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Gr. HS Unit: Extending to Three Dimensions

Unit Overview

Students’ experience with two-dimensional and three-dimensional objects is extended to include informal explanations of circumference, area and volume formulas. Additionally, students apply their knowledge of two-dimensional shapes to consider the shapes of cross-sections and the result of rotating a two-dimensional object about a line.

Essential Questions:

  • How is visualization essential to the study of geometry?
    • In what ways do visualization aids help to analyze the two-dimensional figure formed by a cross section of a three-dimensional figure?
    • In what ways does visualization help to determine what three-dimensional figured is formed by a rotation of a two-dimensional figure about a line?
    • How does visualization facilitate the selection of a geometric figure as a model for a real-world object?
  • How does geometry explain or describe the structure of our world?
    • In what ways do geometric shapes, their measures and their properties, describe real-world objects?
  • How can reasoning be used to establish or refute conjectures?
    • What type of argument must be presented to establish the validity of formulas for circumference of a circle, area of a circle and volume of a cylinder, pyramid or cone?

A question is essential when it stimulates multi-layered inquiry, provokes deep thought and lively discussion, requires students to consider alternatives and justify their reasoning, encourges re-thinking of big ideas, makes meaningful connections with prior learning, and provides students with opportunities to apply problem-solving skills to authentic situations.

Unit Lesson

Additional information such as Teachers Notes, Enduring Understandings,Content Emphasis by Cluster, Focus Standards, Possible Student Outcomes, Essential Skills and Knowledge Statements and Clarifications, and Interdisciplinary Connections can be found in this Lesson Unit.