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
Unit Outline
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
None
Geo U5:

Extending to Three Dimensions

How are two dimensional and three dimensional objects related to each other?
4 weeks
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.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).★

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).★

Common Core: Additional Standards:
G-GMD.A.1

Explain volume formulas and use them to solve problems. Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. (e.g. Use dissection arguments, Cavalieri’s principle, and informal limit arguments.)

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.

Unit five is about describing, representing and using the relationships between two-dimensional and three-dimensional figures to model and solve problems arising in everyday life. Throughout the unit, students examine the relationships between 1-D, 2-D and 3-D geometric representations to determine which ones to apply in describing and modeling situations that are helpful in solving problems. Students study geometric objects by taking cross sections of compound 3-D objects, rotating 2-D figures in space, and analyzing the impact of dimensional changes to measurements, such as perimeter, area, and volume.

Essential Questions:

  • How are two dimensional and three dimensional objects related to each other?
  • How can we use geometric relationships to model the world and solve problems?
Printable Unit Plan
  • Geometry Unit Plan for Unit 5
    Resource:
    Geometry Unit Plan for Unit 5

    This is a printable version of the entire unit plan. You can make a copy of it and edit it or download and print it as needed.

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Unit Outline

9 Components

Every unit begins with an Initial Task and ends with a Balanced Assessment, both focusing on core mathematics of the unit. The core mathematics is developed through a series of resources around Big Ideas; as you move through the unit, keep students focused on how these ideas are connected and how they address mathematical problem solving. Before attempting the Balanced Assessment, students have an opportunity to synthesize their knowledge through a multi-day Formative Assessment Lesson and teacher-designed re-engagement lessons.

Initial Task See 1 itemHide 1 item

Big Ideas See 2 itemsHide 2 items

Formative Assessment Lesson See 1 itemHide 1 item

Re-engagement See 1 itemHide 1 item

End of Unit Assessments See 4 itemsHide 4 items