Student Learning Map

  • Topic:Reasoning and Constructions
  • Subject(s):Math
  • Days:12
  • Grade(s):9, 10, 11, 12
Key Learning:

The use of reasoning is important to make conclusions in all areas of mathematics and other real world situations.

Students must be able to use a compass and straightedge and/or drawing programs.

Unit Essential Question(s):
 
 

What strategies can we use to justify our conclusions in geometry?

What are the basic constructions?

   
Concept: Patterns and Inductive Reasoning
Concept: Logical Statements
Concept: Deductive Reasoning
Lesson Essential Question(s):

Why is pattern recognition important in the inductive reasoning process?

(ET)

What similarities/difference exist between inductive and deductive reasoning? (ET)

What are the similarities/differences between postulates and theorems? (ET)

How can a conjecture be used to help solve a problem?

(ET)

How can a conjecture be used to help solve a problem?

(ET)

Lesson Essential Question(s):

What are the different types of conditional statements and how are they used to describe situations in geometry? (A)

When is a counterexample used in discussing the truth value of a statement and what forms can it take? (A)

Lesson Essential Question(s):

What similarities/differences exist between inductive and deductive reasoning?

(ET)

How do you determine the type of reasoning that should be applied in specific situations? (ET)

Concept:

Other Logical Statements

Concept:

Basic Constructions

Concept: Constructions of Parallels and Perpendiculars
Lesson Essential Question(s):

When is a counterexample used in discussing the true value of a statement and what forms can it take? (A)

What is learned from the investigation of inverses, contrapositives, and indirect reasoning?

(A)

How do you identify the property necessary to justify a statement? (ET)

Lesson Essential Question(s):

How are the straightedge and compass used to construct congruent segments and angles, and to construct bisectors of angles and segments?

(A)

Lesson Essential Question(s):

What are the two methods for constructing parallel lines?

(A)

What are the two methods for constructing perpendicular lines?

(A)

Vocabulary:

Vocabulary:

Additional Info:

Ask an experienced coworker for additional reference texts and/or other materials.

Prentice Hall Geometry Ch.1.1, 2.1-2.2, 5.4, 1.5, 3.7

Text Ancillary Materials

Scientific Calculator, Protractor, Graph Paper

FCAT Explorer

Mission FCAT

Polk County FCAT Item Test Bank

www.PHSchool.com

Kaplan Lesson Plans

Resources:

Vocabulary Report

  • conditional -
  • deductive reasoning -
  • inductive reasoning -
  • inverse -
  • hypothesis -
  • contrapositive -
  • conjecture -
  • conclusion -
  • counterexample -
  • truth value -
  • indirect reasoning -
  • converse -
  • biconditional -