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# Conjectures and Counterexamples

## Learn how to make educated guesses, or conjectures, to problems, as well as how to disprove incorrect guesses with counterexamples.

Levels are CK-12's student achievement levels.
Basic Students matched to this level have a partial mastery of prerequisite knowledge and skills fundamental for proficient work.
At Grade (Proficient) Students matched to this level have demonstrated competency over challenging subject matter, including subject matter knowledge, application of such knowledge to real-world situations, and analytical skills appropriate to subject matter.
Advanced Students matched to this level are ready for material that requires superior performance and mastery.

## Conjectures and Counterexamples

by CK-12 //basic

Make conjectures and provide counterexamples.

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## Conjectures and Counterexamples

This concept teaches students to make conjectures and provide counterexamples.

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• PLIX

## Conjectures and Counterexamples: Most Pizza Pieces with 3 Cuts

Conjectures and Counterexamples Interactive

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• PLIX

## Conjectures and Counterexamples: Maximizing 4 Pizza Slices

Conjectures and Counterexamples Interactive

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• Video

## Conjectures and Counterexamples Principles - Basic

by CK-12 //basic

This video provides the student with a walkthrough on conjecture and counter examples.

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• Video

## Conjectures and Counterexamples Examples - Basic

by CK-12 //basic

This video provides the student with a walkthrough of one or more examples from the concept "Conjectures and Counterexamples".

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• Video

## Conjectures and Counterexamples Principles

This video gives more detail about the mathematical principles presented in Conjectures and Counterexamples.

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• Video

## Conjectures and Counterexamples Examples

This video shows how to work step-by-step through one or more of the examples in Conjectures and Counterexamples.

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• Video

## Inductive Reasoning

by CK-12 //basic

Explains inductive reasoning and counterexamples.

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• Practice
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## Conjectures and Counterexamples Practice

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• Critical Thinking

## Conjectures and Counterexamples Discussion Questions

A list of student-submitted discussion questions for Conjectures and Counterexamples.

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## Conjectures and Counterexamples Pre Read

To activate prior knowledge, make personal connections, reflect on key concepts, encourage critical thinking, and assess student knowledge on the topic prior to reading using a Quickwrite.

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## Conjectures and Counterexamples Post Read

To stress understanding of a concept by summarizing the main idea and applying that understanding to create visual aids and generate questions and comments using a Concept Matrix.

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To encourage students’ critical thinking about vocabulary concepts, to allow students to reflect on their knowledge of individual vocabulary words, and to increase vocabulary comprehension using the Vocabulary Self-Rate.

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• Real World Application

## The Exception Disproves the Rule

Learn how a single example is all it takes to disprove widely accepted conjectures.

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• Real World Application

## Conjectures And Counterexamples

Alice in Wonderland

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• Study Guide

## Types of Reasoning Study Guide

Symbolic notation used in logic, inductive reasoning (patterns), and deductive reasoning are the focus of this study guide.

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## Introduction to Inductive and Deductive Reasoning

by CK-12 //basic

A very helpful interactive that teaches you the concepts of conjectures, inductive and deductive reasoning, and more.

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• Flashcards

## Conjectures and Counterexamples Flashcards

by CK-12 //basic

These flashcards help you study important terms and vocabulary from Conjectures and Counterexamples.

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