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K–12 teaching and learning · from the UNC School of Education

Balancing shapes

http://illuminations.nctm.org/LessonDetail.aspx?ID=L642

A lesson plan for grade 6 Mathematics

Provider: National Council of Teachers of Mathematics


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Students balance shapes on the pan balance applet to study equality, which is essential to understanding algebra. After the teacher demonstrates how the balancing program works, students practice changing the weights in the pans and explain their procedure. Then, the class participates in a discussion about their discoveries about mathematical properties. The lesson provides a recording sheet and a link to a shapes tool for completing the activity.

Students will:

  • Develop an understanding of equality using shapes and a pan balance.
  • Apply the properties of equality to show that the balance is maintained.
  • Informally explore the Reflexive, Symmetric, Multiplication/Division, Transitive, and Addition/Subtraction Properties of Equality.
  • Recognize the relationship between a pan balance and an equation.
  • Draw conclusions based upon patterns in a table.

NCTM Standards and Expectations students cover in this lesson include:

  • Represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic rules.
  • Relate and compare different forms of representation for a relationship.
  • Develop an initial conceptual understanding of different uses of variables.
  • Model and solve contextualized problems using various representations, such as graphs, tables, and equations.

    • North Carolina Curriculum Alignment

    Mathematics (2004)

    Grade 6

    • Goal 1: Number and Operations - The learner will understand and compute with rational numbers.
      • Objective 1.07: Develop flexibility in solving problems by selecting strategies and using mental computation, estimation, calculators or computers, and paper and pencil.
    • Goal 4: Data Analysis and Probability - The learner will understand and determine probabilities.
      • Objective 4.03: Conduct experiments involving simple and compound events.
      • Objective 4.05: Determine and compare experimental and theoretical probabilities for independent and dependent events.
      • Objective 4.06: Design and conduct experiments or surveys to solve problems; report and analyze results