Understand and analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about surface area and volume Use visualization, spatial reasoning, and properties and relationships of geometric figures to solve problems involving geometry including those in real life
Conceptual Framework
form model, space, change in the context of Globalization and Sustainability
Statements of Inquiry
Understanding form and shape enhances creativity and productivity
Factual
How do we measure the surface area and volume of a solid?
Conceptual
For similar 3-D objects how are linear, area and volume scale factors related?
How are the area and volume formulae derived?
Debatable
What is changed and unchanged when we make a scale model?
Why do babies lose heat more quickly than adults?
Description
The purpose of this unit is to consolidate understanding of perimeter and area triangles, quadrilaterals, and other irregularly shaped polygons, including composite figures and then extend that knowledge into three dimensional space. Students will explore volume and capacity in familiar 3-D shapes and extend understanding to determine surface area of right prisms, pyramids, cylinders and spheres. Google provides excellent tools to allow students to explore relative areas and to measure famous structures to develop a greater sense of spatial awareness. Students will observe and investigate how quantities such as surface area and volume change when objects are enlarged or reduced in size. We hope to build an appreciation of three dimensional form and how knowledge of shape can help students solve real life problems by creating sustainable models to find optimal solutions.
Learning Outcomes
Use formulas to find the areas of rectangles, parallelograms, triangles, trapezoids, rhombi, kites, polygons and composite shapes
Use area formulas to solve problems
Investigate and use formulas to find the surface areas of prisms, pyramids, cylinders and cones
Investigate and use formulas for finding the volumes of prisms, pyramids, cylinders, cones and spheres.
Derive a formula for the surface area of a sphere
Solve problems involving volumes and surface areas of objects
Define similar polygons and 3-D solids
Investigate area and volume relationships in similar polygons and 3-D solids
Select and use appropriate units for perimeter, area, surface area, volume, and circumference
Use a tool to investigate relative areas of structures, countries and continents
Design and construct an optimal geometric object to solve a real world problem