Computation of Fractions: Math Intervention for Elementary and Middle Grades Students

Drawing on their years of classroom experience working with struggling students and their teachers, Dr. Brad Witzel and Dr. Paul Riccomini present elementary and middle school teachers  with practical strategies and activities for promoting academic success and mastery of key mathematical concepts. They offer insight into what really helps students learn math including friendly descriptions of the concrete to representational to abstract sequence of instruction, procedural instruction that can be expanded from one topic to the next, assessment guides for placement and measurement, and retention of content through mixed reviews and assessments. In addition, the authors provide teachers with clear direction to implement each research-based lesson plan with answer sheets to grade student work as well as pictures of manipulations and accompanying vocabulary so that teachers know exactly how to show concrete and pictorial steps.   Give your students who struggle with fractions the support they need! Aligns each lesson to the CRA instruction sequence and effectively leads teachers through classroom instruction. Offers step-by-step direction to coach teachers through each lesson plan. Includes a complete list of manipulative resources for each lesson.

Table of Contents:
Introduction ..............................................................................6   NCTM Process Standards...........................................................8   The Sequence and Standards .....................................................9   Description of Manipulatives ....................................................11   Organization of Materials ........................................................14   Who Can Use this Intervention? ................................................15   How to Use this Intervention ....................................................16   Pretest Assessment .................................................................22   Instructional Lessons ...............................................................23   Lesson 1 — Division with Fractional Answers — concrete level learning sheet...................................................................................24   Teaching Lesson 1 — Division with Fractional Answers — concrete level lesson plan.......................................................................................25   Lesson 2 — Division with Fractional Answers — representational level learning sheet ...........................................................................30   Teaching Lesson 2 — Division with Fractional Answers — representational level lesson plan ...............................................................................31   Lesson 3 — Division with Fractional Answers — abstract level learning sheet...................................................................................34   Teaching Lesson 3 — Division with Fractional Answers — abstract level lesson plan.......................................................................................35   Lesson 4 — Division with Fractional Answers — generalized abstract level learning sheet ...........................................................................38   Lesson 5 — Division with Fractional Answers — concrete level learning sheet...................................................................................39   Teaching Lesson 5 — Division with Fractional Answers — concrete level lesson plan.......................................................................................40   Lesson 6 — Division with Fractional Answers — representational level learning sheet ...........................................................................46   Teaching Lesson 6 — Division with Fractional Answers — representational level lesson plan ...............................................................................47   Lesson 7 – Division with Fractional Answers – abstract level learning sheet...................................................................................50   Teaching Lesson 7 – Division with Fractional Answers – abstract level lesson plan.......................................................................................51   Lesson 8 – Multiplication of Fractions – concrete level learning sheet ...............................................................................................54   Teaching Lesson 8 – Multiplication of Fractions – concrete level lesson plan.......................................................................................55   Lesson 9 – Multiplication of Fractions – representational level learning sheet...................................................................................62 Teaching Lesson 9 – Multiplication of Fractions – representational level lesson plan.......................................................................................63   Lesson 10 – Multiplication of Fractions – abstract level learning sheet ...............................................................................................67   Teaching Lesson 10 – Multiplication of Fractions – abstract level lesson plan .................................................................................................68   Lesson 11 – Multiplication of Fractions – generalized abstract level learning sheet...................................................................................71   Lesson 12 – Division of Fractions – abstract level learning sheet .........72   Teaching Lesson 12 – Division of Fractions – abstract level lesson plan....73   Lesson 13 – Division of Fractions – abstract level learning sheet .........76   Teaching Lesson 13 – Division of Fractions – abstract level lesson plan....77   Lesson 14 – Division of Fractions – abstract level learning sheet .........80   Teaching Lesson 14 – Division of Fractions – abstract level lesson plan .....81   Lesson 15 – Finding Equivalent Fractions – concrete level learning sheet...................................................................................83   Teaching Lesson 15 – Finding Equivalent Fractions – concrete level lesson plan.......................................................................................84   Lesson 16 – Finding Equivalent Fractions – representational level learning sheet...................................................................................89   Teaching Lesson 16 – Finding Equivalent Fractions – representational level lesson plan ...............................................................................90   Lesson 17 – Finding Equivalent Fractions – abstract level learning sheet ...............................................................................................93   Teaching Lesson 17 – Finding Equivalent Fractions – abstract level lesson plan.......................................................................................94   Lesson 18 – Finding Equivalent Fractions – generalized abstract level learning sheet ...........................................................................97   Lesson 19 – Reducing and Comparing Fractions – concrete level learning sheet...................................................................................98   Teaching Lesson 19 – Reducing and Comparing Fractions – concrete level lesson plan ...............................................................................99   Lesson 20 – Reducing and Comparing Fractions – representational level learning sheet .........................................................................103   Teaching Lesson 20 — Reducing and Comparing Fractions — representational level lesson plan ....................................................104   Lesson 21 — Reducing and Comparing Fractions — abstract level learning sheet.................................................................................107   Teaching Lesson 21 — Reducing and Comparing Fractions — abstract level lesson plan.....................................................................................108   Lesson 22 — Reducing and Comparing Fractions — generalized abstract level learning sheet ............................................................111   Lesson 23 — Adding and Subtracting Fractions with Like   Denominators — concrete level learning sheet ...................................112   Teaching Lesson 23 — Adding and Subtracting Fractions with Like   Denominators — concrete level lesson plan .......................................113   Lesson 24 — Adding and Subtracting Fractions with Like   Denominators — representational level learning sheet .......................120   Teaching Lesson 24 — Adding and Subtracting Fractions with Like   Denominators — representational level lesson plan ...........................121   Lesson 25 — Adding and Subtracting Fractions with Like   Denominators — abstract level learning sheet....................................124   Teaching Lesson 25 — Adding and Subtracting Fractions with Like   Denominators — abstract level lesson plan........................................125   Lesson 26 — Adding and Subtracting Fractions with Like   Denominators — generalized abstract level learning sheet..................127   Lesson 27 — Adding and Subtracting Fractions with Unlike   Denominators — concrete level learning sheet ...................................128   Teaching Lesson 27 — Adding and Subtracting Fractions with Unlike   Denominators — concrete level lesson plan .......................................129   Lesson 28 — Adding and Subtracting Fractions with Unlike   Denominators — representational level learning sheet .......................139   Teaching Lesson 28 — Adding and Subtracting Fractions with Unlike   Denominators — representational level lesson plan ...........................140   Lesson 29 — Adding and Subtracting Fractions with Unlike   Denominators — abstract level learning sheet....................................145   Teaching Lesson 29 — Adding and Subtracting Fractions with Unlike   Denominators — abstract level lesson plan........................................146   Lesson 30 — Adding and Subtracting Fractions with Unlike   Denominators — generalized abstract level learning sheet..................149   Cumulative Review Problem Sets A—G ....................................150   Posttest ................................................................................159   Answer Key...........................................................................160   References............................................................................182   Appendix ..............................................................................183

