathematics Consultant Robin Barbour, Secondary Mathematics Consultant Not Just a New Name CCSA Conference April, 2011

YearStandards To Be TaughtStandards To Be Assessed 2010 – NCSCOS 2011 – NCSCOS 2012 – 2013CCSS 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 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 Standards for Mathematical Practices

Format of the Common Core State Standards

Critical Areas Critical Area Focal Points

2/10/2014 page 10 Mathematical Practices Grade Level Overview

K – 8 Domains 2/10/2014 page 11 DomainsK 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 Level DomainDomain Standards

High School Themes Number and Quantity Algebra Functions Modeling Geometry Statistics and Probability

Overview of Themes

Mathematical Practices Overview of Themes

Standards DomainDomain ClusterCluster Conceptual Categories 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 2/10/2014 page 23

2/10/2014 page 24 Traditional Pathway Overview

Course Critical Areas 2/10/2014 page 25

2/10/2014 page 26 Unit Planning

2/10/2014 page 27 Integrated Pathway Overview

High School Courses in Middle School

Accelerated Traditional Pathway 2/10/2014 page 29

Accelerated Integrated Pathway 2/10/2014 page 30

High School Courses in Middle School Getting Students Ready GradeOption 1Option 2Option % 6 th grade content 100% 6th grade content; 50% 7th grade content 7 100% 7 th grade content; 50% 8 th grade content 50% 7th grade content; 100% 8th grade content 8 50% 8 th grade content; 100% Algebra I 50% 8 th grade content; 100% Integrated Mathematics Algebra I or CC Integrated Mathematics

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 Standards for Mathematical Practices

Jigsaw

Now Lets 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.

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 = /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 /standards/support-tools/ Crosswalks Unpacking

YearStandards To Be TaughtStandards To Be Assessed 2010 – NCSCOS 2011 – NCSCOS 2012 – 2013CCSS Common Core State Standards Adopted June, 2010

QUESTIONS COMMENTS

Mathematics Section Contact Information 49 Kitty Rutherford Elementary Mathematics Consultant Robin Barbour Middle Grades Mathematics Consultant Carmella Fair High School Mathematics Consultant Johannah Maynor High School Mathematics Consultant Barbara Bissell K-12 Mathematics Section Chief Susan Hart Program Assistant