Does it always work?
Take a stance about whether the claim is true or not?
Time To Complete
I Can Statements
I can make conjectures by:
- Extending my thinking about what I already know.
- Using both formal and informal reasoning.
- Applying mathematical operations correctly and accurately.
- Using tools, such as truth tables, counter-examples, and other aides to reasoning.
I will know my conjectures are of high quality when they:
- Are extensions of my thinking about what I already know.
- Use both formal and informal reasoning.
- Apply mathematical operations correctly and accurately.
- Use tools, such as truth tables, counter-examples, and other aides to reasoning.
Ask students to create a truth table to test and track the logic of their premises.
Provide students sentence starters to help them frame their examination of the claim.
Ask students to generate lists of examples and non-examples for the generalization.
Provide a mini-lesson on the differences among empirical, anecdotal, and logical proofs and evidence.
Provide students with examples of empirical, anecdotal, and logical proofs and evidence, asking them to differentiate and sort them.
Provide students with both examples and non-examples and ask them to sort them and record their strategies and processes as they do so. Once they are sorted, ask students to reflect on the process and strategies they used.
- Resource discussing the distinction between empirical examples and proof (within the context of the claim that the sum of two odd numbers is always an even number): http://nrich.maths.org/6664
- How to Build a Truth Table: http://www.idiotsguides.com/education/geometry/geometry-101-how-to-build-truth-table/
- Sample math sentence starters: https://elementarynumbertalks.files.wordpress.com/2016/08/math_talk_sentence_starters.pdf
- Using examples and non-examples: http://theelearningcoach.com/elearning_design/examples-and-nonexamples/
- Differentiate among empirical, anecdotal, and logical evidence (ELA examples, but can be used as is or adapted): https://www.texasgateway.org/resource/differentiate-among-empirical-anecdotal-and-logical-evidence-english-ii-reading