Kindergarten to Grade 3 eWorkshop

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Kindergarten to Grade 3,Number Sense and Numeration. Ministry of Education,Printed on recycled paper,ISBN 0 7794 5402 2. Queen s Printer for Ontario 2003,Introduction vii,The 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 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. Une publication quivalente est disponible en fran ais sous le titre suivant. Guide d enseignement efficace des math matiques de la maternelle. la 3e ann e G om trie et sens de l espace,Quantity 32.
Overview 32,Understanding Quantity 34, Characteristics of Student Learning and Instructional Strategies. by Grade 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 71. Counting The Counting Game 73,Blackline masters CK BLM1 CK BLM2. Operational Sense Anchoring 5 79,Blackline masters OSK BLM1 OSK BLM5.
Quantity Toothpick Gallery 85,Blackline masters QK BLM1 QK BLM2. Relationships In the Bag 91,Blackline masters RelK BLM1 RelK BLM3. iv A Guide to Effective Instruction in Mathematics Kindergarten to Grade 3 Number Sense and Numeration. Representation I Spy a Number 97,Blackline masters RepK BLM1 RepK BLM2. Appendix B Grade 1 Learning Activities 103,Counting Healing Solutions 105. Blackline masters C1 BLM1 C1 BLM3,Operational Sense Train Station 111.
Blackline masters OS1 BLM1 OS1 BLM7,Quantity The Big Scoop 119. Blackline masters Q1 BLM1 Q1 BLM7,Relationships Ten in the Nest 125. Blackline masters Rel1 BLM1 Rel1 BLM6,Representation The Trading Game 131. Blackline masters Rep1 BLM1 Rep1 BLM4,Appendix C Grade 2 Learning Activities 139. Counting The Magician of Numbers 141,Blackline masters C2 BLM1 C2 BLM3.
Operational Sense Two by Two 147,Blackline masters OS2 BLM1. Quantity What s Your Estimate 155,Blackline masters Q2 BLM1 Q2 BLM4. Relationships Hit the Target 161,Blackline masters Rel2 BLM1 Rel2 BLM5. Representation Mystery Bags 167,Blackline masters Rep2 BLM1 Rep2 BLM9. Appendix D Grade 3 Learning Activities 177,Counting Trading up to 1000 179.
Blackline masters C3 BLM1 C3 BLM5, Operational Sense What Comes in 2 s 3 s and 4 s 185. Blackline masters OS3 BLM1 OS3 BLM2,Quantity Estimate How Many 193. Blackline masters Q3 BLM1 Q3 BLM6,Relationships What s the Relationship 201. Blackline masters Rel3 BLM1 Rel3 BLM3,Representation What Fraction Is It 207. Blackline masters Rep3 BLM1 Rep3 BLM5,Contents v, Appendix E Correspondence of the Big Ideas and the Curriculum.
Expectations in Number Sense and Numeration 213,Glossary 221. vi A Guide to Effective Instruction in Mathematics Kindergarten to Grade 3 Number Sense and Numeration. Introduction, This document is a practical guide that teachers will find useful in helping. students to achieve the curriculum expectations for mathematics outlined in the. Number Sense and Numeration strand of The Kindergarten Program 1998 and. the expectations outlined for Grades 1 3 in the Number Sense and Numeration. strand of The Ontario Curriculum Grades 1 8 Mathematics 1997 It is a compan. ion document to the forthcoming Guide to Effective Instruction in Mathematics. Kindergarten to Grade 3, 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 2003 effective instruction is identified as critical. to 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 Guide. to Effective Instruction in Mathematics Kindergarten to Grade 3 is being produced. to provide a framework for teaching mathematics This framework will include. specific strategies for developing an effective program and for creating a com. munity of learners in which students mathe,matical thinking is nurtured The strategies. 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 will also. provide strategies for assessment the use of,manipulatives and home connections. Purpose and Features of This Document, The present document was developed as a practical application of the principles. and theories behind good instruction that are elaborated in A Guide to Effective. Instruction in Mathematics Kindergarten to Grade 3. The present document provides, an overview of each of the big ideas in the Number Sense and Numeration.
