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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.
• PLIX

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

by CK-12 //at grade

Conjectures and Counterexamples Interactive

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• PLIX

## Conjectures and Counterexamples: Maximizing 4 Pizza Slices

by CK-12 //at grade

Conjectures and Counterexamples Interactive

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• Video

## Conjectures and Counterexamples Principles

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

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• Video

## Conjectures and Counterexamples Examples

by CK-12 //at grade

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

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

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• Pre Read

## Conjectures and Counterexamples Pre Read

by CK-12 //at grade

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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• Post Read

## Conjectures and Counterexamples Post Read

by CK-12 //at grade

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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• Pre and Post Read

## Conjectures and Counterexamples PrePostRead

by CK-12 //at grade

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

by CK-12 //at grade

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

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• Real World Application

## Conjectures And Counterexamples

by CK-12 //at grade

Alice in Wonderland

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• Study Guide

## Types of Reasoning Study Guide

by CK-12 //at grade

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

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