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Big Ideas
Formative Assessment Lesson
End of Unit Assessments
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Big Ideas
Formative Assessment Lesson
End of Unit Assessments
Big Idea:

### Three dimensional objects are composed of several two dimensional shapes.

1 week

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
• 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)
• describe three-dimensional objects generated by rotations of two-dimensional objects
• use tools to illustrate the images being created

• 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

Develop conceptual understanding:

net, surface area, cylinders, pyramids, cones, spheres, density

Supporting terms to communicate:

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

No Core Resource for this Big Idea.

Consider using the Instructional Routines linked below for teaching towards this Big Idea.

Instructional Routine: Contemplate then Calculate
These tasks are embedded within the instructional routine called Contemplate then Calculate.
• Lots of Dots
Use the structure of a set of dots to connect the density of dots to the area of dots and use proportional reasoning to quickly count the number of dots.
Resource:
Lots of Dots

Use the structure of a set of dots to connect the density of dots to the area of dots and use proportional reasoning to quickly count the number of dots.

All Resources From:
• Unit 5