Relationships of 2 & 3 Dimensional Figures

February 25 - March 26

Introduction

This unit bundles student expectations that address exploring geometric relationships between sides, angles, and diagonals of various quadrilaterals to justify the type of quadrilateral; investigating patterns to make conjectures and generalizations about polygons; and identifying two-dimensional cross-sections of three-dimensional figures as well as identifying three-dimensional objects generated by rotations of two-dimensional shapes. Concepts are incorporated into both mathematical and real-world problem situations. According to the Texas Education Agency, mathematical process standards including application, tools and techniques, communication, representations, relationships, and justifications should be integrated (when applicable) with content knowledge and skills so that students are prepared to use mathematics in everyday life, society, and the workplace.

During this Unit

Students define types of quadrilaterals with a focus on identifying the characteristics (including sides, angles, and diagonal relationships) of parallelograms, rectangles, rhombi, and squares. Students use the characteristics of the quadrilateral to prove quadrilaterals are parallelograms, rectangles, rhombi, or squares using coordinate geometry, two column proofs, paragraph proofs, and flow charts. Students apply quadrilateral relationships to solve real-world problems involving lengths of sides, angles, and midpoints. Students define and identify polygons, including regular polygons by number of sides. Students use tabular, graphical, and symbolic generalization to develop formulas for interior and exterior angles in terms of number of sides. Students extend and apply the properties of quadrilaterals and other polygons and interior and exterior angle theorems to determine lengths of sides, diagonals, midpoints, and all angle measures. Students identify shapes of two-dimensional cross sections of prisms, pyramids, cylinders, cones, and spheres. Students explore and identify three-dimensional objects generated by rotations of two-dimensional shapes.