Kindergarten to Grade 3

1 Kindergarten to Grade 3 Number Sense and NumerationPrinted on recycled paperISBN 0-7794-5402-203-345 (gl) Queen s Printer for Ontario, 2003 Ministry of EducationIntroduction .. viiThe Big Ideas in Number Sense and Numeration ..1 Overview ..1 General Principles of Instruction ..3 Counting ..5 Overview ..5 Key Concepts of Counting ..7 Instruction in Counting ..8 Characteristics of Student Learning and Instructional Strategies by Grade ..9 Kindergarten ..9 Grade 1 .. 11 Grade 2 .. 13 Grade 3 .. 14 Operational Sense .. 17 Overview .. 17 Understanding the Properties of the Operations.

2 22 Instruction in the Operations .. 23 Characteristics of Student Learning and Instructional Strategies by Grade .. 23 Kindergarten .. 23 Grade 1 .. 25 Grade 2 .. 27 Grade 3 .. 28 ContentsUne publication quivalente est disponible en fran ais sous le titre suivant :Guide d enseignement efficace des math matiques, de la maternelle la 3eann e G om trie et sens de l Guide to Effective Instruction in Mathematics, Kindergarten to Grade 3 Number Sense and NumerationQuantity .. 32 Overview .. 32 Understanding Quantity .. 34 Characteristics of Student Learning and Instructional Strategiesby Grade .

3 36 Kindergarten .. 36 Grade 1 .. 38 Grade 2 .. 40 Grade 3 .. 43 Relationships .. 46 Overview .. 46 Characteristics of Student Learning and Instructional Strategies by Grade .. 50 Kindergarten .. 50 Grade 1 .. 51 Grade 2 .. 52 Grade 3 .. 53 Representation .. 55 Overview .. 55 Characteristics of Student Learning and Instructional Strategies by Grade .. 57 Kindergarten .. 57 Grade 1 .. 59 Grade 2 .. 60 Grade 3 .. 62 References .. 64 Learning Activities for Number Sense and Numeration .. 67 Introduction .. 69 Appendix A: Kindergarten Learning Activities.

4 71 Counting: The Counting Game .. 73 Blackline masters: Operational Sense: Anchoring 5 .. 79 Blackline masters: Quantity: Toothpick Gallery! .. 85 Blackline masters: Relationships: In the Bag .. 91 Blackline masters: ContentsvRepresentation: I Spy a Number .. 97 Blackline masters: Appendix B: Grade 1 Learning Activities .. 103 Counting: Healing Solutions .. 105 Blackline masters: Operational Sense: Train Station .. 111 Blackline masters: Quantity: The Big Scoop .. 119 Blackline masters: : Ten in the Nest .. 125 Blackline masters: Representation: The Trading Game.

5 131 Blackline masters: Appendix C: Grade 2 Learning Activities .. 139 Counting: The Magician of Numbers .. 141 Blackline masters: Operational Sense: Two by Two .. 147 Blackline masters: Quantity: What s Your Estimate? .. 155 Blackline masters: Relationships: Hit the Target .. 161 Blackline masters: Representation: Mystery Bags .. 167 Blackline masters: Appendix D: Grade 3 Learning Activities .. 177 Counting: Trading up to 1000 .. 179 Blackline masters: Operational Sense: What Comes in 2 s, 3 s, and 4 s? .. 185 Blackline masters: Quantity: Estimate How Many.

6 193 Blackline masters: Relationships: What s the Relationship? .. 201 Blackline masters: Representation: What Fraction Is It? .. 207 Blackline masters: Guide to Effective Instruction in Mathematics, Kindergarten to Grade 3 Number Sense and NumerationAppendix E: Correspondence of the Big Ideas and the Curriculum Expectations in Number Sense and Numeration .. 213 Glossary .. 221viiThis document is a practical guide that teachers will find useful in helpingstudents to achieve the curriculum expectations for mathematics outlined in theNumber Sense and Numeration strand of The Kindergarten Program, 1998andthe expectations outlined for Grades 1 3 in the Number Sense and Numerationstrand of The Ontario Curriculum, Grades 1 8: Mathematics, 1997.

7 It is a compan-ion document to the forthcoming Guide to Effective Instruction in Mathematics, Kindergarten to Grade expectations outlined in the curriculum documents describe the knowledgeand skills that students are expected to acquire by the end of each Grade . InEarly Math Strategy: The Report of the Expert Panel on Early Math in Ontario(Expert Panel on Early Math, 2003), effective instruction is identified as criticalto the successful learning of mathematical knowledge and skills, and the compo-nents of an effective program are described. As part of the process of implement-ing the panel s vision of effective mathematics instruction for Ontario, A Guideto Effective Instruction in Mathematics, Kindergarten to Grade 3is being producedto provide a framework for teaching mathematics.

8 This framework will includespecific strategies for developing an effective program and for creating a com-munity of learners in which students mathe-matical thinking is nurtured. The strategiesfocus on the big ideas inherent in theexpectations; on problem-solving as themain context for mathematical activity; andon communication, especially student talk,as the conduit for sharing and developingmathematical thinking. The guide will alsoprovide strategies for assessment, the use ofmanipulatives, and home Guide to Effective Instruction in Mathematics, Kindergarten to Grade 3 Number Sense and NumerationPurpose and Features of This DocumentThe present document was developed as a practical application of the principlesand theories behind good instruction that are elaborated in A Guide to EffectiveInstruction in Mathematics, Kindergarten to Grade present document provides: an overview of each of the big ideas in the Number Sense and Numerationstrand.

9 Four appendices (Appendices A D), one for each Grade from Kindergarten toGrade 3, which provide learning activities that introduce, develop, or help toconsolidate some aspect of each big idea. These learning activities reflect theinstructional practices recommended in A Guide to Effective Instruction inMathematics, Kindergarten to Grade 3; an appendix (Appendix E) that lists the curriculum expectations in the Num-ber Sense and Numeration strand under the big idea(s) to which they corre-spond. This clustering of expectations around each of the five big ideas allowsteachers to concentrate their programming on the big ideas of the strandwhile remaining confident that the full range of curriculum expectations isbeing addressed.

10 Big Ideas in the Curriculum for Kindergarten to Grade 3In developing a mathematics program, it is important to concentrate on impor-tant mathematical concepts, or big ideas , and the knowledge and skills that gowith those concepts. Programs that are organized around big ideas and focus onproblem solving provide cohesive learning opportunities that allow students toexplore concepts in learning, especially new learning, should be embedded in a contexts for learning are those that are broad enough toallow students to explore and develop initial understandings, to identifyand develop relevant supporting skills, and to gain experience with inter-esting applications of the new knowledge.