Extending to Three Dimensions

9 Components
Initial Task
Unfolding a Box
Big Ideas
Big Idea 1 Big Idea 2
Formative Assessment Lesson
Evaluating Statements About Enlargements
Re-engagement
Re-engagement for Unit 5
End of Unit Assessments
End of Unit Assessment for Unit 5 Performance Task for Unit 5 End of Unit Assessment Teacher Resources for GEO Unit 5 Find aligned Regents questions with Quiz Banker
Geo U5: Extending to Three Dimensions
Browse Components
Initial Task
Unfolding a Box
Big Ideas
Big Idea 1 Big Idea 2
Formative Assessment Lesson
Evaluating Statements About Enlargements
Re-engagement
Re-engagement for Unit 5
End of Unit Assessments
End of Unit Assessment for Unit 5 Performance Task for Unit 5 End of Unit Assessment Teacher Resources for GEO Unit 5 Find aligned Regents questions with Quiz Banker
Big Idea:

Big Idea 2

Three dimensional objects are composed of several two dimensional shapes.

1 week
See Standards
Common Core: Major Standards:
G-MG.A.1

Apply geometric concepts in modeling situations. Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).

G-MG.A.3

Apply geometric concepts in modeling situations. 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).★

G-MG.A.2

Apply geometric concepts in modeling situations. Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).★

Common Core: Additional Standards:
G-GMD.A.3

Explain volume formulas and use them to solve problems. Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.★

G-GMD.B.4

Visualize relationships between two‐dimensional and three‐dimensional objects. Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.

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.