Properties of Real Numbers 1
Lesson Plan

Developed byDavid McAdams
Last update29 Dec 2006
Grade Level10
SubjectIntermediate Algebra
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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
    Link Memorization 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

  7. Instructional Procedure
    1. Pre-Quiz
      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

  • Other Resources
    Representation of the Distributive Property

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