Math Content Standards
This PBL is suitable for a Geometry classroom comprised primarily of freshman students. The PBL will primarily focus on solving a real world design problem incorporating volume and surface area attributes. The following is a list of Indiana Academic Standards (2014) that will be addressed within our PBL. Each listed standard is followed by a description of the student activities that support the standard.
GEOMETRY
The Mathematics standards for Geometry are supplemented by the Process Standards for Mathematics.
The Mathematics standards for Geometry are made up of 5 strands: Logic and Proofs; Points, Lines, Angles, and Planes; Triangles; Quadrilaterals and Other Polygons; Circles; Transformations; and Three-dimensional Solids. The skills listed in each strand indicate what students should know and be able to do in Geometry.
Quadrilaterals and Other Polygons
G.QP.5: Deduce formulas relating lengths and sides, perimeters, and areas of regular polygons. Understand how limiting cases of such formulas lead to expressions for the circumference and the area of a circle.
Three Dimensional Solids
G.TS.1: Describe relationships between the faces, edges, and vertices of three-dimensional solids. Create a net for a given three-dimensional solid. Describe the three-dimensional solid that can be made from a given net (or pattern).
G.TS.5: Solve real-world and other mathematical problems involving volume and surface area of prisms, cylinders, cones, spheres, and pyramids, including problems that involve algebraic expressions.
G.TS.6: Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).
The Mathematics standards for Geometry are supplemented by the Process Standards for Mathematics.
The Mathematics standards for Geometry are made up of 5 strands: Logic and Proofs; Points, Lines, Angles, and Planes; Triangles; Quadrilaterals and Other Polygons; Circles; Transformations; and Three-dimensional Solids. The skills listed in each strand indicate what students should know and be able to do in Geometry.
Quadrilaterals and Other Polygons
G.QP.5: Deduce formulas relating lengths and sides, perimeters, and areas of regular polygons. Understand how limiting cases of such formulas lead to expressions for the circumference and the area of a circle.
- Learners will analyze the relationship between the dimensions of a polygon and the resulting surface area and volume through the "Shape and Surface Area/Volume" activity and will be able to conclude how the surface area to volume ratio has a strong effect at the nanoscale.
Three Dimensional Solids
G.TS.1: Describe relationships between the faces, edges, and vertices of three-dimensional solids. Create a net for a given three-dimensional solid. Describe the three-dimensional solid that can be made from a given net (or pattern).
- Learners will create a three-dimensional scaled model of their final device using their knowledge of nets of a three-dimensional solid.
G.TS.5: Solve real-world and other mathematical problems involving volume and surface area of prisms, cylinders, cones, spheres, and pyramids, including problems that involve algebraic expressions.
- Learners will compose a plan to develop various technological devices from analyzing real-world industry standards.
- Learners will analyze the results of their research and apply it to their understanding of surface area and volume relationships when evaluating the materials and product costs to help create their device.
G.TS.6: Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).
- Learners will design the "Next Big Thing" to satisfy project criteria, which may include cost, functionality, size, and/or marketability.