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

Supreme Court handshake

http://illuminations.nctm.org/LessonDetail.aspx?ID=L630

A lesson plan for grades 6–8 Mathematics

Provider: National Council of Teachers of Mathematics


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During this lesson, students will explore the handshake problem, a classic problem in mathematics that asks, “How many handshakes occur when n people shake hands with each other?” Groups work to determine how many handshakes take place among the nine Supreme Court justices, and then generalize to the number of handshakes in any size group. Students explore the problem using a verbal description, a table, a graph, a picture, and an algebraic formula. Illuminations provides an activity sheet and detailed instructions for completing the lesson.

Students will:

  • Explain the generalized solution to the handshake problem.
  • Understand the handshake problem is non-linear, and be able to explain how you know.

NCTM Standards and Expectations:

  • 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.
  • Use symbolic algebra to represent situations and to solve problems, especially those that involve linear relationships.
  • Model and solve contextualized problems using various representations, such as graphs, tables, and equations.

North Carolina Curriculum Alignment

Mathematics (2004)

Grade 6

  • Goal 5: Algebra - The learner will demonstrate an understanding of simple algebraic expressions.
    • Objective 5.02: Use and evaluate algebraic expressions.
    • Objective 5.03: Solve simple (one- and two-step) equations or inequalities.
    • Objective 5.04: Use graphs, tables, and symbols to model and solve problems involving rates of change and ratios.

Grade 7

  • 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 5.02: Translate among different representations of algebraic expressions, equations and inequalities.
    • Objective 5.03: Use and evaluate algebraic expressions, linear equations or inequalities to solve problems.

Grade 8

  • Goal 5: Algebra - The learner will understand and use linear relations and functions.
    • Objective 5.02: Write an equation of a linear relationship given: two points, the slope and one point on the line, or the slope and y-intercept.
    • Objective 5.03: Solve problems using linear equations and inequalities; justify symbolically and graphically.
    • Objective 5.04: Solve equations using the inverse relationships of addition and subtraction, multiplication and division, squares and square roots, and cubes and cube roots.