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

2. DeAnn Huinker & Judy Winn, University of Wisconsin-Milwaukee Leah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools 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. DeAnn Huinker & Judy Winn, University of Wisconsin-Milwaukee Leah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools Agenda Background Screener Intervention Impact on Student Learning Classroom Carryover

4. DeAnn Huinker & Judy Winn, University of Wisconsin-Milwaukee Leah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools Background RtI, DWW, CCSSM

5. DeAnn Huinker & Judy Winn, University of Wisconsin-Milwaukee Leah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools Wisconsin Model of RtI Wisconsin Response to Intervention: A Guiding Document Culturally Responsive Practices Culturally Responsive Practices

6. DeAnn Huinker & Judy Winn, University of Wisconsin-Milwaukee Leah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools Wisconsin Response to Intervention Roadmap A Model for Academic and Behavioral Success for All Students Using Culturally Responsive

7. DeAnn Huinker & Judy Winn, University of Wisconsin-Milwaukee Leah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools URL: dww.ed.gov US Department of Education Research-based education practices IES Practice Guide Developing Effective Fractions Instruction for Kindergarten Through 8th Grade

8. DeAnn Huinker & Judy Winn, University of Wisconsin-Milwaukee Leah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools

9. DeAnn Huinker & Judy Winn, University of Wisconsin-Milwaukee Leah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools 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. DeAnn Huinker & Judy Winn, University of Wisconsin-Milwaukee Leah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools 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. Fractions in Grade 2 (Geometry Domain)

11. DeAnn Huinker & Judy Winn, University of Wisconsin-Milwaukee Leah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools Screener

12. DeAnn Huinker & Judy Winn, University of Wisconsin-Milwaukee Leah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools 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. DeAnn Huinker & Judy Winn, University of Wisconsin-Milwaukee Leah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools 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. DeAnn Huinker & Judy Winn, University of Wisconsin-Milwaukee Leah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools 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. DeAnn Huinker & Judy Winn, University of Wisconsin-Milwaukee Leah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools 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. DeAnn Huinker & Judy Winn, University of Wisconsin-Milwaukee Leah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools Selecting Students for the Intervention

17. DeAnn Huinker & Judy Winn, University of Wisconsin-Milwaukee Leah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools Analysis of Student Work Non-Fractional Reasoning Transitional Strategy Fractional Strategy Early Fractional Strategy Adapted from OGAP Fraction Framework (VMP, 2009 http://margepetit.com/FractionFrameworkSept2011V19.pdf) - 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 - 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

18. DeAnn Huinker & Judy Winn, University of Wisconsin-Milwaukee Leah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools Nathan has of a pan of brownies. Amber has of a pan of brownies. Who has more and why? Non-Fractional Reasoning

19. DeAnn Huinker & Judy Winn, University of Wisconsin-Milwaukee Leah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools Nathan has of a pan of brownies. Amber has of a pan of brownies. Who has more and why? Transitional Strategy Early Fractional Strategy

20. DeAnn Huinker & Judy Winn, University of Wisconsin-Milwaukee Leah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools Analysis of Student Work Non-Fractional Reasoning Transitional Strategy Fractional Strategy Early Fractional Strategy Adapted from OGAP Fraction Framework (VMP, 2009) - 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 - 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

21. DeAnn Huinker & Judy Winn, University of Wisconsin-Milwaukee Leah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools Design of the Intervention

22. DeAnn Huinker & Judy Winn, University of Wisconsin-Milwaukee Leah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools Intervention Flow Fair Shares Halves Fourths Unit Fractions Fourths Unit Fractions Fourths Non-unit Fractions & Equivalency Fourths Non-unit Fractions & Equivalency Diagrams & Symbols Diagrams & Symbols

23. DeAnn Huinker & Judy Winn, University of Wisconsin-Milwaukee Leah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools 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. DeAnn Huinker & Judy Winn, University of Wisconsin-Milwaukee Leah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools Key Resource Extending Children's Mathematics: Fractions & Decimals Authors: Susan Empson & Linda Levi Date of Publication: 2011 Publisher: Heinemann

25. DeAnn Huinker & Judy Winn, University of Wisconsin-Milwaukee Leah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools “Nuts and Bolts” of the Intervention

26. DeAnn Huinker & Judy Winn, University of Wisconsin-Milwaukee Leah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools How it was done… Ms. O’NeilMs. Le FloreMs. Schlichtholz Fourth GradeFourth/Fifth GradesSpecial education students 5 students 5 students (3 in fourth grade and 2 in fifth grade) 8 sessions10 sessions8 sessions Before Fraction unitDuring Fraction unitBefore unit for some; During for others After schoolDuring school In classroom In resource room 30 minutes over the course of three weeks 20 minutes over the course of a month 30 minutes on consecutive days

27. DeAnn Huinker & Judy Winn, University of Wisconsin-Milwaukee Leah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools Intervention Examples

28. DeAnn Huinker & Judy Winn, University of Wisconsin-Milwaukee Leah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools

29. DeAnn Huinker & Judy Winn, University of Wisconsin-Milwaukee Leah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools 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?

30. DeAnn Huinker & Judy Winn, University of Wisconsin-Milwaukee Leah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools

31. DeAnn Huinker & Judy Winn, University of Wisconsin-Milwaukee Leah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools Describe the shares. Justify why they are fair. Turn and Talk

32. DeAnn Huinker & Judy Winn, University of Wisconsin-Milwaukee Leah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools Task 2: Re-composing Wholes and Equivalent Fractions

33. DeAnn Huinker & Judy Winn, University of Wisconsin-Milwaukee Leah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools Impact on Students

34. DeAnn Huinker & Judy Winn, University of Wisconsin-Milwaukee Leah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools Four children are sharing 3 candy bars. If the children share the candy bars equally, how much can each child have? Pre-AssessmentPost-Assessment Miracle

35. DeAnn Huinker & Judy Winn, University of Wisconsin-Milwaukee Leah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools Two children are sharing 5 candy bars. If the children share the candy bars equally, how much can each child have? Achantia Pre-AssessmentPost-Assessment

36. DeAnn Huinker & Judy Winn, University of Wisconsin-Milwaukee Leah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools Four children are sharing 3 candy bars. If the children share the candy bars equally, how much can each child have? Jordan Pre-AssessmentPost-Assessment

37. DeAnn Huinker & Judy Winn, University of Wisconsin-Milwaukee Leah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools Classroom Carryover

38. DeAnn Huinker & Judy Winn, University of Wisconsin-Milwaukee Leah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools 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. DeAnn Huinker & Judy Winn, University of Wisconsin-Milwaukee Leah Schlichtholz, Frelesha LeFlore, & Jennifer O’Neil, Milwaukee Public Schools Thank you! DeAnn Huinker huinker@uwm.edu Judy Winnjwinn@uwm.edu Leah Schlichtholzschlicle@milwaukee.k12.wi.us Frelesha A LeFlore parkerfa@milwaukee.k12.wi.us Jennifer O'Neil oneiljs@milwaukee.k12.wi.us