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