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  • Kindergarten to Grade 3

    Measurement

  • Printed on recycled paper

    ISBN 978-1-4249-4585-6

    07-007

    Queens Printer for Ontario, 2007

    Every effort has been made in this publication to identify mathematics resources andtools (e.g., manipulatives) in generic terms. In cases where a particular product is usedby teachers in schools across Ontario, that product is identified by its trade name, in theinterests of clarity. Reference to particular products in no way implies an endorsementof those products by the Ministry of Education.

    Ministry of Education

  • cm

    kg

    mL

    Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

    Purpose and Features of the Document . . . . . . . . . . . . . . . . . . . . . . . . 2

    Big Ideas in the Curriculum for Kindergarten to Grade 3 . . . . . . . . . 2

    The Big Ideas in Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

    Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

    General Principles of Instruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

    Working Towards Equitable Outcomes for Diverse Students . . . . . . . . 6

    Attributes, Units, and Measurement Sense . . . . . . . . . . . . . . . . . . . 8

    Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

    Measurable Attributes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

    Measurement Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

    Measurement Sense . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

    Characteristics of Student Learning and Instructional Strategies by Grade . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

    Kindergarten . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21Grade 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23Grade 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26Grade 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

    Measurement Relationships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

    Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

    Comparing and Ordering Objects According to Measurable Attributes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

    Relationships Between Measurement Units . . . . . . . . . . . . . . . . . . . . . 33

    Characteristics of Student Learning and Instructional Strategies by Grade . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

    Kindergarten . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34Grade 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35Grade 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37Grade 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

    References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

    Contents

  • iv A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 3 Measurement

    Learning Activities for Measurement . . . . . . . . . . . . . . . . . . . . . . . 43

    Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45The Mathematical Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46Accommodations and Modifications . . . . . . . . . . . . . . . . . . . . . . . 48A Special Note About Kindergarten . . . . . . . . . . . . . . . . . . . . . . . . 51

    Appendix A: Kindergarten Learning Activities . . . . . . . . . . . . . . . . 53

    Attributes, Units, and Measurement Sense Length: Measuring Up! . . . 55Blackline masters: LengthK.BLM1 LengthK.BLM3

    Measurement Relationships Area: Islands . . . . . . . . . . . . . . . . . . . . . 61Blackline master: AreaK.BLM1

    Measurement Relationships Mass: Mass-ive Animals . . . . . . . . . . . . 67Blackline master: MassK.BLM1

    Appendix B: Grade 1 Learning Activities . . . . . . . . . . . . . . . . . . . . . 73

    Measurement Relationships Length: Measuring Snakes . . . . . . . . . . 75Blackline masters: Length1.BLM1 Length1.BLM3

    Measurement Relationships Area: Newspaper Photographs . . . . . . . 83Blackline masters: Area1.BLM1 Area1.BLM3

    Attributes, Units, and Measurement Sense Capacity: Hungry Hounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

    Blackline masters: Cap1.BLM1 Cap1.BLM3

    Appendix C: Grade 2 Learning Activities . . . . . . . . . . . . . . . . . . . . . 97

    Attributes, Units, and Measurement Sense Length: If the Shoe Fits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

    Blackline masters: Length2.BLM1 Length2.BLM3

    Attributes, Units, and Measurement Sense Area: Wet Paintings . . . . 107Blackline masters: Area2.BLM1 Area2.BLM2

    Measurement Relationships Capacity: Sizing Up Containers . . . . . . 115Blackline masters: Cap2.BLM1 Cap2.BLM2

    Appendix D: Grade 3 Learning Activities . . . . . . . . . . . . . . . . . . . . 119

    Attributes, Units, and Measurement Sense Perimeter: A Geometry Mobile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

    Blackline masters: Per3.BLM1 Per3.BLM4

    Attributes, Units, and Measurement Sense Area: Toy House Carpets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

    Blackline masters: Area3.BLM1 Area3.BLM5

    Measurement Relationships Mass: Kilogram Comparisons . . . . . . . . 135Blackline master: Mass3.BLM1

  • Contents v

    Appendix E: Correspondence of the Big Ideas and the CurriculumExpectations in Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

    Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147

  • 1

    cm kgmL

    This document is a practical guide that teachers will find useful in helping

    students achieve the curriculum expectations for mathematics outlined in

    The Kindergarten Program, 2006 (on page 46, under the subheading Measurement)

    and the expectations outlined in the Measurement strand for Grades 1 to 3 in

    The Ontario Curriculum, Grades 18: Mathematics, 2005. It is a companion document

    to A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 6, 2006.

    The expectations outlined in the curriculum documents describe the knowledge

    and skills that students are expected to acquire by the end of each grade. In Early

    Math Strategy: The Report of the Expert Panel on Early Math in Ontario (Expert Panel

    on Early Math in Ontario, 2003), effective instruction is identified as critical to

    the successful learning of mathematical knowledge and skills, and the components

    of an effective program are described. As part of the process of implementing

    the panels vision of effective mathematics instruction for Ontario, A Guide to

    Effective Instruction in Mathematics, Kindergarten to Grade 6, 2006 provides a

    framework for teaching mathematics. This framework includes specific strategies

    for developing an effective program and for creating a community of learners

    in which students mathematical thinking is nurtured. The strategies described

    in the guide focus on the big ideas inherent in the expectations; on problem

    solving as the main context for mathematical activity; and on communication,

    especially student talk, as the conduit for sharing and developing mathematical

    thinking. The guide also provides strategies for assessment, the use of manipula-

    tives, and home connections.

    Introduction

  • 2 A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 3 Measurement

    Purpose and Features of the DocumentThe present document was developed to provide practical applications of the

    principles and theories behind good instruction that are elaborated in A Guide

    to Effective Instruction in Mathematics, Kindergarten to Grade 6, 2006.

    The present document provides:

    an overview of each of the big ideas in the Measurement strand;

    four appendices (Appendices AD), one for each grade from

    Kindergarten to Grade 3, which provide learning activities that

    introduce, develop, or help to consolidate some aspect of each big idea.

    These learning activities reflect the instructional practices recommended

    in A Guide to Effective Instruction in Mathematics, Kindergarten to

    Grade 6, 2006 ;

    an appendix (Appendix E) that lists the curriculum expectations in

    the Measurement strand under the big idea to which they correspond.

    This clustering of expectations around each of the two big ideas allows

    teachers to concentrate their programming on the big ideas of the

    strand while remaining confident that the full range of curriculum

    expectations is being addressed;

    a glossary that provides definitions of mathematical terms used in this

    document.

    Big Ideas in the Curriculum for Kindergarten to Grade 3In developing a mathematics program, it is vital to concentrate on important

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