Evidence of Understanding

**visualize relationships between two-dimensional and three-dimensional objects**- explain the relationship between the 3-D geometric figure used to describe a physical object and a
**net**that is a 2-D representation of the surfaces of the 3-D geometric figure- make conjectures about reasonable shapes for calculating
**surface area** - describe the net as a single object or as an image that is composed of several objects
- partition nets using auxiliary lines to decompose the figure into triangles, rectangles, or semicircles

- make conjectures about reasonable shapes for calculating
- describe the two-dimensional cross-sections of three-dimensional objects
- explain that a two-dimensional cross-section can be used to know what that 2-D object looks like when rotated into a 3-D object
*(Example: a rectangle rotates into a cylinder)*

- explain that a two-dimensional cross-section can be used to know what that 2-D object looks like when rotated into a 3-D object
- describe three-dimensional objects generated by rotations of two-dimensional objects
- use tools to illustrate the images being created

- use tools to illustrate the images being created

- explain the relationship between the 3-D geometric figure used to describe a physical object and a
**use geometric shapes and their properties to describe and model a real world situation**- use formulas for surface areas or volumes to create and explain a model within the context of solving a design problem
*Example: designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios*

- approximate reasonable solutions to problems using volume and surface area formulas for
**cylinders, pyramids, cones, and spheres**- make choices, assumptions and approximations to simplify a complicated situation
- routinely interpret the results in the context of the situation and reflect on whether the results make sense

- apply concepts of
**density**based on area and volume in modeling situations*(Example: persons per square mile, BTUs per cubic foot)*- explain that density is a ratio between two quantities
- interpret ratios within the context of a situation

- use formulas for surface areas or volumes to create and explain a model within the context of solving a design problem

Develop conceptual understanding:

net, surface area, cylinders, pyramids, cones, spheres, densitySupporting terms to communicate:

area, volume, circumference, length, height, ratio, proportion, approximate, estimate, assume, constraints, per square unit, per cubic unit