# Computation of Fractions: Math Intervention for Elementary and Middle Grades Students, CourseSmart eTextbook

Published Date: Oct 29, 2008

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## Description

Give your special education and general education students who struggle with mathematical fractions the support they need to succeed with these easy-to-implement, research-based lesson plans.

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, step-by-step 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 are confident helping every student succeed.

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

References............................................................................182

Appendix ..............................................................................183

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\$19.99 | ISBN-13: 978-0-13-715413-5