Kindergarten to Grade 3
Data Management and Probability
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.
Printed on recycled paper
ISBN 978-1-4249-4587-0
07-015
Queens Printer for Ontario, 2007
Ministry of Education
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Purpose and Features of the Document . . . . . . . . . . . . . . . . . . . . . . . 2
Big Ideas in the Curriculum for Kindergarten to Grade 3 . . . . . . . . . 2
The Big Ideas in Data Management and Probability . . . . . . . . . . . 4
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
General Principles of Instruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Working Towards Equitable Outcomes for Diverse Students . . . . . . . . 6
Collection and Organization of Data . . . . . . . . . . . . . . . . . . . . . . . . 8
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8Collecting and Organizing Data to Answer Questions . . . . . . . . . . 9Sorting and Classifying . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13Organizing Data in Graphs, Charts, and Tables . . . . . . . . . . . . . . . . 14Graphs as a Means for Displaying Data and Communicating Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
Characteristics of Student Learning and Instructional Strategies by Grade . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Kindergarten . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19Grade 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20Grade 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21Grade 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
Data Relationships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24Levels of Comprehension in Reading Data . . . . . . . . . . . . . . . . . . . 24Analysing Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
Characteristics of Student Learning and Instructional Strategies by Grade . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
Kindergarten . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27Grade 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28Grade 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29Grade 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
Contents
iv A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 3 Data Management and Probability
Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31Likelihood as a Continuum From Impossible to Certain . . . . . . . . . 32Probability as a Basis for Predictions . . . . . . . . . . . . . . . . . . . . . . . . 33
Characteristics of Student Learning and Instructional Strategies by Grade . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
Kindergarten . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34Grade 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35Grade 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35Grade 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
Learning Activities for Data Management and Probability . . . . . . 39
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41The Mathematical Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42Accommodations and Modifications . . . . . . . . . . . . . . . . . . . . . . . 44
Providing Accommodations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44Modifying Curriculum Expectations . . . . . . . . . . . . . . . . . . . . . . 46
A Special Note About Kindergarten . . . . . . . . . . . . . . . . . . . . . . . . 47
Appendix A: Kindergarten Learning Activities . . . . . . . . . . . . . . . . 49
Collection and Organization of Data: Button, Button, Whos Lost a Button? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
Blackline masters: COK.BLM1 COK.BLM5
Data Relationships: What Kinds of Shoes Are We Wearing? . . . . . . . . . 59Blackline masters: DRK.BLM1 DRK.BLM3
Probability: What Will We See on Our Walk? . . . . . . . . . . . . . . . . . . . 67Blackline masters: ProbK.BLM1 ProbK.BLM14
Appendix B: Grade 1 Learning Activities . . . . . . . . . . . . . . . . . . . . . 71
Collection and Organization of Data: Our Favourite Things . . . . . . . . 73Blackline masters: CO1.BLM1 CO1.BLM3
Data Relationships: A Day of Favourite Activities . . . . . . . . . . . . . . . . . 79Blackline masters: DR1.BLM1 DR1.BLM2
Probability: Predictions for the Week . . . . . . . . . . . . . . . . . . . . . . . . . 85Blackline masters: Prob1.BLM1 Prob1.BLM2
Contents v
Appendix C: Grade 2 Learning Activities . . . . . . . . . . . . . . . . . . . . . 91
Collection and Organization of Data: Party Packs . . . . . . . . . . . . . . . . 93Blackline masters: CO2.BLM1 CO2.BLM3
Data Relationships: What Is the Graph About? . . . . . . . . . . . . . . . . . 99Blackline masters: DR2.BLM1 DR2.BLM7
Probability: Game Testers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107Blackline masters: Prob2.BLM1 Prob2.BLM5
Appendix D: Grade 3 Learning Activities . . . . . . . . . . . . . . . . . . . . 115
Collection and Organization of Data: Lost and Found . . . . . . . . . . . . 117Blackline masters: CO3.BLM1 CO3.BLM3
Data Relationships: A Good Nights Sleep . . . . . . . . . . . . . . . . . . . . . . 123Blackline masters: DR3.BLM1 DR3.BLM3
Probability: Take Off . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129Blackline masters: Prob3.BLM1 Prob3.BLM2
Appendix E: Correspondence of the Big Ideas and the CurriculumExpectations in Data Management and Probability . . . . . . . . . . . . 135
Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
1
This document is a practical guide that teachers will find useful in helping
students to achieve the curriculum expectations for mathematics outlined
in The Kindergarten Program, 2006 (on pages 4748, under the subheading
Data Management and Probability) and the expectations outlined in the
Data Management and Probability 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 Data Management and Probability
Purpose and Features of the DocumentThe present document was developed to provide practical applications of theprinciples 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 Da
