California Common Core State Standards

MathematicsRowland Unified School District

Geometry

October 1, 2014Le Anderson & Gus Lopez

Day 1 Agenda

Overview of the CCSS in Mathematics Math Content and Structure Mathematical Practices Instruction Assessment Next Steps

Let’s do Math…….

Mc Donald’s Claim: Wikipedia reports that 8% of all Americans eat at Mc Donald’s. In the US there are approximately 310 million Americans and 12,800 Mc Donald restaurants.

Do you believe the Wikipedia report to be true? Create a mathematical argument to justify your position.

Be prepared to present your argument.

States that Adopted

© Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved

© Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved

Why?To ensure that our students are… meeting college and career expectations

(Text Complexity needs to be increased K-12); provided a vision of what it means to be

an academically literate person in the twenty-first century;

prepared to succeed in our global economy and society; and

provided with rigorous content and applications of higher knowledge through higher order thinking skills.

2011 © CA County Superintendents Educational Services Association

So What is Different?

Focus on College & Career Pathways Emphasis on Mathematical Modeling Standards of Mathematical Practice Multiple Formats for Testing Alignment with current and future

business and professional needs

We are here

Significantly Higher Rigor

97 Algebra 1 ≠ CCSSM Algebra I

97 Geometry ≠ CCSSM Geometry

97 Algebra 2 ≠ CCSSM Algebra II

97 Algebra 1 ≠ CCSSM Algebra I

97 Geometry ≠ CCSSM Geometry

97 Algebra 2 ≠ CCSSM Algebra II

“The CCSS for Mathematics move instruction and assessment beyond

the notion of answer getting driven by procedurally-based questions to one that focuses attention on studentsstudents’’ mathematical sense making and mathematical sense making and understandingunderstanding.”

Understanding Language

“Teacher Development to Support English Language Learners in the Context Of Common Core State Standards”

Stanford University, 2012

What’s new in curriculum?

Algebra Topics Moved to 8th Grade Common Core Math Properties Liner equations with one variable Graphing of linear equations Systems of equations and two variables

using graphing Radicals and integer exponents

Geometry Topics Moved to 8th Grade Math

Parallel lines with transversal Supplementary and complementary

angles Pythagorean Theorem and right triangles Properties of rotations, reflections

translations Congruence and similarity Volumes of cylinders, cones and spheres

What’s left?

Focus in Algebra is on functions of linear equations & inequalities, function of exponential equations, and function of quadratic equations.

Focus in Geometry is on Volume 3-Dimemsion Transformations Proofs

Focus in Algebra is on functions of linear equations & inequalities, function of exponential equations, and function of quadratic equations.

Focus in Geometry is on Volume 3-Dimemsion Transformations Proofs

Geometry

Algebra I

Algebra II

Geometry

Algebra I

Math III

Math II

Math I

Statistics & Probability

Pre- Calculus

N-Q 1-3A-SSE 1

A-CED 1-4A-REI 1, 3, 3.1, 5, 6, 10, 11, 12

F-IF 1-7, 9 F-BF 1-3

F-LE 1-3, 5 S-ID 1-3, 5-9

N-RN 1-3A-SSE 2-3A-APR 1A-REI 4, 7F-IF 8F-BF 4F-LE 6

G-CO 1-8, 12-13G-GPE 4, 5, 7

Algebra I Math I

Underlined standard is California revised addition

Geometry Math II

G-CO 9-11G-STR 1-8, 8.1

G-C 1-5G-GPE 1-2, 4

G-GMD 1, 3, 5, 6S-CP 1-9S-MD 6-7

G-CO 1-8, 12-13G-SRT 9-11GPE 5-7G-GMD 4G-MG 1-3

N-RN 1-3 N-CN 1-2, 7-9 A-SSE 1, 2, 3 A-APR 1 A-CED 1, 2, 4

A-REI 4, 7F-IF 4-7, 8, 9F-BF 1, 3, 4 F-LE 3, 6F-TF 8

Underlined standards are California revised addition.Standards in blue are also in Math I.

