1. Common Core: Shifts, Practices, Rigor Cathy Battles Consultant UMKC-Regional Professional Development Center battlesc@umkc.edu

2. Starter Problem Using each of the digits 1 through 9 only once, find two 3- digit numbers whose sum uses the remaining three digits

3. Some Answers

4. Partner Time Turn to your partner and tell them what you know about the common core and what you or your district has done.

5. About the Common Core Standards Clarity: The standards are focused, coherent, and clear. Clearer standards help students (and parents and teachers) understand what is expected of them. Collaboration: The standards create a foundation to work collaboratively across states and districts, pooling resources and expertise, to create curricular tools, professional development, common assessments and other materials. Source: Adapted From Student Achievement Partners Education Week: COMMON STANDARDS www.edweek.org/go/standardsreportwww.edweek.org/go/standardsreport 4/25/12

6. Common Core Standards Shifts Significantly narrow the scope of content and deepen how time and energy is spent in the classroom Focus deeply on what is emphasized in the standards, so students gain strong foundations Equity: Expectations are consistent for all – and not dependent on a student’s zip code. Level the playing field for students across the country…

7. CCSS Domain Progression K12345678HS Counting & Cardinality Number and Operations in Base Ten Ratios and Proportional Relationships Number & Quantity Number and Operations – Fractions The Number System Operations and Algebraic Thinking Expressions and EquationsAlgebra Functions Geometry Measurement and DataStatistics and Probability Statistics & Probability

8. 2. Reason abstractly and quantitatively. 1. Make sense of problems and persevere in solving them. 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. Counting and Cardinality Kindergarten Numbers and Operations in Base Ten Grades K-5 Operations and Algebraic Thinking Grades K-5 Measurement and Data Grades K-5 Geometry Grades K-5 Fractions Grades 3-5 Kathy Anderson http://northstartechnologyguide.com/wp-content/uploads/2010/07/apple-core-250x238.jpg

9. 2. Reason abstractly and quantitatively. 1. Make sense of problems and persevere in solving them. 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. Ratios and Proportional Relationships Grades 6-7 Expressions and Equations Grades 6-8 Statistics and Probability Grades 6-8 Geometry Grades 6-8 The Number System Grades 6-8 Functions Grade 8 Kathy Anderson http://northstartechnologyguide.com/wp-content/uploads/2010/07/apple-core-250x238.jpg

10. 2. Reason abstractly and quantitatively. 1. Make sense of problems and persevere in solving them. 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. Kathy Anderson Number and Quantity Algebra Functions Statistics and Probability Geometry Modeling http://northstartechnologyguide.com/wp-content/uploads/2010/07/apple-core-250x238.jpg

11. Mathematical Practices are Not: A checklist Disconnected from content standards Grade specific New Restricted to math Taught in isolation Sequential A Friday problem solving activity

12. CORE ACADEMIC STANDARDS(CAS) Missouri’s Core Academic Standards are the same as the Common Core Standards for Math and ELA but also include Social Studies and Science

13. RIGOR A balance of :  Conceptual Understanding  Fluency  Application

14. Of all pre-college curricula, the highest level of mathematics in secondary school has the strongest continuing influence on bachelor’s degree completion. Finishing a course beyond Algebra 2 more than doubles the odds that a student who enters post-secondary education will complete a bachelor’s degree. National Mathematics Advisory Panel Adams, C. (2006). Answers in the toolbox: academic intensity, attendance patterns, and bachelor’s degree attainment. (Office of Educational Research and Improvement Publication.) http://www.ed.gov/pubs/Toolbox/Title.htm.

15. National Mathematics Advisory Panel Recommendations 1.A focused, coherent progression of mathematics learning, with an emphasis on proficiency with key topics, should become the norm in elementary and middle school mathematics curricula; the most important topics underlying success in school algebra.

16. National Mathematics Advisory Panel Recommendations 2. A major goal of K – 8 mathematics education should be proficiency with fractions (including decimals, percent, and negative fractions), for such proficiency is foundational for algebra and seems to be severely underdeveloped. In addition, the Panel identified Critical Foundations of Algebra (p 17).

17. Fractions Turn to your neighbor and share one thing that you know about the Common Core and changes with fractions

18. 18 “It is possible to have good number sense for whole numbers, but not for fractions.” Sowder, J. and Schappelle, Eds. 1989

19. Problem: 7/8 – 1/8 = ? Fraction Sense? Interviewer: Melanie these two circles represent pies that were each cut into eight pieces for a party. This pie on the left had seven pieces eaten from it. How much pie is left there? Melanie: One- eighth, writes 1/8 Interviewer: The pie on the right had three pieces eaten from it. How much is left of that pie? Melanie: Five- eighths, writes 5/8 Interviewer: If you put those two together, how much of a pie is left? Melanie: Six- eighths, writes 6/8. Interviewer: Could you write a number sentence to show what you just did? Melanie: Writes 1/8 + 5/8 = 6/16. Interviewer: That’s not the same as you told me before. Is that OK? Melanie: Yes, this is the answer you get when you add.

20. American students’ weak understanding of fractions 2004 NAEP - 50% of 8th-graders could not order three fractions from least to greatest (NCTM, 2007)

21. American students’ weak understanding of fractions 2004 NAEP, Fewer than 30% of 17- year-olds correctly translated 0.029 as 29/1000 (Kloosterman, 2010)

22. American students’ weak understanding of fractions One-on-one controlled experiment tests - when asked which of two decimals, 0.274 and 0.83 is greater, most 5th- and 6th-graders choose 0.274 (Rittle-Johnson, Siegler, and Alibali, 2001)

23. American students’ weak understanding of fractions Knowledge of fractions differs even more between students in the U.S. and students in East Asia than does knowledge of whole numbers (Mullis, et al., 1997)

24. You can’t make this stuff up! The weather reporter on WCRB (a Boston radio station) said there was a 30% chance of rain. The host of the show asked what that meant. The weather reporter said, ``It will rain on 30% of the state.'' ``What are the chances of getting wet if you are in that 30% of the state?'' ``100%.” Fractions

25. Not viewing fractions as numbers at all, but rather as meaningless symbols that need to be manipulated in arbitrary ways to produce answers that satisfy a teacher Focusing on numerators and denominators as separate numbers rather than thinking of the fraction as a single number. Confusing properties of fractions with those of whole numbers Fractions Facets of the lack of student conceptual understanding:

26. 3 rd Grade Number and Operations Fractions(3.NF) Develop understanding of fractions as numbers. Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.

27. 3 rd Grade Fractions (Cont) Understand a fraction as a number on the number line; represent fractions on a number line diagram. Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line. Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.

28. Build fraction understanding from whole number understanding. 28

29. Build fraction understanding from whole number understanding. 29

30. Build fraction understanding from whole number understanding. 30 Fraction equivalence on the number line. number line.