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Conditional Statement Transformer

Run the Conditional Statement Transformer Fullscreen

You can include this MicroSim on your website using the following iframe:

<iframe src="https://dmccreary.github.io/geometry-course/sims/conditional-statement-transformer/main.html" height="702px" scrolling="no"></iframe>

Description

This MicroSim allows students to explore the four related forms of any conditional statement: the original conditional, converse, inverse, and contrapositive. Students cycle through 10 geometric conditional statements and see each form automatically generated in a color-coded 2x2 grid.

Key features:

  • Four statement boxes display the original, converse, inverse, and contrapositive with symbolic notation and verbal phrasing
  • Truth value indicators show whether each form is true or false for the given geometric context
  • Connection lines highlight that the original and contrapositive are always logically equivalent, and the converse and inverse are equivalent to each other
  • 10 geometric examples ranging from biconditionals (all four true) to statements where the converse is false
  • Toggle controls let students hide connections or truth values to test their own predictions before revealing answers

How to Use

  1. Click Next or Prev to cycle through the 10 example statements
  2. Click New Random to jump to a random statement
  3. Toggle Show Truth Values off to predict truth values before checking
  4. Toggle Show Connections to see which statement pairs are logically equivalent
  5. Notice that the original and contrapositive always share the same truth value

Lesson Plan

Learning Objective

Students will be able to create converse, inverse, and contrapositive statements from any given conditional statement and test their truth values (Bloom's Taxonomy: Creating).

Activities

  1. Predict and Check (10 min): Turn off truth values. For each statement, have students write the converse, inverse, and contrapositive on paper, predict which are true, then toggle truth values on to check.

  2. Pattern Discovery (10 min): Cycle through all 10 statements and have students record which statements have all four forms true. Ask: "What makes these statements special?" (Answer: They are biconditional/definitions.)

  3. Counterexample Hunt (10 min): For statements where the converse is false, have students identify a specific geometric counterexample. For example, statement 2: "A rectangle has four right angles but is not a square."

  4. Create Your Own (15 min): Have students write their own geometric conditional statements, determine all four forms, and evaluate truth values using the patterns they observed.

Assessment

  • Can the student correctly form all four related statements from a given conditional?
  • Can the student determine truth values and provide counterexamples for false forms?
  • Does the student understand that the original and contrapositive are always logically equivalent?

Prerequisites

  • Understanding of conditional statements (if-then form)
  • Familiarity with basic geometric vocabulary (triangle, quadrilateral, angle types)
  • Knowledge of negation in logic

References

Note: Please take a screenshot of this MicroSim and save it as conditional-statement-transformer.png in this directory for social media previews.