About the Author :
Dr. Paul J. Riccomini is a former high school math teacher and special education teacher. He provides numerous professional development workshops focused on improving mathematics education through the application of evidenced-based practices. Paul is the author of several research and practitioner articles describing instruction strategies to more effectively teach math.   Dr. Bradley Witzel is an assistant professor of special education at Winthrop University in Rock Hill, South Carolina. He has experience in the classroom as an inclusive and self contained teacher of students with higher incidence disabilities as well as a classroom assistant and classroom teacher of students with low incidence disabilities. Dr. Witzel has taught undergraduate and graduate courses in educational methods for students with disabilities and secondary students with disabilities coupled with ELL and LEP needs, introduction to learning disabilities, introduction to special education, functional behavior assessment, motivation and behavioral methods, elementary math methods, learning theories and strategies, and he has supervised interns in elementary, secondary, and special education certification tracks as well as inclusion practices. He has given numerous professional presentations including strategic math, algebra instruction, word problem solving, community and parent involvement for reading programs, motivational classroom management, and student-led IEPs. He has published research and practitioner articles in algebra education and math education for students with and without learning disabilities as well as functional assessment and motivation procedures. Additionally, he patented an algebra technique and is the author of the book, Multisensory Algebra, a hands-on resoure of pictorial algebra techniques. Dr. Witzel currently focuses on the development of special education teachers and works to provide researched-validated practices and interventions to pre-service and in-service teachers. Brad holds his B.S. in psychology and special education from James Madison University and his M.Ed. and Ph.D. in special education from the University of Florida.