Kindergarten to Grade 3 Geometry and Spatial Sense

Purpose 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 6, 2005.The present document provides:• an overview of each of the big ideas in the Geometry and Spatial Sense strand;• four appendices (Appendices A–D), one for each grade from Kindergartento Grade 3, which provide learning activities that introduce, develop, or helpto consolidate some aspect of each big idea. These learning activities reflectthe instructional practices recommended in A Guide to Effective Instructionin Mathematics, Kindergarten to Grade 6, 2005;• an appendix (Appendix E, forthcoming) that lists the curriculum expectationsin the Geometry and Spatial Sense strand under the big idea(s) to whichthey correspond. This clustering of expectations around each of the threebig ideas allows teachers to concentrate their programming on the big ideasof the strand while remaining confident that the full range of curriculumexpectations is being addressed;• a glossary that provides definitions of geometric 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 importantmathematical concepts, or “big ideas”, and the knowledge and skills that gowith those concepts. Programs that are organized around big ideas and focuson problem solving provide cohesive learning opportunities that allow studentsto explore concepts in depth.All learning, especially new learning, should be embedded in well-chosencontexts for learning – that is, contexts that are broad enough to allowstudents to investigate initial understandings, identify and developrelevant supporting skills, and gain experience with varied and interestingapplications of the new knowledge. Such rich contexts for learning openthe door for students to see the “big ideas”, or key principles, of mathematics,such as pattern or relationship. (Ontario Ministry of Education,2005b, p. 6)Students are better able to see the connections in mathematics and thus tolearn mathematics when it is organized in big, coherent “chunks”. In organizinga mathematics program, teachers should concentrate on the big ideas in2 A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 3 – Geometry and Spatial Sense