Park City Mathematics Institute
Geometrical Concepts from Constructions, Models, and Investigations

Build It as A Group
Ginny Burton and Kelley Butler

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Group activity.

Grades 7-9


Two-50 minute class periods.

Group interaction is a highlight of this lesson.

  • Student roles are clearly defined. Participation by all students is necessary to complete the activity.
  • There are multiple entry points for students to succeed, as well as the expectation that multiple representations are given.
  • Student and Teacher Task Cards are attached.

The Lesson is divided into three parts:
Task 1: Each student in a group builds a different shape and increases each of its dimensions by a scale factor of two.

  • They use Cuisenaire Rods to form the shapes.
  • They discover relationships about the surface area and volume of the original shape.

Task 2: Students with the same model are grouped together to become "experts" of their shape. Each group is devoted to one shape.

Task 3: Students return to original groups (Task 1 groups) to develop a poster to communicate their findings.

There is an optional Gallery Walk for groups to share their conclusions and representations.


  • Students understand and communicate the relationships among scale factors in one-, two-, and three-dimensional geometry.
  • Students will also demonstrate the ability to work effectively as a group.
  • Students may use different construction methods to scale up the shapes.

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This material is based upon work supported by the National Science Foundation under DMS-0940733 and DMS-1441467. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.