MA.912.G.8.4Archived Standard

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Make conjectures with justifications about geometric ideas. Distinguish between information that supports a conjecture and the proof of a conjecture.

Remarks

Example: Calculate the ratios of side lengths in several different-sized triangles with angles of 90°, 50°, and 40°. What do you notice about the ratios? How might you prove that your observation is true (or show that it is false)?
General Information
Subject Area: X-Mathematics (former standards - 2008)
Grade: 912
Body of Knowledge: Geometry
Idea: Level 3: Strategic Thinking & Complex Reasoning
Standard: Mathematical Reasoning and Problem Solving - In a general sense, mathematics is problem solving. In all mathematics, use problem-solving skills, choose how to approach a problem, explain the reasoning, and check the results. At this level, apply these skills to making conjectures, using axioms and theorems, constructing logical arguments, and writing geometric proofs. Learn about inductive and deductive reasoning and how to use counterexamples to show that a general statement is false.
Date Adopted or Revised: 09/07
Content Complexity Rating: Level 3: Strategic Thinking & Complex Reasoning - More Information
Date of Last Rating: 06/07
Status: State Board Approved - Archived
Assessed: Yes
Test Item Specifications
  • Item Type(s): This benchmark may be assessed using: MC item(s)

  • Clarification :
    Students will provide statements and/or reasons in a formal or informal proof or distinguish between mere examples of a geometric idea and proof of that idea.
  • Content Limits :

    Items must adhere to the content limits stated in other benchmarks.

    Items may include proofs about congruent/similar triangles and parallel lines.

Sample Test Items (1)
  • Test Item #: Sample Item 1
  • Question:

    For his mathematics assignment, Armando must determine the conditions that will make quadrilateral ABCD, shown below, a parallelogram.

     

    Given that the m∠DAB = 40°, which of the following statements will guarantee that ABCD is a parallelogram?

  • Difficulty: N/A
  • Type: MC: Multiple Choice

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.

Related Resources

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Lesson Plan

Detemination of the Optimal Point:

Students will use dynamic geometry software to determine the optimal location for a facility under a variety of scenarios. The experiments will suggest a relation between the optimal point and a common concept in geometry; in some cases, there will be a connection to a statistical concept. Algebra can be used to verify some of the conjectures.

Type: Lesson Plan

Student Resources

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