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

Magic Squares

http://illuminations.nctm.org/LessonDetail.aspx?ID=L263

A lesson plan for grades 6–7 Mathematics

Provider: National Council of Teachers of Mathematics


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This lesson explores magic squares from both a historical and mathematical perspective. The mathematical analysis leads into symbolic algebraic representation of the patterns. Illuminations provides an activity sheet that explains the historical context of magic squares for students to use when completing the activity.

Students will be able to:

  • Use operations with integers to solve problems.
  • Analyze and represent patterns with symbolic rules.

NCTM Standards and Expectations covered in this lesson include:

  • Representing, analyzing, and generalizing a variety of patterns with tables, graphs, words, and, when possible, symbolic rules.
  • Developing meaning for integers and representing and comparing quantities with them.
  • Developing and using strategies to estimate the results of rational-number computations and judging the reasonableness of the results.

North Carolina Curriculum Alignment

Mathematics (2004)

Grade 6

  • Goal 1: Number and Operations - The learner will understand and compute with rational numbers.
    • Objective 1.04: Develop fluency in addition, subtraction, multiplication, and division of non-negative rational numbers.
      • Analyze computational strategies.
      • Describe the effect of operations on size.
      • Estimate the results of computations.
      • Judge the reasonableness of solutions.
    • 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 4.06: Design and conduct experiments or surveys to solve problems; report and analyze results
  • Goal 5: Algebra - The learner will demonstrate an understanding of simple algebraic expressions.
    • Objective 5.04: Use graphs, tables, and symbols to model and solve problems involving rates of change and ratios.

Grade 7

  • Goal 1: Number and Operations - The learner will understand and compute with rational numbers.
    • Objective 1.02: Develop fluency in addition, subtraction, multiplication, and division of rational numbers.
      • Analyze computational strategies.
      • Describe the effect of operations on size.
      • Estimate the results of computations.
      • Judge the reasonableness of solutions.
    • Objective 1.03: Develop flexibility in solving problems by selecting strategies and using mental computation, estimation, calculators or computers, and paper and pencil.
  • Goal 5: Algebra - The learner will demonstrate an understanding of linear relations and fundamental algebraic concepts.
    • Objective 5.01: Identify, analyze, and create linear relations, sequences, and functions using symbols, graphs, tables, diagrams, and written descriptions.
    • Objective 5.04: Develop fluency in the use of formulas to solve problems.