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

### 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.
• Comparing Perimeter, Area, and Volume
Resource:
Comparing Perimeter, Area, and Volume

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.

All Resources From:
• Unit 5