Zooming In On Figures

Unit Overview

Type of Unit: Concept; Project

Length of Unit: 18 days and 5 days for project

Prior Knowledge

Students should be able to:

  • Find the area of triangles and special quadrilaterals.
  • Use nets composed of triangles and rectangles in order to find the surface area of solids.
  • Find the volume of right rectangular prisms.
  • Solve proportions.

Lesson Flow

  • After an initial exploratory lesson that gets students thinking in general about geometry and its application in real-world contexts, the unit is divided into two concept development sections: the first focuses on two-dimensional (2-D) figures and measures, and the second looks at three-dimensional (3-D) figures and measures.
  • The first set of conceptual lessons looks at 2-D figures and area and length calculations. Students explore finding the area of polygons by deconstructing them into known figures. This exploration will lead to looking at regular polygons and deriving a general formula. The general formula for polygons leads to the formula for the area of a circle. Students will also investigate the ratio of circumference to diameter ( pi ). All of this will be applied toward looking at scale and the way that length and area are affected. All the lessons noted above will feature examples of real-world contexts.
  • The second set of conceptual development lessons focuses on 3-D figures and surface area and volume calculations. Students will revisit nets to arrive at a general formula for finding the surface area of any right prism. Students will extend their knowledge of area of polygons to surface area calculations as well as a general formula for the volume of any right prism. Students will explore the 3-D surface that results from a plane slicing through a rectangular prism or pyramid. Students will also explore 3-D figures composed of cubes, finding the surface area and volume by looking at 3-D views.
  • The unit ends with a unit examination and project presentations.
Mathematics, Geometry
Material Type:
Unit of Study
Middle School
  • 3D
  • Geometry
  • Models
  • Polygons
  • Surface Area

    Lesson 2

    · Scissors (one pair for each student)

    · Rulers (one for each student)

    · Print copies of Area of Regular Polygons (one for each student). Print out, cut apart, and laminate if desired.

    Lesson 3

    • Graphing chart paper that is 12-inch by 12-inch with 1-inch spacing (one for each student)
    • A 12-inch by 12-inch piece of cardboard (one for each student)
    • Glue (one for each pair of students)
    • Ruler (one for each student)

    Lesson 4

    · String (several spools for the class)

    · Rulers (one for each student)

    · Scissors (one for each student)

    Lesson 6

    Ruler (one for each student)

    Lesson 7

    · Centimeter grid paper (one for each student)

    · Ruler (one for each student)

    · Compass (one for each student)

    Lesson 8

    · Base sheets for project (one for each student)

    · Square foot cardboard pieces to mount base sheets on (one for each student)

    · Rulers (one for each pair of students)

    · Protractors (one for each pair of students)

    Lesson 16

    Students’ centimeter grid layout to draw the nets

    Lesson 17

    · Origami cubes

    · Cardboard

    Lesson 18

    · Centimeter grid layout

    · 1-inch grid paper

    · Rulers

    · Scissors, tape, protractors (available as needed)

    Unit 4 Zooming In On Figures
    Zooming In On Figures

    Education Standards