LEARN NC

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

Understanding ratios of areas of inscribed figures using interactive diagrams

http://standards.nctm.org/document/eexamples/chap7/7.3/

A lesson plan for Grades 9–12 Technical Mathematics 1, Geometry, Integrated Mathematics 3, Technical Mathematics 2, Integrated Mathematics 4, Pre-Calculus, and Algebra 1

Provider: National Council of Teachers of Mathematics

About this resource

Appropriate grades
9–12
Subjects
mathematics (algebra, geometry)
Provider
National Council of Teachers of Mathematics

Legal

Creative Commons License

This catalog record is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 2.5 License. This license applies to the content of this page only and does not apply to the referenced website.

This example illustrates how students can understand connections between algebra and geometry using dynamic and interactive geometric figures. They can develop an understanding of how to justify geometric relationships in a technological environment.

E-Math Investigations are selected e-examples from the electronic version of the Principles and Standards of School Mathematics (PSSM). The e-examples are part of the electronic version of the PSSM document. Given their interactive nature and focused discussion tied to the PSSM document, the e-examples are natural companions to the i-Math investigations.

North Carolina Curriculum Alignment

Mathematics (2004)

Grades 9–12 — Algebra 1

  • Goal 2: Geometry and Measurement - The learner will describe geometric figures in the coordinate plane algebraically.
    • Objective 2.01: Find the lengths and midpoints of segments to solve problems

Grades 9–12 — Geometry

  • Goal 1: Number and Operations - The learner will perform operations with real numbers to solve problems.
    • Objective 1.02: Use length, area, and volume of geometric figures to solve problems. Include arc length, area of sectors of circles; lateral area, surface area, and volume of three-dimensional figures; and perimeter, area, and volume of composite figures.

Grades 9–12 — Integrated Mathematics 3

  • Goal 3: Algebra - The learner will use relations and functions to solve problems.
    • Objective 3.02: Use quadratic functions and inequalities to model and solve problems; justify results.
      • Solve using tables, graphs, and algebraic properties.
      • Interpret the constants and coefficients in the context of the problem.

Grades 9–12 — Integrated Mathematics 4

  • Goal 2: Geometry and Measurement - The learner will describe geometric figures in the coordinate plane algebraically.
    • Objective 2.02: Estimate the area and volume of continuously varying quantities.
  • Goal 4: Algebra - The learner will use relations and functions to solve problems.
    • Objective 4.02: Use recursively-defined functions to model and solve problems.
      • Find the sum of a finite sequence.
      • Find the sum of an infinite sequence.
      • Determine whether a given series converges or diverges.
      • Translate between recursive and explicit representations.

Grades 9–12 — Pre-Calculus

  • Goal 1: Number and Operations - The learner will describe geometric figures in the coordinate plane algebraically.
    • Objective 1.01: Transform relations in two dimensions; describe the results algebraically and geometrically.

Grades 9–12 — Technical Mathematics 1

  • Goal 2: Geometry and Measurement - The learner will measure and apply geometric concepts to solve problems.
    • Objective 2.03: Use the length, area, and volume of geometric figures to solve problems. Include arc length, area of sectors of circles; lateral area, surface area, and volume of three-dimensional figures; and perimeter, area, and volume of composite figures.

Grades 9–12 — Technical Mathematics 2

  • Goal 2: Algebra - The learner will use relations and functions to solve problems.
    • Objective 2.01: Use quadratic equations to model and solve problems; justify results.
      • Solve using tables, graphs, and algebraic properties.
      • Interpret the constants and coefficients in the context of the problem.