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Geometry and Spatial Sense Every Effort Has Been Made in This Publication to Identify Mathematics Resources and Tools (E.G., Manipulatives) in Generic Terms

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Geometry and Spatial Sense Every Effort Has Been Made in This Publication to Identify Mathematics Resources and Tools (E.G., Manipulatives) in Generic Terms Grades 1 to 3 Geometry and Spatial Sense 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. Ministry of Education Printed on recycled paper ISBN 978-1-4606-8924-0 (Print) ISBN 978-1-4606-8925-7 (PDF) © Queen’s Printer for Ontario, 2016 Contents Introduction ......................................................................................... 1 Purpose and Features of This Document ................................................ 2 “Big Ideas” in the Curriculum for Grades 1 to 3 ..................................... 2 The “Big Ideas” in Geometry and Spatial Sense ................................. 5 Overview ............................................................................................... 5 General Principles of Instruction ............................................................ 6 Geometric Properties of Two-Dimensional Shapes and Three-Dimensional Figures.................................................................. 9 Overview ............................................................................................... 9 Levels of Geometric Thinking ................................................................ 14 What Geometric Properties Should Students Learn About? .................... 15 Characteristics of Student Learning and Instructional Strategies by Grade ............................................................................................... 19 Grade 1 ............................................................................................ 19 Grade 2 ............................................................................................ 21 Grade 3 ............................................................................................ 23 Geometric Relationships ..................................................................... 25 Overview ............................................................................................... 25 Characteristics of Student Learning and Instructional Strategies by Grade ............................................................................................... 31 Grade 1 ............................................................................................ 31 Grade 2 ............................................................................................ 34 Grade 3 ............................................................................................ 37 Une publication équivalente est disponible en français sous le titre suivant : Guide d’enseignement efficace des mathématiques de la maternelle à la 3e année – Géométrie et sens de l’espace, 2003. Location and Movement ..................................................................... 41 Overview ............................................................................................... 41 Characteristics of Student Learning and Instructional Strategies by Grade ............................................................................................... 45 Grade 1 ............................................................................................ 45 Grade 2 ............................................................................................ 46 Grade 3 ............................................................................................ 47 References ........................................................................................... 51 Learning Activities for Geometry and Spatial Sense .......................... 53 Introduction .......................................................................................... 55 Appendix A: Grade 1 Learning Activities ............................................ 57 Geometric Properties of Two-Dimensional Shapes: Explore-a-Shape ...... 59 Blackline masters: Prop2D1.BLM1 – Prop2D1.BLM5 Geometric Properties of Three-Dimensional Figures: Famous Figures ..... 67 Blackline masters: Prop3D1.BLM1 – Prop3D1.BLM4 Geometric Relationships: Pattern Block Pets ........................................... 75 Blackline masters: GeoRel1.BLM1 – GeoRel1.BLM5 Location and Movement: Simply Symmetrical ....................................... 83 Blackline masters: Loc1.BLM1 – Loc1.BLM3 Appendix B: Grade 2 Learning Activities ............................................ 89 Geometric Properties of Two-Dimensional Shapes: Polygons on Parade ... 91 Blackline masters: Prop2D2.BLM1 – Prop2D2.BLM4 Geometric Properties of Three-Dimensional Figures: Build It in 3-D ....... 99 Blackline masters: Prop3D2.BLM1 – Prop3D2.BLM2 Geometric Relationships: Geometry Exploration Centres ....................... 105 Blackline masters: GeoRel2.BLM1 – GeoRel2.BLM9 Location and Movement: Are We There Yet? ......................................... 113 Blackline masters: Loc2.BLM1 – Loc2.BLM4 Appendix C: Grade 3 Learning Activities ............................................ 119 Geometric Properties of Two-Dimensional Shapes: Geoboard Gems ...... 121 Blackline masters: Prop2D3.BLM1 – Prop2D3.BLM2 Geometric Properties of Three-Dimensional Figures: Nets or Not ........... 129 Blackline masters: Prop3D3.BLM1 – Prop3D3.BLM4 iv A Guide to Effective Instruction in Mathematics, Grades 1 to 3 – Geometry and Spatial Sense Geometric Relationships: Shapes From Shapes ...................................... 137 Blackline masters: GeoRel3.BLM1 – GeoRel3.BLM3 Location and Movement: Quite the Quilts ............................................. 147 Blackline masters: Loc3.BLM1 – Loc3.BLM6 Appendix D: Correspondence of the Big Ideas and the Curriculum Expectations in Geometry and Spatial Sense ..................................... 157 Overall Expectations .............................................................................. 159 Specific Expectations in Relation to the Big Ideas ................................... 159 Glossary ............................................................................................... 165 Contents v Introduction This document is a practical guide that teachers will find useful in helping students to achieve the curriculum expectations outlined in the Geometry and Spatial Sense strand for Grades 1 to 3 in The Ontario Curriculum, Grades 1–8: Mathematics, 2005. 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 components of an effective program are described. As part of the process of implementing the panel’s vision of effective mathematics instruction for Ontario, A Guide to Effective Instruction in Mathematics, Grades 1 to 3 provides a framework for teach- ing 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 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 shar- ing and developing mathematical thinking. The guide also provides strategies for assessment, the use of manipulatives, and home connections. 1 Purpose and Features of This Document This present document provides: • an overview of each of the big ideas in the Geometry and Spatial Sense strand; • three appendices (Appendices A–C), one for each of Grades 1 to 3, which provide learning activities that introduce, develop, or help to consolidate some aspect of each big idea; • an appendix (Appendix D) that lists the curriculum expectations in the Geometry and Spatial Sense strand under the big idea(s) to which they correspond. 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; • a glossary that provides definitions of geometric terms used in this document. “Big Ideas” in the Curriculum for Grades 1 to 3 In developing a mathematics program, it is essential to concentrate on important 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 well-chosen contexts for learning – that is, contexts that are broad enough to allow students to investigate initial understandings, iden- tify and develop relevant supporting skills, and gain experience with varied and interesting applications of the new knowledge. Such rich contexts for learning open the door for students to see the “big ideas”, or key principles, of mathematics, such as pattern or relationship. This understanding of key principles will enable and encourage students to use mathematical reasoning throughout their lives. (Ontario Ministry of Education, 2005, p. 25) Students are better
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