Tài liệu Number Sense and Numeration, Grades 4 to 6 Volume 4 Division docx

Number Sense

and Numeration,

Grades 4 to 6

Volume 4

Division

A Guide to Effective Instruction

in Mathematics,

Kindergarten to Grade 6

2006

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Every effort has been made in this publication to identify mathematics resources and tools

(e.g., manipulatives) in generic terms. In cases where a particular product is used by teachers

in schools across Ontario, that product is identified by its trade name, in the interests of clarity.

Reference to particular products in no way implies an endorsement of those products by

the Ministry of Education.

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Number Sense

and Numeration,

Grades 4 to 6

Volume 4

Division

A Guide to Effective Instruction

in Mathematics,

Kindergarten to Grade 6

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CONTENTS

Introduction 5

Relating Mathematics Topics to the Big Ideas............................................................................. 6

The Mathematical Processes............................................................................................................. 6

Addressing the Needs of Junior Learners ..................................................................................... 8

Learning About Division in the Junior Grades 11

Introduction.......................................................................................................................................... 11

Interpreting Division Situations...................................................................................................... 13

Relating Multiplication and Division............................................................................................. 14

Using Models to Represent Division ............................................................................................ 14

Learning Basic Division Facts.......................................................................................................... 16

Considering the Meaning of Remainders................................................................................... 16

Developing a Variety of Computational Strategies.................................................................. 17

Developing Estimation Strategies for Division.......................................................................... 23

A Summary of General Instructional Strategies........................................................................ 24

Appendix 4–1: Using Mathematical Models to Represent Division 25

References 31

Learning Activities for Division 33

Introduction.......................................................................................................................................... 33

Grade 4 Learning Activity................................................................................................................. 35

Grade 5 Learning Activity................................................................................................................. 48

Grade 6 Learning Activity................................................................................................................. 58

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INTRODUCTION

Number Sense and Numeration, Grades 4 to 6 is a practical guide, in six volumes, that teachers

will find useful in helping students to achieve the curriculum expectations outlined for Grades

4 to 6 in the Number Sense and Numeration strand of The Ontario Curriculum, Grades 1–8:

Mathematics, 2005. This guide provides teachers with practical applications of the principles

and theories behind good instruction that are elaborated on in A Guide to Effective Instruction

in Mathematics, Kindergarten to Grade 6, 2006.

The guide comprises the following volumes:

• Volume 1: The Big Ideas

• Volume 2: Addition and Subtraction

• Volume 3: Multiplication

• Volume 4: Division

• Volume 5: Fractions

• Volume 6: Decimal Numbers

The present volume – Volume 4: Division – provides:

• a discussion of mathematical models and instructional strategies that support student

understanding of division;

• sample learning activities dealing with division for Grades 4, 5, and 6.

A glossary that provides definitions of mathematical and pedagogical terms used throughout

the six volumes of the guide is included in Volume 1: The Big Ideas. Each volume also contains

a comprehensive list of references for the guide.

The content of all six volumes of the guide is supported by “eLearning modules” that are

available at www.eworkshop.on.ca. The instructional activities in the eLearning modules

that relate to particular topics covered in this guide are identified at the end of each of the

learning activities (see pp. 44, 55, and 68).

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