LEARN NC

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

Patterns and functions

http://illuminations.nctm.org/LessonDetail.aspx?ID=L269

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, geometry)
Provider
National Council of Teachers of Mathematics

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Students investigate properties of perimeter, area, and volume related to various geometric two- and three-dimensions shapes. They conjecture, test, discuss, verbalize, and generalize patterns. Through this process they discover the salient features of the pattern, construct understandings of concepts and relationships, develop a language to talk about the pattern, integrate, and discriminate between the pattern and other patterns. This lesson provides activity sheets to guide students through assignments.

In this lesson, students will:

  • Compute perimeter, area, and volume of various geometric figures.
  • Compute maximum and minimum area of geometric figures, given linear dimensions restrictions.

NCTM Standards and Expectations:

  • Use symbolic algebra to represent situations and to solve problems, especially those that involve linear relationships.
  • Identify functions as linear or nonlinear and contrast their properties from tables, graphs, or equations.
  • Model and solve contextualized problems using various representations, such as graphs, tables, and equations.
  • Create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship.
  • Understand the meaning and effects of arithmetic operations with fractions, decimals, and integers.

North Carolina Curriculum Alignment

Mathematics (2004)

Grade 6

  • Goal 2: Measurement - The learner will select and use appropriate tools to measure two- and three-dimensional figures.
    • Objective 2.01: Estimate and measure length, perimeter, area, angles, weight, and mass of two- and three-dimensional figures, using appropriate tools.
    • Objective 2.02: Solve problems involving perimeter/circumference and area of plane figures.
  • Goal 3: Geometry -The learner will understand and use properties and relationships of geometric figures in the coordinate plane.
    • Objective 3.04: Solve problems involving geometric figures in the coordinate plane.
  • Goal 5: Algebra - The learner will demonstrate an understanding of simple algebraic expressions.
    • Objective 5.02: Use and evaluate algebraic expressions.
    • Objective 5.04: Use graphs, tables, and symbols to model and solve problems involving rates of change and ratios.

Grade 7

  • Goal 3: Geometry - The learner will understand and use properties and relationships in geometry.
    • Objective 3.01: Using three-dimensional figures:
      • Identify, describe, and draw from various views (top, side, front, corner).
      • Build from various views.
      • Describe cross-sectional views.
  • Goal 4: Data Analysis and Probability - The learner will understand and use graphs and data analysis.
    • Objective 4.01: Collect, organize, analyze, and display data (including box plots and histograms) to solve problems.
  • 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 3: Geometry - The learner will understand and use properties and relationships in geometry.
    • Objective 3.01: Represent problem situations with geometric models.
    • Objective 3.02: Apply geometric properties and relationships, including the Pythagorean theorem, to solve problems.
  • Goal 4: Data Analysis and Probability - The learner will understand and use graphs and data analysis.
    • Objective 4.01: Collect, organize, analyze, and display data (including scatterplots) to solve problems.
  • 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.