Introduction to Mathematical Visualization
Lesson Plan

Developed byDavid McAdams
Last update28 Dec 2006
Grade Level10
SubjectIntermediate Algebra
Online HTML
CopyrightUnpublished copyright work © 2006, David McAdams, Orem Utah. This document may be duplicated for non-commercial educational use only.
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  1. Lesson Model
    Direct Instruction Model

  2. Goal(s)/Standards

  3. Specific Objectives
    At the end of the lesson the student will be able to:

  4. Materials and Preparation

  5. Prerequisite Vocabulary

  6. Prerequisite Methodology
    Direct Instruction Model

  7. Instructional Procedure
    1. Gathering Activity - Think, Pair, Share.
      Have the students write in their journals how they might represent the equation 3 + 5 = 8 using a drawing. After a few minutes, have the students pair up and compare their representations. Have them discuss the relative merits of the various representations. Have each pair share with the class their representation and its merits.

    2. Internet Activity (optional)
      Explore representations using Introduction to Geometric Representation in Algebra. This activity can be used in conjunction with the worksheet.

    3. Review - Measurement Activate prior knowledge of measurement of lengths by discussing various ways to measure the length of a line. Then ask the class to identify the area of a 3 x 5 rectangle. Ask if this is a reasonable representation of the algebraic fact 3 · 5 = 15.

    4. State the problem and objective
      1. State that geometric representations of algebraic principles can help us understand.
      2. State and write on the board that the student will be able to:
        • Represent addition and multiplication with arrays of dots and with lines.
        • Identify strengths and weaknesses of geometric figures.
        • Identify parts of a graph in Cartesian Coordinates.
        • Show an emerging ability to represent three dimensional mathematics operation by building and explaining a three dimensional model of (a + b)3.

    5. Guided Practice - Visualization Worksheet

    6. Introduce the idea of three dimensional models of algebraic relationships.
      1. Refer to the one dimensional model of a + b and the two dimensional model of (a + b)2 = a2 + 2ab + b2 in the worksheet.
      2. Ask the students how they might represent (a + b)3 = a3 + 3a2b + 3ab2 + b3.
      3. Pass out the template for (a + b)3. Have the students assemble the three dimensional figure, and then explain it to their partner. When they are ready, have them explain it to the teacher.

  8. Differentiation for Diverse Student Needs

  9. Assessments

  10. Fast Finishers
    1. Math Line Art
      Thumbnail of circle 1 line art page. Circle 1 Line Art Do-it-yourself circle line art page to print and draw.
      Thumbnail of circle 2 line art page. Circle 2 Line Art Do-it-yourself circle line art page to print and draw.
      Thumbnail of triangle 22 line art page. Triangle 22 Line Art Do-it-yourself triangle line art page to print and draw.
      Thumbnail of pentagon 17 line art page. Pentagon 17 Line Art Do-it-yourself pentagon line art page to print and draw.
      Thumbnail of square 22 line art page. Square 22 Line Art Do-it-yourself square line art page to print and draw.
      Thumbnail of intersection 1 line art page. Line Intersection 1 Line Art Do-it-yourself line intersection line art page to print and draw.
    2. Geometric Nets
      ExampleNameDescriptionPrintable Net
      Example of a geometric net for a cube.


      A cube is a regular polyhedron made up of squares

      Geometric net for a cuboctahedron.



      Geometric net for a dodecahedron.



      Geometric net for a icosahedron.



      Geometric net for a icosidodecahedron.



      Example of a geometric net for a pentagonal antiprism.

      Pentagonal antiprism

      A pentagonal antiprism is a 12 sided solid consisting of two pentagons connected by alternating triangles.

      Example of a geometric net for a rectangular pyramid.

      Rectangular pyramid

      A rectangular pyramid has a square base and triangles coming to a point. In this example, isosceles triangles are used.

      Example of a geometric net for a snub cube.

      Snub cube

      A snub cube

      Example of a geometric net for a square antiprism.

      Square antiprism

      A square antiprism consists of two squares connected by alternating triangles.

      Example of a geometric net for a tetrahedron.


      A tetrahedron

      Example of a geometric net for a dodecahedron.


      A dodecahedron

      Example of a geometric net for a truncated cube.

      Truncated cube

      A truncated cube is a cube whose corners have been truncated, or 'cut off'. Each side of the cube becomes a regular octahedron (an eight sided figure where the length of each side is the same), and the corners become isosceles triangles.


  11. Other Resources

  12. Materials Masters
    Download Template for (a + b)3 = a3 + 3a2b + 3ab2 + b3
    Download Visualization Worksheet.