LEARN NC

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

Constant dimensions

http://illuminations.nctm.org/LessonDetail.aspx?ID=L572

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, measurement)
Provider
National Council of Teachers of Mathematics

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Students will measure the length and width of a rectangle using both standard and non-standard units of measure. In addition to providing measurement practice, this lesson allows students to discover that the ratio of length to width of a rectangle is constant, in spite of the units. After measuring the length and width of a rectangle in inches and centimeters, students practice measurement using alternative units. Then, students graph the different units of measurement and determine whether the points on the graph are random or patterned. The lesson ends with students creating a scatterplot and determining the line of best fit. Illuminations provides an activity sheet and detailed instructions necessary for completing this lesson.

Students will:

  • Critique various units of measure based on their appropriateness for this particular activity.
  • Use a linear graph to model, analyze and make predictions.
  • Draw conclusions about the relationship of two dimensions based on collected data.

NCTM Standards and Expectations:

  • Use graphs to analyze the nature of changes in quantities in linear relationships.
  • Represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic rules.
  • Explore relationships between symbolic expressions and graphs of lines, paying particular attention to the meaning of intercept and slope.
  • Use common benchmarks to select appropriate methods for estimating measurements.
  • Select and apply techniques and tools to accurately find length, area, volume, and angle measures to appropriate levels of precision.

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.
  • 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 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 5.03: Use and evaluate algebraic expressions, linear equations or inequalities to solve problems.

Grade 8

  • Goal 2: Measurement - The learner will understand and use measurement concepts.
  • Goal 5: Algebra - The learner will understand and use linear relations and functions.
    • Objective 5.03: Solve problems using linear equations and inequalities; justify symbolically and graphically.