LEARN NC

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

Beyond handshakes

http://illuminations.nctm.org/LessonDetail.aspx?ID=L631

A lesson plan for Grades 6–8 Mathematics

Provider: National Council of Teachers of Mathematics

About this resource

Appropriate grades
6–8
Subjects
mathematics (algebra)
Provider
National Council of Teachers of Mathematics

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Using spreadsheets, students will explore another pattern, that of the triangular numbers. This exploration will enhance students’ ability to generalize a pattern with variables. Illuminations provides handouts and detailed instructions for completing the activity.

Students will:

  • Understand the connections among the handshake problem, the triangular numbers, and the sums of positive integers.
  • Use formulas to extend patterns in a spreadsheet, and graph those relationships.

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 5.01: Simplify algebraic expressions and verify the results using the basic properties of rational numbers.
      • Identity.
      • Commutative.
      • Associative.
      • Distributive.
      • Order of operations.
    • 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 5.01: Develop an understanding of function.
      • Translate among verbal, tabular, graphic, and algebraic representations of functions.
      • Identify relations and functions as linear or nonlinear.
      • Find, identify, and interpret the slope (rate of change) and intercepts of a linear relation.
      • Interpret and compare properties of linear functions from tables, graphs, or equations.
    • Objective 5.03: Solve problems using linear equations and inequalities; justify symbolically and graphically.