Focus: To begin grade 6, students extend their prior knowledge about area to include shapes that are composed of more than just rectangles. Doing this draws on abilities developed in earlier grades to compose and decompose shapes, for example, to see a rectangle as composed of two congruent right triangles. Through activities sequenced to allow students to make sense of problems, students build on these abilities and their knowledge of area to find the areas of polygons by decomposing and rearranging them. They learn strategies for finding areas of parallelograms and triangles, and use regularity in repeated reasoning to develop formulas for these areas, using geometric properties to justify the correctness of these formulas.
They then use these formulas to solve problems. They build an understanding that any polygon can be decomposed into triangles, and use this knowledge to find areas of polygons. Students then apply this understanding to find the surface areas of polyhedra with triangular and rectangular surfaces. They study, assemble, and draw nets for polyhedra and use nets to determine surface areas. Students will also, throughout this unit, discuss their mathematical ideas and respond to the ideas of others.
Number of Lessons: 19
Lesson Time: Approximately 45 minutes. Please note that each lesson is designed for one instructional block, and may be divided into shorter segments based on teacher pacing and student needs.
Additional Search Terms:
region • quadrilateral • parallelogram • vertex • opposite vertex • edge • face • polyhedron • base • prism • pyramid • volume • exponent • squared • cubed • mathematical practices