1. RED CLAY CONSOLIDATED SCHOOL DISTRICT 4 th – 6 th Partnership Institute Building a Conceptual Understanding of Fractions: A 4 th Through 6 th Grade Partnership

2. A CALL TO ACTION "These Standards are not intended to be new names for old ways of doing business. They are a call to take the next step." Common Core State Standards for Mathematics RCCSD

3. District Mathematics Department Jodi Albers, Supervisor of Mathematics Lou Mingione, Secondary Mathematics Specialist Eric Shane, Elementary Mathematics Specialist Shirl Ellison, Elementary Mathematics Specialist Participants 23 District Schools 15 Elementary 8 Secondary Institute of Higher Education University of Delaware, MSERC Janice McCarthy Val Maxwell Instructional Technology Coaches Karen Ammann Vicki Green Funding Delaware Department of Education $122,600 4 th – 6 th Partnership Institute RCCSD INVESTED PARTNERS

4. EXAMINING THE DATA Count Pre Assessment Post Assessment Change Total12811.5313.30+1.77 0 - 9397.5910.92+3.33 10 – 157412.5714.05+1.48 Mathematical Knowledge for Teaching Survey (MKT) RCCSD

5. FRACTIONAL UNDERSTANDING “The coherence and sequential nature of mathematics dictate the foundational skills that are necessary for the learning of algebra. The most important foundational skill not presently developed appears to be proficiency with fractions (including decimals, percents, and negative fractions). The teaching of fractions must be acknowledged as critically important and improved before an increase in student achievement in algebra can be expected.” National Mathematics Advisory Panel RCCSD

6. GOALS Explore what educators need to know and be able to do in order to effectively instruct students in the area of fractions using visual models, number talks, and additional research-based strategies. Examine and reflect on research that explores best practices for teaching the essential ideas that students must grasp about fractions. Examine and implement rich mathematical tasks that align to CCSSM. Explore the understanding of rigor within CCSSM through the development and implementation of model lessons. RCCSD

7. A TYPICAL DAY IN THE INSTITUTE Formulated Norms Conducted Exit Ticket Summary Reviewed Homework Participated in a Team Builder Examined the Common Core State Standards Examined the Standards for Mathematical Practices Engaged in Rich Mathematical Tasks Participated in a Book Study Enhanced Smarter Balanced Assessment Items RCCSD

8. PARTICIPANTS 167 total participants 72 fourth grade teachers 67 fifth grade teachers 26 sixth grade teachers 84 participants from Title I buildings 8 participants from special schools RCCSD

9. PARTICIPANT STRUCTURE 167 Teachers 4 Cohorts 6 Teams per Cohort 8 players per team (maximum) At least 2 fourth, 2 fifth and 1 sixth grade teacher per team No more than 1 person per building per team RCCSD

10. RESEARCH Developing Effective Fractions Instruction for Kindergarten Through 8th Grade Practice Guide RCCSD

11. RESEARCH Putting Essential Understanding of Fractions into Practice in Grades 3-5 RCCSD

12. CONTENT FOCI The Institute Session 1: Equivalence and Comparison Session 2: Addition and Subtraction Session 3: Addition, Subtraction, and Multiplication Session 4: Multiplication, Division, and Ratios Session 5: Ratios RCCSD

13. CCSSM Domains from Grade 3 to Grade 7: Number and Operations – Fractions Ratios and Proportional Relationships RCCSD Progressions Documents for the Common Core Math Standards

14. ICEBERG RCCSD

15. CCSSM The Standards for Mathematical Practices Reasoning abstractly and quantitatively Construct viable arguments and critique the reasoning of others RCCSD

16. CCSSM Delaware Department of Education RCCSD Mathematical PracticesStudent DispositionsTeacher Actions to Engage Students in Practices: Reasoning and Explaining Reason abstractly and quantitatively Create multiple representations Interpret problems in contexts Estimate first/answer reasonable Make connections Represent symbolically Talk about problems, real-life situations Attend to units Use context to think about a problem Develop opportunities for problem-solving strategies Give time for processing and discussing Tie content areas together to help make connections Give real-world situations Demonstrate thinking aloud for students’ benefit Value invented strategies and representations More emphasis on the process instead of on the answer Construct viable arguments and critique the reasoning of others Ask questions Use examples and counter examples Reason inductively and make plausible arguments Use objects, drawings, diagrams, and actions Develop ideas about mathematics and support their reasoning Analyze others arguments Encourage the use of mathematics vocabulary Create a safe environment for risk-taking and critiquing with respect Provide complex, rigorous tasks that foster deep thinking Provide time for student discourse Plan effective questions and student grouping Probe students

17. SMARTER BALANCED The Four Mathematical Claims Concepts and Procedures Problem Solving Communicating Reasoning Modeling and Data Analysis Enhancing the Technology-Enabled questions RCCSD

18. SBAC – GRADE 5 MATHEMATICS Mr. Jones will cut 6 identical loaves of bread into pieces that are loaf each. Part A After he cuts the 6 loaves, how many pieces will Mr. Jones have? Show your work using numbers, words, and/ or pictures. pieces RCCSD

19. CONTENT FOCI The Institute Session 1: Equivalence and Comparison Session 2: Addition and Subtraction Session 3: Addition, Subtraction, and Multiplication Session 4: Multiplication, Division, and Ratios Session 5: Ratios RCCSD

20. MRI – MARILYN BURNS Which fraction is greater? or How did you decide? RCCSD Session 1: Equivalence and Comparison

21. CONTENT FOCI The Institute Session 1: Equivalence and Comparison Session 2: Addition and Subtraction Session 3: Addition, Subtraction, and Multiplication Session 4: Multiplication, Division, and Ratios Session 5: Ratios RCCSD

22. Book Study RCCSD Session 2: Addition and Subtraction Putting Essential Understandings of Fractions into Practice - NCTM

23. CONTENT FOCI The Institute Session 1: Equivalence and Comparison Session 2: Addition and Subtraction Session 3: Addition, Subtraction, and Multiplication Session 4: Multiplication, Division, and Ratios Session 5: Ratios RCCSD

24. CMP2 Connected Mathematics Project RCCSD Session 3: Addition, Subtraction, and Multiplication

25. CONTENT FOCI The Institute Session 1: Equivalence and Comparison Session 2: Addition and Subtraction Session 3: Addition, Subtraction, and Multiplication Session 4: Multiplication, Division, and Ratios Session 5: Ratios RCCSD

26. NUMBER STRING RCCSD Session 4: Multiplication, Division, and Ratios

27. CONTENT FOCI The Institute Session 1: Equivalence and Comparison Session 2: Addition and Subtraction Session 3: Addition, Subtraction, and Multiplication Session 4: Multiplication, Division, and Ratios Session 5: Ratios RCCSD

28. CMP2 Connected Mathematics Project RCCSD Session 5: Ratios

29. MEASURING IMPACT Mathematical Knowledge for Teaching District Created Walkthrough Tool PLC Minutes District Coach Observations Anecdotal Information RCCSD

30. FEEDBACK What made learning easy or hard for you today? Group work with our tables is nice. It is always great to work cooperatively. I am in an awesome group! Discussions within the group was easy. Great group I work with! Collaboration with teammates made it easier. Staying in groups produced a lot of responses. At this point we are getting comfortable with each other and can share at will. RCCSD

31. FINAL THOUGHTS Questions? RCCSD jodi.albers@redclay.k12.de.us louis.mingione@redclay.k12.de.us courtney.flounders@redclay.k12.de.us