four appendices Appendices A D 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 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 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,Big Ideas in the Curriculum for,Kindergarten to Grade 3. In developing a mathematics program it is important to concentrate on impor. tant mathematical concepts or big ideas and the knowledge and skills that go. with those concepts Programs that are organized around big ideas and focus on. problem solving provide cohesive learning opportunities that allow students to. explore concepts in depth, All learning especially new learning should be embedded in a context. Well chosen contexts for learning are those that are broad enough to. allow students to explore and develop initial understandings to identify. and develop relevant supporting skills and to gain experience with inter. esting applications of the new knowledge Such rich environments open. the door for students to see the big ideas of mathematics the major. underlying principles such as pattern or relationship Ontario Ministry. of Education and Training 1999 p 6, Children are better able to see the connections in mathematics and thus to learn. mathematics when it is organized in big coherent chunks In organizing a. mathematics program teachers should concentrate on the big ideas in mathe. matics and view the expectations in the curriculum policy documents for Kinder. garten and Grades 1 3 as being clustered around those big ideas. viii A Guide to Effective Instruction in Mathematics Kindergarten to Grade 3 Number Sense and Numeration. The clustering of expectations around big ideas provides a focus for student. learning and for teacher professional development in mathematics Teachers. will find that investigating and discussing effective teaching strategies for a big. idea is much more valuable than trying to determine specific strategies and. approaches to help students achieve individual expectations In fact using big. ideas as a focus helps teachers to see that the concepts represented in the cur. riculum expectations should not be taught as isolated bits of information but. rather as a connected network of interrelated concepts In building a program. teachers need a sound understanding of the key mathematical concepts for their. students grade level as well as an understanding of how those concepts connect. with students prior and future learning Ma 1999 Such knowledge includes. an understanding of the conceptual structure and basic attitudes of mathemat. ics inherent in the elementary curriculum Ma 1999 p xxiv as well as an. understanding of how best to teach the concepts to children Concentrating on. developing this knowledge will enhance effective teaching. Focusing on the big ideas provides teachers with a global view of the concepts. represented in the strand The big ideas also act as a lens for. making instructional decisions e g deciding on an emphasis for a lesson or. set of lessons,identifying prior learning, looking at students thinking and understanding in relation to the mathemati.
cal concepts addressed in the curriculum e g making note of the strategies. a child uses to count a set, collecting observations and making anecdotal records. providing feedback to students,determining next steps. communicating concepts and providing feedback on students achievement. to parents1 e g in report card comments, Teachers are encouraged to focus their instruction on the big ideas of mathemat. ics By clustering expectations around a few big ideas teachers can teach for depth. of understanding This document provides models for clustering the expectations. around a few major concepts and also includes activities that foster an under. standing of the big ideas in Number Sense and Numeration Teachers can use. these models in developing other lessons in Number Sense and Numeration as. well as lessons in the other strands of mathematics. 1 In this document parent s refers to parent s and guardian s. Introduction ix,The Big Ideas in,Number Sense and Numeration. Number is a complex and multifaceted concept A well developed. understanding of number includes a grasp not only of counting and. numeral recognition but also of a complex system of more and less. relationships part whole relationships the role of special numbers such. as five and ten connections between numbers and real quantities and. measures in the environment and much more, Ontario Ministry of Education and Training 1997 p 10.
To assist teachers in becoming familiar with using the big ideas of mathematics. in their instruction and assessment this section focuses on Number Sense. and Numeration one of the strands of the Ontario mathematics curriculum for. Kindergarten and Grades 1 3 This section identifies the five big ideas that form. the basis of the curriculum expectations in Number Sense and Numeration dur. ing the primary years and elaborates on the key concepts embedded within each. The big ideas or major concepts in Number Sense and. Numeration are the following,operational sense,relationships. representation,These big ideas are conceptually interdependent. equally significant and overlapping For example, meaningful counting includes an understanding that. there is a quantity represented by the numbers in the. count Being able to link this knowledge with the rela. tionships that permeate the base ten number system. gives students a strong basis for their developing number. sense And all three of these ideas counting quantity. RELATIONSHIPS,QUANTITY COUNTING,OPERATIONAL,REPRESENTATION. relationships have an impact on operational sense which incorporates the. actions of mathematics Present in all four big ideas are the representations that. are used in mathematics namely the symbols for numbers the algorithms and. other notation such as the notation used for decimals and fractions. In this section the five big ideas of Number Sense and Numeration are described. and explained examined in the light of what students are doing discussed in. terms of teaching strategies and finally in Appendices A D addressed through. appropriate grade specific learning activities,For each big idea in this section there is.
an overview which includes a general discussion of the development of the. big idea in the primary grades a delineation of some of the key concepts. inherent in the big idea and in some instances additional background infor. mation on the concept for the teacher, grade specific descriptions of 1 characteristics of learning evident in stu. dents who have been introduced to the concepts addressed in the big idea. under consideration and 2 instructional strategies that will support those. learning characteristics in the specific grade, 2 A Guide to Effective Instruction in Mathematics Kindergarten to Grade 3 Number Sense and Numeration. General Principles of Instruction, In this section specific instructional strategies are provided for each big idea in. Number Sense and Numeration in each primary grade However there are. many principles of instruction that apply in all the primary grades and in all the. Number Sense and Numeration strand of The Kindergarten Program 1998 and the expectations outlined for Grades 1 3 in the Number Sense and Numeration strand of The Ontario Curriculum Grades 1 8 Mathematics 1997 It is a compan ion document to the forthcoming Guide to Effective Instruction in Mathematics Kindergarten to Grade 3 The expectations outlined in the curriculum documents

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