LEARN NC

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

Algebra in balance

http://illuminations.nctm.org/LessonDetail.aspx?ID=L641

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, applied mathematics)
Provider
National Council of Teachers of Mathematics

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Students use the balance pans tool to explore algebraic expressions and determine if algebraic expressions are equal. After demonstrating how to use the interactive balance plan application, the teacher leads students in activities to better understand the coordinate plane. Illuminations provides links to an interactive learning tool, detailed directions, and an activity sheet necessary for completing the lesson.

Students will:

  • Understand that balance pans actually balance when an equation is solved.
  • Recognize that the intersection of two graphs indicates the solution a system of equations.

NCTM Standards and Expectations:

  • Represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic rules.
  • Identify functions as linear or nonlinear and contrast their properties from tables, graphs, or equations.
  • Relate and compare different forms of representation for a relationship.
  • Develop an initial conceptual understanding of different uses of variables.
  • Recognize and generate equivalent forms for simple algebraic expressions and solve linear equations.
  • Model and solve contextualized problems using various representations, such as graphs, tables, and equations.
  • Use graphs to analyze the nature of changes in quantities in linear relationships.

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.
    • Objective 5.04: Develop fluency in the use of formulas 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 5.02: 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.