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2022 G-RL-1-2

Page history last edited by Brigit Minden 11 months, 3 weeks ago

G.RL.1.2

G.RL.1.2 Analyze and draw conclusions based on a set of conditions using inductive and deductive reasoning. Recognize the logical relationships between a conditional statement and its inverse, converse, and contrapositive.

In a Nutshell

The ability to take a set of statements or a diagram to draw a conclusion is fundamental in Geometry. Skills involving the use of inductive and deductive reasoning begin the process of preparing students to support their reasoning more formally. Students recognize the structural patterns of conditional statements including converse, inverse, and contrapositive. Assigning a truth value to these statements, and discovering the patterns, leads to the introduction of postulates and theorems.

Student Actions	Teacher Actions
Develop Mathematical Reasoning by examining patterns and examples or rules to draw conclusions and create counterarguments for a given context. Develop a Deep and Flexible Conceptual Understanding by examining various geometric diagrams and/or models to make conjectures and then prove their validity. Develop the Ability to Communicate Mathematically when using appropriate terminology and conditional statement variations in both written and verbal explanations. Develop Accurate and Appropriate Procedural Fluency by writing conditional statements and the inverse, converse, and contrapositive of the statement, along with identifying the truth values of the statements.	Implement tasks that promote reasoning and problem-solving through explorations that will support student recognition of desired patterns and conclusions. Pose purposeful questions that require students to use various forms of conditional statements to support their reasoning. Elicit and use evidence of student thinking to analyze student reasoning when applying inductive or deductive reasoning and accurate conditional statements.
Key Understandings	Misconceptions
Inductive reasoning is based on observations and deductive reasoning is based on accepted patterns of logic. Conditional statements are also known as “if-then” statements. A conditional statement and its contrapositive will always share the same truth value. Definitions can be written as biconditional statements.	Students confuse inductive and deductive reasoning. Students make grammatical errors with the subject of the conditional statement. Students confuse inverse and converse. Students confuse contrapositive with one of the other forms of the conditional statement. Students believe that the contrapositive of a true conditional statement can be false.
Knowledge Connections
Prior Knowledge	Leads to
Given a Venn diagram, determine the probability of the union of events, the intersection of events, and the complement of an event. Understand the relationships between these concepts and the words “AND,” “OR,” and “NOT.” (A1.D.2.2)	Evaluate reports by making inferences, justifying conclusions, and determining appropriateness of data collection methods. Show how graphs and data can be distorted to support different points of view. (A2.D.2.1) Identify and explain misleading conclusions and graphical representations of data sets. (A2.D.2.2) Differentiate between correlation and causation when describing the relationship between two variables. (A2.D.2.3)