Download Teacher Talk-Standards behind Reasoning

EOC
Navigation Geometry EOC: The
Proof Is In The Put-in
Jacqueline Hailey
Erik Hailey
CAMT July 19,
2012
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Logic Proof
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Pre AP High School Mathematics with
Geometry Focus (p 2)
• The rule of four (analytical, numerical, graphical,
verbal) limits, sequences, rate of change,
functions, area under a curve, variation,
trigonometry, geometric means, construction,
areas of plane figures, areas and volumes of
solids, coordinate geometry, and
transformations .
• Using manipulatives to develop geometric
concepts before rigorous application .
• Assessment in geometry. Connecting geometric
proof with the Pre-AP idea of "justifying your
answer".
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STAAR: Geometry EOC FORMAT
Reporting Categories
Reporting Category 1:
Geometric Structure
Reporting Category 2:
Geometric Patterns and
Representations
Number of Standards
Number of Questions
Readiness Standards
G.2B, 3C
Supporting Standards
G.1B, 1C, 2A, 3A, 3B,
3D, 3E
Total
Readiness Standards
G.5A, 5D
2
Supporting Standards
G.4A, 5B, 5C
3
Total
5
7
9
2
10/52
10/47
19-21%
Not tested: G.1A: Develop an awareness of the structure of a mathematical system, connecting
definitions, postulates, logical reasoning, and
theorems.
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Italicized TEKS were not tested on TAKS.
G.1 Geometric structure: Basic Elements. The
student understands the structure of, and
relationships within, an axiomatic system.
• (B)recognize the historical development of
geometric systems and know mathematics is
developed for a variety of purposes; and
• (C)compare and contrast the structures and
implications of Euclidean and non-Euclidean
geometries.
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G.2 Geometric structure: Making Conjectures.
The student analyzes geometric relationships in
order to make and verify conjectures (P3)
• (A) use constructions to explore attributes of
geometric figures and make conjectures about
geometric relationships; and
• (B) make conjectures about angles, lines,
polygons, circles, and three-dimensional figures
and determine the validity of the conjectures,
choosing from a variety of approaches such as
coordinate, transformational, or axiomatic
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G.3 Geometric structure: Axiomatic Systems.
The student applies logical reasoning to justify
and prove mathematical statements.
• (A)determine the validity of a conditional
statement, its converse, inverse, and
contrapositive;
• (B) construct and justify statements about
geometric figures and their properties;
• (C) use logical reasoning to prove statements are
true and find counter examples to disprove
statements that are false;
• (D) use inductive reasoning to formulate a
conjecture; and
• (E) use deductive reasoning to prove a statement
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G.4 Geometric structure.
The student uses a variety of representations to
describe geometric relationships and solve
problems.
• (A) select an appropriate representation
(concrete, pictorial, graphical, verbal, or
symbolic) in order to solve problems.
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G.5 Geometric patterns: Patterns and
Transformations. The student uses a variety of
representations to describe geometric relationships
and solve problems.
• (A) use numeric and geometric patterns to develop algebraic
expressions representing geometric properties;
• (B) use numeric and geometric patterns to make generalizations
about geometric properties, including properties of polygons,
ratios in similar figures and solids, and angle relationships in
polygons and circles;
• (C) use properties of transformations and their compositions to
make connections between mathematics and the real world, such
as tessellations; and
• (D) identify and apply patterns from right triangles to solve
meaningful problems, including special right triangles (45-45-90
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and 30-60-90) and triangles whose
sides are Pythagorean triples.
Essential Questions
• What is the relationship between reasoning,
justification, and proof in geometry?
• What is a truth-value?
• How does a truth-value apply to conditional
statements?
• How do deductive reasoning and Truth Tables
help judge the validity of logical arguments?
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