Interventions for Fractions based on Critical Point Assessments Grades 3-5

1. Interventions for Fractions based on Critical Point AssessmentsGrades 3-5 DeAnn Huinker & Judy Winn University of Wisconsin-Milwaukee Leah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil Hi-Mount Community SchoolMilwaukee Public Schools Wisconsin Mathematics Council Annual Meeting, May 4, 2012 Green Lake, Wisconsin

2. Our Purpose Share our experiences in designing and implementing an intervention for fractions with students in Grades 4 and 5, including students with and without Individual Evaluation Plans (IEPs) in mathematics.

3. Agenda Background Screener Intervention Impact on Student Learning Classroom Carryover

4. BackgroundRtI, DWW, CCSSM

5. Wisconsin Model of RtIWisconsin Response to Intervention: A Guiding Document Balanced Assessment Collaboration Culturally Responsive Practices High Quality Instruction MULTI-LEVEL SYSTEM OF SUPPORT

6. Wisconsin Response to Intervention Roadmap A Model for Academic and Behavioral Success for All Students Using Culturally Responsive

7. URL: dww.ed.gov US Department of Education Research-based education practices IES Practice Guide Developing Effective Fractions Instruction for Kindergarten Through 8th Grade

9. Grades 1-2 Fractions Domain: Geometry Standards 1.G.3 and 2.G.3 Grades 3-5 Fractions Domain: Number and Operations – Fractions Standards 3.NF.1, 3.NF.2, 3.NF.3

10. Fractions in Grade 2 (Geometry Domain) • 2.G.3. • Partition circles and rectangles into two, three, or four equal shares, • describe the shares using the words halves, thirds, half of, a third of, etc., and • describe the whole as two halves, three thirds, four fourths. • Recognize that equal shares of identical wholes need not have the same shape.

11. Screener

12. Developing the Screener Reviewed IES, CCSSM, research on fractions, curriculum materials. Developed framework of 5 key understandings. Created a draft of a screener: 13 items. Piloted with a range of students. Reviewed student work. Selected items that differentiated students and fraction ideas. Revised the screener: 7 items.

13. Screener Framework: Key Understandings (KU) to Assess KU1. Partitioning and fair shares KU2. Comparing, ordering, and equivalence KU3. Fraction symbols and landmarks KU4. Fractions as a point on the number line KU5. Informal use of operations in context

14. Study the Screener - Work in pairs Identify which key understanding from the framework is being assessed in each item. KU1. Partitioning and fair shares KU2. Comparing, ordering. and equivalence KU3. Fraction symbols and landmarks KU4. Fractions as a point on the number line KU5. Informal use of operations in context

15. Screener Items & Key Understandings (KU) Item 1: KU1 Partitioning Item 2: KU1 Partitioning Item 3: KU5 Operations in context Item 4: KU2 Comparing, ordering, equivalence Item 5: KU3 Symbols and landmarks Item 6: KU5 Operations in context Item 7: KU4 Point on a number line

16. Selecting Students for the Intervention

17. Analysis of Student Work Non-Fractional Reasoning Early Fractional Strategy Fractional Strategy Transitional Strategy -Generate a model - Strategy works but not efficient - Some gaps in fraction understanding -Fraction sense - Correct models - Efficient strategies - Reasoning with benchmarks, equivalence, and relative magnitude -Whole number reasoning - Rule based - No or very little evidence of fraction ideas -Semi-appropriate model or idea - Misconception or error - Some notion of partitioning to build upon Adapted from OGAP Fraction Framework (VMP, 2009 http://margepetit.com/FractionFrameworkSept2011V19.pdf)

18. Nathan has of a pan of brownies. Amber has of a pan of brownies. Who has more and why? Non-Fractional Reasoning

19. Nathan has of a pan of brownies. Amber has of a pan of brownies. Who has more and why? Early Fractional Strategy Transitional Strategy

20. Analysis of Student Work Non-Fractional Reasoning Early Fractional Strategy Fractional Strategy Transitional Strategy -Generate a model - Strategy works but not efficient - Some gaps in fraction understanding -Fraction sense - Correct models - Efficient strategies - Reasoning with benchmarks, equivalence, and relative magnitude -Whole number reasoning - Rule based - No or very little evidence of fraction ideas -Semi-appropriate model or idea - Misconception or error - Some notion of partitioning to build upon Adapted from OGAP Fraction Framework (VMP, 2009)

21. Design of the Intervention

22. Intervention Flow Fair Shares Halves Fourths Unit Fractions Diagrams & Symbols Fourths Non-unit Fractions & Equivalency

23. Checklist Provided… • A frame for the instructional sequence. • A record of instruction. • A record of students’ understanding. Could be used for a group of students or for individual students.

24. Key Resource Extending Children's Mathematics: Fractions & Decimals Authors: Susan Empson & Linda Levi Date of Publication: 2011
 Publisher: Heinemann

25. “Nuts and Bolts”of the Intervention

26. How it was done…

27. Intervention Examples

29. Task 1: Fair Shares Jayson has a bag of 10 pieces of licorice. He wants to share the licorice with 4 friends. How much licorice would each friend get?

31. Turn and Talk • Describe the shares. • Justify why they are fair.

32. Task 2: Re-composing Wholes and Equivalent Fractions

33. Impact on Students

34. Four children are sharing 3 candy bars. If the children share the candy bars equally, how much can each child have? Miracle Pre-Assessment Post-Assessment

35. Two children are sharing 5 candy bars. If the children share the candy bars equally, how much can each child have? Achantia Pre-Assessment Post-Assessment

36. Four children are sharing 3 candy bars. If the children share the candy bars equally, how much can each child have? Jordan Pre-Assessment Post-Assessment

37. Classroom Carryover

38. Back in the classroom… Students had the fraction language to participate in class discourse. Students showed increased confidence, volunteered more – they raised their hands! Students had access to the math content. Still some struggles with transfer...

39. Thank you! DeAnn Huinker huinker@uwm.edu Judy Winn jwinn@uwm.edu Leah Schlichtholz schlicle@milwaukee.k12.wi.us Frelesha A LeFlore parkerfa@milwaukee.k12.wi.us Jennifer O'Neil oneiljs@milwaukee.k12.wi.us