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 1

Physical objects can be described using 1-D, 2-D and 3-D geometric objects.

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).★

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.★

Evidence of Understanding

  • describe how dimensional changes impact perimeter, area, and volume
    • measure and compare different lengths of objects, compare units of measure and understand their size and scale in relation to one another (for example, size of meter vs inch)
      • set up ratios and proportionsto convert units
    • use units to explain the relationship between one, two, and three dimensions
    • investigate how perimeter, area and volume scales under similarity transformations
      • given different length measures, compare the area or volume of the same object
    • determine dimensions of a figure using its perimeter, area, or volume
      • use constraints within a situation to solve problems across dimensions and justify solutions
  • explain perimeter, area, and volume formulas and use them to solve problems
    • justify the formulas for the circumference and the area of a circle
    • make comparisons between areas of different objects using dissection arguments
    • partition three-dimensional shapes into smaller shapes to compare these shapes
      • make conjectures and justify how 3-D objects that have the same height and cross-sections of equal area will have equal volume
      • use dissection arguments, Cavalieri’s principle, similarityand informal limit arguments
    • give an informal argument for the formulas for the volume of a cylinder, pyramid, and cone
      • describe how area formulas extend into three dimensions to create volume formulas
    • identify geometric shapes that best describe a real world shape and determine which dimension to work with (Example: modeling a tree trunk or a human torso as a cylinder)
      • approximate reasonable solutions to problems using volume formulas
      • work backwards from a formula to determine the value of a specific measurement within the context of the situation
    • calculate the perimeter, area, or volume of an irregular shape by partitioning it into “familiar” pieces and summing the pieces (or finding the difference between the pieces)

Develop conceptual understanding:

scale, perimeter, area, volume, circumference, cross-section, cylinder, pyramid, cone

Supporting terms to communicate:

length, units of measure, scale, ratios, radius, proportions, similarity, decompose
Core Resource
A core resource supports multiple days of instruction.
  • Comparing Perimeter, Area, and Volume
    Resource:
    Comparing Perimeter, Area, and Volume

    Geometry & Algebra II Archive

    Geo U5: Extending to Three Dimensions

    Big Idea: Big Idea 1

    These three parts are intended to support students in making connections between 2 dimensional and 3 dimensional objects, especially how scaling changes these objects and how we can carefully partition objects in order to make relationships between two otherwise different geometric shapes.

    Preview ResourceAdd a Copy of Resource to my Google Drive
    Type
    Geometry: Extending to Three Dimensions
    File
    Google Doc
    Tags
    cavalieri's principle, perimeter, similarity, surface area, volume
    Standards
    Common Core: Major Standards ( G-MG.A.1, G-MG.A.3 ) Common Core: Additional Sta…
    +— Details
    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).★

    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.★

    All Resources From: