Standard 8 : Mathematical Reasoning and Problem Solving (Archived)



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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.

General Information

Number: MA.912.G.8
Title: Mathematical Reasoning and Problem Solving
Type: Standard
Subject: X-Mathematics (former standards - 2008) - Archived
Grade: 912
Body of Knowledge: Geometry

Related Benchmarks

This cluster includes the following benchmarks
Code Description
MA.912.G.8.1: Analyze the structure of Euclidean geometry as an axiomatic system. Distinguish between undefined terms, definitions, postulates, and theorems.
MA.912.G.8.2: Use a variety of problem-solving strategies, such as drawing a diagram, making a chart, guess-and-check, solving a simpler problem, writing an equation, and working backwards.
MA.912.G.8.3: Determine whether a solution is reasonable in the context of the original situation.
MA.912.G.8.4: Make conjectures with justifications about geometric ideas. Distinguish between information that supports a conjecture and the proof of a conjecture.
MA.912.G.8.5: Write geometric proofs, including proofs by contradiction and proofs involving coordinate geometry. Use and compare a variety of ways to present deductive proofs, such as flow charts, paragraphs, two-column, and indirect proofs.
MA.912.G.8.6: Perform basic constructions using straightedge and compass, and/or drawing programs describing and justifying the procedures used. Distinguish between sketching, constructing, and drawing geometric figures.


Related Access Points

This cluster includes the following access points.

Independent

Access Point Number Access Point Title
MA.912.G.8.In.a: Use problem-solving strategies, including visual and physical models and tools, for solving real-world problems involving geometry concepts and skills.
MA.912.G.8.In.b: Use estimation and resources to determine if solutions to problems involving geometry concepts and skills are reasonable.

Supported

Access Point Number Access Point Title
MA.912.G.8.Su.b: Use given problem-strategies, including using visual or physical models, for solving real-world problems involving geometry concepts and skills.
MA.912.G.8.Su.a: Use resources, such as calculators and conversion charts to verify accuracy of solutions to problems involving geometry concepts.

Participatory

Access Point Number Access Point Title
MA.912.G.8.Pa.a: Solve real-world problems involving objects with two- and three-dimensional shapes and match the result to the correct answer to determine accuracy.


Related Resources

Vetted resources educators can use to teach the concepts and skills in this topic.

Lesson Plan

Name Description
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.

Unit/Lesson Sequence

Name Description
Variables and Patterns of Change: Translating Words Into Symbols; Linear Equations: Lesson Plan 1: Miles of Tiles - The Pool Border Problem, students will recognize patterns and represent situations using algebraic notation and variables. Lesson Plan 2: Cups and Chips - Solving Linear Equations Using Manipulatives, students use manipulatives to represent visually the steps they take to obtain a solution to an algebraic equation. They develop an understanding of the connections between the solution involving manipulatives and the symbolic solution. Students work in teams of four. Site includes a Topic Overview, Lesson Plans, Student Work, Teaching Strategies, Resources, and a video of Workshop 1; Part 1.