1 1 Common Core State Standards The Mathematics Standards Tere Hirsch Cheryl Avalos Math Consultant Division of Curriculum and Instructional Services commoncore.lacoe.edu

2 2 Agenda – Three Days Day 1 – Overview – Content and Curriculum Day 2 – Instruction Day 3 – Assessment – Instructional Materials 2

3 3 Day 1: Agenda Introductions, Logistics Overview of the Mathematics CaCCSS –Break Mathematical Practices Math Task –Lunch Domains Formats Comparisons of 1997 Standards Closure

Introductions, Logistics Who am I? Who are you? Who are we altogether? Breaks Restrooms Lunch Ending time 4

KWL Chart What I already KNOW about the Common Core State Standards What I WOULD like to learn about the Common Core State Standards What I LEARNED about the Common Core State Standards 2011 © CA County Superintendents Educational Services Association 5

6 6 Common Core State Standards The Mathematics Standards Part 1: Overview commoncore.lacoe.edu

CST – Released Items Algebra 1 7

8 Erica is putting up lines of colored flags for a party. The flags are all the same size and are spaced equally along the line. 1.Calculate the length of the sides of each flag, and the space between flags. Show all your work clearly. 2. How long will a line of n flags be? Write down a formula to show how long a line of n flags would be.

9 The California Algebra Experiment In 2012, 59% of all eighth grade students took the CST Algebra 1 exam and more than half were not successful. Even more will repeated the class again in high school. In 9 th grade, 49% of the students took CST Algebra 1 exam and 75% of those students did not pass. Research studies indicate nearly 65% of the students who were placed in Algebra in eighth grade are placed in the same level of Algebra in ninth grade. About 46% of the students who were successful in Algebra in the eighth grade (B- grade and Proficient) and who were placed again in Algebra in ninth grade were less successful in their second experience. It is Algebra Forever not Algebra for All

10 The Findings from Party Flags The task may be approached as a system of simultaneous equations, almost no algebra students used such an approach. 49% of algebra students had no success. 44% accurately found the two lengths (most commonly by an estimation strategy only using one constraint). 21% correctly used both constraints (the length of three flags is 80 cm. and the length of 6 flags is 170 cm.). 7% of the students were able to develop a valid generalization for n flags.

11 Three Central Authors Common Core State Standards in Mathematics Charges given to the authors: All students College and Career Ready by 11 th grade Internationally Benchmarked Make the standards “ Fewer, Clear and Higher ”

12 The CCSS for Mathematics are focused, coherent, and rigorous aim for clarity and specificity balance mathematical understanding & procedural skills stress conceptual understanding of key ideas are internationally benchmarked are research based ……are not a mile wide & an inch deep……

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14 TIPS Think–Ink–Pair–Share What does it mean to be college ready? What does it mean to be career ready? 14

15 College & Career Readiness American College Testing (ACT) defines college & career readiness as the acquisition of the knowledge & skills a student needs to enroll & succeed in credit-bearing, first year courses at a postsecondary institution without the need for remediation. ACT’s definition of college & career readiness was adopted by the Common Core State Standards Initiative & provides a unifying goal upon which educators & policymakers now must act.

16 Big Picture in Mathematics Standards of Mathematical Practice Grades K-5Grades 6-8 High School Math CCSS Grade Level Standards

17 Standards for Mathematical Practice The Eight Standards for Mathematical Practice place an emphasis on student demonstrations of learning that describe the thinking processes, habits of mind, and dispositions that students need to develop. adapted from Briars & Mitchell (2010) Getting Started with the Common Core State Standards 17

18 Standards for Mathematical Practice Locate the CCSS for Mathematic Practice and underline the first three words after “Mathematically proficient students…”. What do notice about these standards? Briars & Mitchell (2010) Getting Started with the Common Core State Standards 18 Activity

19 Part 1: Standards for Mathematical Practice 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 2011 © CA County Superintendents Educational Services Association 19

20 National Council of Supervisors of Mathematics CCSS Standards of Mathematical Practice: Reasoning and Explaining Common Core Standards of Mathematical Practice Gym Membership Work on the gym membership problem on the next slide. –Decide how you would determine which gym to join based on the cost. –Share your ideas with a neighbor. Activity

21 National Council of Supervisors of Mathematics CCSS Standards of Mathematical Practice: Reasoning and Explaining Using Formative Assessment to Plan Instruction Carlo thinks he will go to the gym about 20 times a month. Calculate how much each of these options would cost Carlo for one month. Which of these options is the least expensive for Carlo? Pay as you go Pay only $6 each time you work out Regular deal Pay $50 a month and $2 each time you work out All-in-one price! Pay just $100 per month for unlimited use of our great facilities Activity

22 Think in Terms of Units Phil Daro has suggested that it is not the lesson or activity, but rather the unit that is the “ optimal grain-size for the learning of mathematics ”. Hence that was the starting point for our Scope and Sequence. Developers of High School: Patrick Callahan, Dick Stanley, David Foster, Brad Findell, Phil Daro, Marge Cappo

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28 Challenges??? In your group, discuss the challenges that you foresee in implementing the Common Core Standards. Be ready to share out.

29 Implementing CCSS Challenge: –CCSS assessments not available for several years ( deadline) –Recognizing that CCSS are not “business as usual” –Providing assistance to teachers with understanding of the Mathematical Practices –Textbooks materials will not be available before the first assessments. 29

30 CCCS: An Opportunity National dialogue about learning expectations Fewer, clearer standards Refocusing on college and career readiness that begins earlier in standards Research-based, builds on strengths of best state and international standards Equity 30