Measurement of 3D Figures

April 26 - May 19

Introduction

This unit bundles student expectations that address perimeter, area, and volume of two- and three-dimensional figures and composite figures, including effects of proportional and non-proportional dimensional changes. Concepts are incorporated into both non-contextual 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 explore surface area using concrete objects and nets of prisms, pyramids, cylinders and cones and make connections to formulas for lateral and total surface area for prisms, pyramids, cylinders and cones. Students are introduced to the formula for surface area of a sphere. Students apply formulas to determine lateral and total surface area of prisms, pyramids, cylinders, cones, and spheres from diagrams and attribute information, including composite figures. Students apply formulas to determine lateral and total surface area of prisms, pyramids, cylinders, cones, and spheres in real-world problem situations with appropriate measures, including effects of proportional and non-proportional linear dimension changes. Students explore volume using concrete models and investigate the differences between cylinders/cones and prisms/pyramids with congruent bases and heights and make connections to formulas for volume. Students are introduced to the formula for volume of a sphere. Students apply formulas to determine volume of prisms, pyramids, cylinders, cones, and spheres from diagrams and attribute information, including composite figures. Students apply formulas to determine lateral and total surface area and volume of prisms, pyramids, cylinders, cones, spheres, and composite figures in real-world problem situations with appropriate measures, including effects of proportional and non-proportional linear dimension changes.