Algebra II Math III

N-CN 1-2, 7A-REI 3.1F-TF 8

N-CN 8-9A-SSE 1, 2, 4 A-APR 1, 2-7A-CED 1-4A-REI 2, 11F-IF 4-9F-BF 1, 3, 4F-LE 4, 4.1, 4.2, 4.3F-TF 1, 2, 2.1, 5G-GPE 3.1S-ID 4S-IC 1-6S-MD 6-7

G-SRT 9-11G-GMD 4G-MG 1-3

Underlined standards are California revised.Standards in purple are also in Math I, II and Algebra 1.

Algebra/ Functons

Geometry (Transformations & Triangle Proofs)

Bivariate Data

Cross Concept Project

Algebra/ Functons

Geometry (Transformations & Triangle Proofs)

Bivariate Data

Cross Concept Project

CCSSM 8th Grade Are HS Standards

CCSSM 8th Grade Are HS Standards

67%67%

20%20%

10%10%

3%3%

Suggested Scope & Sequence from .SVMI & PearsonSuggested Scope & Sequence from .SVMI & Pearson

Conceptual Categories

Number and Quantities (N) Algebra (A) Geometry (G) Function (F) Statistics and Probability (S) Modeling (*)

High School

Mathematics StandardsModeling:Links classroom mathematics and statistics to everyday life, work, and decision-makingIs the process of choosing and using appropriate mathematics and statisticsUses technology to explore consequences and compare predictions with data

Conceptual Categories Number & Quantity Algebra Functions Modeling Geometry Statistics & Probability

21

Acceleration

Districts are encouraged to work with their mathematics leadership, teachers, parents, and curriculum coordinators to design pathways that best meet the needs of their students.

“When students have mastered the content described in the Common Core State Standards for Mathematics with California Additions for kindergarten through grade eight, they will be ready to complete Common Core Algebra I or Common Core Mathematics I. ”

2013 CA Mathematics Framework- Instructional Materials to Support the California Common Core State Standards for Mathematics - pg 6 (200-202) 2013 CA Mathematics Framework- Instructional Materials to Support the California Common Core State Standards for Mathematics - pg 6 (200-202)

Compacting in Middle School

Acceleration Decision Point

Acceleration Decision Point

Doubling Up in High School

Acceleration Suggestions from the 2013 CA Mathematics Framework

2013 CA Mathematics Framework- Appendix A: Course Placement and Sequences - pg 182013 CA Mathematics Framework- Appendix A: Course Placement and Sequences - pg 18

Acceleration Decision Point

Accelerated Integrated Pathway

Acceleration Decision Point

Enhanced Pathway

2013 CA Mathematics Framework- Appendix A: Course Placement and Sequences - pg 19, & 20 2013 CA Mathematics Framework- Appendix A: Course Placement and Sequences - pg 19, & 20

21st Century Thinking Critical Thinking and Problem Solving Communication Collaboration Creativity and Innovation Construction of Knowledge

Part 1: Standards for

Mathematical Practice1. Make sense of problems and persevere in

solving them…start by explaining the meaning of a problem and looking for entry points to its solution

2. Reason abstractly and quantitatively…make sense of quantities and their relationships to problem situations

3. Construct viable arguments and critique the reasoning of others…understand and use stated assumptions, definitions, and previously established results in constructing arguments

4. Model with mathematics…can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace

2011 © CA County Superintendents Educational Services Association

Part 2: Standards for

Mathematical Practice

5. Use appropriate tools strategically…consider the available tools when solving a mathematical problem

6. Attend to precision…communicate precisely using clear definitions and calculate accurately and efficiently

7. Look for and make use of structure…look closely to discern a pattern or structure

8. Look for and express regularity in repeated reasoning…notice if calculations are repeated, and look for both general methods and for shortcuts

2011 © CA County Superintendents Educational Services Association

Dan Meyer

Math Class Needs a Makeoverhttp://www.ted.com/talks/view/lang/en//id/855

Task: “Over the Hill”

29

A cell phone tower will be built on the west side A cell phone tower will be built on the west side of a hill (see handout). How far up the hill must of a hill (see handout). How far up the hill must the tower be placed to provide a signal to the tower be placed to provide a signal to anyone on the east side of the lake?anyone on the east side of the lake?

