Common Core State Standards Regional Institutes Presented by K-12 Mathematics Section NC Department of Public Instruction

Agenda Overview of CCSS Mathematical Standards and Practices Dive into the Mathematical Practices via mathematical tasks Lunch Grade level sharing District planning Where do we go from here?

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

Instructional Support Tools Unpacked Content A response, for each standard, to the question “What does this standard mean?” The unpacked content is text that describes carefully and specifically what the standards mean a child will know, understand and be able to do and explains the different knowledge or skills that constitute that standard.

Instructional Support Tools Unpacked Content Unpacked Content may break the standards into sub-standards, point out key concepts implied in the standard, show example student performances or include any other text vital to understanding the important aspects of the standard.

Common Core Standard and Cluster Multiply and divide within OA.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. Unpacking What will a child know and be able to do? 3.OA.7 uses the word fluently, which means accuracy (correct answer), efficiency (within 3-4 seconds), and flexibility (using strategies such as the distributive property). “Know from memory” should not focus only on timed tests and repetitive practice, but ample experiences working with manipulatives, pictures, arrays, word problems, and numbers to internalize the basic facts (up to 9 x 9).

Outcomes for Today To become familiar with the CCSS Mathematical Practices To begin development of an implementation plan to apply CCSS Mathematical Practices

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

Grade or course introductions give 2- 4 focal points K-8 presented by grade level Organized into domains that progress over several grades High school standards presented by conceptual theme (Number & Quantity, Algebra, Functions, Modeling, Geometry, Statistics & Probability) Standards for Mathematical Content

Format of the Common Core State Standards

Grade Level Focus Critical Area Focal Points

Mathematical Practices

Reading the Grade Level Standards

Grade Level DomainDomain Standards

Other Common Core Resources Glossary

Common Core Glossary Table 1. Common addition and subtraction situations

Other Common Core Resources Operations and Properties Information Tables

Common Core Glossary Table 3. The properties of operations

Other Common Core Resources Appendix A High School Pathways Compacted Middle School Courses

Common Core State Standards Phil Daro says CCSS is not a compromise or consensus is a next step

TODAY’S TASK To examine the practices of Common Core, not the content of the Common Core

Old Boxes People are the next step If people just swap out the old standards and put the new CCSS in the old boxes –Into old systems and procedures –Into the old relationships –Into old instructional materials formats –Into old assessment tools, Then nothing will change, and perhaps nothing will

CCSS is a result of extensive research and reflection Asking teachers to teach too much, hence the mile wide and inch deep concept

Hong Kong / US Data Hong Kong had the highest scores in the most recent TIMMS. Hong Kong students were taught 45% of objectives tested. Hong Kong students outperformed US students on US content that they were not taught. US students ranked near the bottom. US students ‘covered’ 80% of TIMMS content. US students were outperformed by students not taught the same objectives.

Lessons Learned Mile wide and inch deep does not work. The task ahead is not so much about how many specific topics are taught; rather, it is more about ways of thinking. To change students’ ways of thinking, we must change how we teach.

Jigsaw

Question: So how do we help kids develop these behaviors? As Cathy Seeley said: In your math class, who is doing the talking? Who is doing the math?

Now Let’s Do Some Math!

Instructional Task I What rectangles can be made with a perimeter of 30 units? Which rectangle gives you the greatest area? How do you know? What do you notice about the relationship between area and perimeter?

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?

Compared to… What is the area of this rectangle? What is the perimeter of this rectangle?

Common Core State Standards Third GradeMeasurement and Data Geometric measurement: understand concepts of area and relate area to multiplication and to addition. 5. Recognize area as an attribute of plane figures and understand concepts of area measurement. a.A square with side length 1 unit, called “a unit square,” is said to have “one square unit” of area, and can be used to measure area. b.A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units. 6. Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).

7. Relate area to the operations of multiplication and addition. a.Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths. b.Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning. c.Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a × b and a × c. Use area models to represent the distributive property in mathematical reasoning. d.Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems.

BREAK

Types of Math Problems Presented

How Teachers Implemented Making Connections Math Problems

Lesson Comparison Japan and United States The emphasis on skill acquisition is evident in the steps most common in U.S. classrooms The emphasis on understanding is evident in the steps of a typical Japanese lesson Teacher instructs students in concept or skill Teacher solves example problems with class Students practice on their own while teacher assists individual students Teacher poses a thought provoking problem Students and teachers explore the problem Various students present ideas or solutions to the class Teacher summarizes the class solutions Students solve similar problems 39

Instructional Task The Border Problem Sue wanted to tile a 10 x 10 patio. She wanted darker tiles on the border. How many tiles will she need for the border? Show the arithmetic you used to get your answer.

How many tiles will she need for the border? Show the arithmetic you used to get your answer.

Instructions Part 2 Write an algebraic expression to represent each method for finding the number of tiles around the boarder. Then write a rule or function for each method.

Sam’s Method Sam said = 36. Sam’s rule is: edge + edge + edge – 2 + edge – 2 = border 2e + 2(e - 2) = b

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?

Compared To… Simplify the following expressions: 1.4(x – 3) 2.2x + 2x + 3(x – 5) Etc…

Something to Think About The value of the common core is only as good as the implementation of the mathematical practices. What if we didn’t have a requirement for math – how would we lure students in? -- Jere Confrey

QUESTIONS COMMENTS

Mathematics Section Contact Information 48 Kitty Rutherford Elementary Mathematics Consultant Robin Barbour Middle Grades Mathematics Consultant Mary Russell Middle Grades Mathematics Consultant Carmella Fair Secondary Mathematics Consultant Johannah Maynor Secondary Mathematics Consultant Barbara Bissell K-12 Mathematics Section Chief Susan Hart Program Assistant

Lunch

Compare current instructional practice to the vision of the mathematical practices in the Common Core State Standards (CCSS) of mathematics.

Grade Level Sharing 1.What mathematical practices are teachers already doing well, what practices do you see as challenges, and how do we address those challenges - For students, - For teachers, - For administrators? 2. Where are our teachers now in their instructional practices?

District Planning We have a year and a half before the Common Core is fully implemented and assessed. As you make long range plans for district implementation of the mathematical practices; - What would you consider essential, - Where will you start, - Who will be on your planning team, - What initiatives/structures does your district have in place to support the teaching and learning, and for professional development?

Quotes to think about! Covering does not translate to achievement The answer is part of the process not the product. Once you show them how, you cannot find out how they are thinking. When a child makes a mistake, they are showing a way of thinking that needs to be addressed to the whole class.