Big Idea:

Big Idea 1

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

1 week

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.