From NCTM Secondary Institute - June 2012 From NCTM Secondary Institute - June 2012

Activity

A Model

Approach to Problem Solving

Maintain the level of difficulty. Require problem solving with peers. Encourage a variety of media. Ask students to generate solutions that

can be shared and generalized. Assess how students’ assumptions and

approaches change.DeMatteo (2010)

Informing Practice

30

A National Consortium of States

28 states representing 44% of K-12 students

21 governing,

7 advisory states

Washington state is fiscal agent

What is Depth of Knowledge (DOK)?

A scale of cognitive demand (thinking) to align standards with assessments

Based on the research of Norman Webb, University of Wisconsin Center for Education Research and the National Institute for Science Education.

Karen Hess on Depth of Knowledge

http://youtu.be/Cu8SfdLfbm8http://vimeo.com/20998609

http://youtu.be/Cu8SfdLfbm8http://vimeo.com/20998609

Depth Of Knowledge in the Common Core Assessments

Mathematics

ELA/Literacy

DOK3

DOK4

DOK3DOK

4

Current Assessments

<2% 0% 20% 2%

New SBAC Assessments

49% 21% 43% 25%What are the implications for the classroom?

Yuan & Le (2012); Herman & Linn (2013) from Linda Darling- Hammond, Assembly Hearing,3.6.13‐

If there is only one correct answer, it is probably level DOK 1 or DOK 2:

• DOK 1: you either know or you don’t. • DOK 2: (conceptual): apply one concept, then make a decision before going on to apply a second concept.

If more than one solution/approach, requiring evidence, it is DOK 3 or 4

• DOK 3: Must provide supporting evidence and reasoning (not just HOW it was solved, but WHY – explain reasoning).• DOK 4: all of “3”+ use of multiple sources or texts.

Some general rules of thumb...

Karin Hess January 2012

Assessment Claims

1. Concepts and Procedures: Students can explain and apply mathematical problems with precision and fluency.

2. Problem Solving: Students can frame and solve a range of complex problems in pure and applied mathematics.

3. Communicating Reasoning: Students can clarify and precisely conduct viable arguments to support their reasoning and to critique the reasoning of others.

4. Modeling and Data Analysis: Students can analyze complex, real-world scenarios and can use mathematical models to interpret and solve problems.

Test Questions Types and Designs

Items and the collection of items MUST measure deeper understanding and application of concepts.

Therefore, a variety of item types are necessary.

Item Types Selected-response

Multiple choice items designed to determine student’s understanding while eliminating obtaining the correct answer through “test-taking” skills

Constructed-response Complex thinking skills, comparison and

contrast, cause and effect, patterns, conflicting points of view, categorizing, summarizing, interpreting information

Extended constructed-response Assess knowledge and skills not easily accessed

with selected response or constructed response (e.g., oral presentations, exhibitions, product

Performance Tasks Integrate knowledge and skills across multiple

standards Technology-enhanced

Requires productive use of technology

Performance Task Items

Collections of questions and real-world tasks connected to a single theme or scenario:

A student may be presented with reading material on a given topic, and asked questions about the reading

That may be followed by reading on the same topic, but from a different perspective, with questions on that reading, plus some compare/contrast questions

Finally, the student may be provided additional readings on the same, or an associated topic, and asked to take a position or provide an argument

Each performance task could take place across more than one sitting of 45-60 minutes each

Explore the SBAC website Go to:

http://www.smarterbalanced.org/sample-items-and-performance-tasks/

direct link to sbac assessment files by grade level:http://www.dese.mo.gov/divimprove/assess/sbac.html#sbacsample

Try some technology-enhanced items. Look at other items, including those with DOK 3

and 4.

Next Steps

Start now with new instructional techniques and real-world problems

Have students explain verbally how they worked the problem, then begin to have them write the explanation.

Focus on conceptual understanding Review your pacing plans to reflect the

CCSS curriculum Implement the new 8th grade math class for

8th grades and HS Algebra Readiness (transition).