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Should be designed to draw out conceptual understandings.
Should be student-centered.
Should be fun!

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Start with specific examples. This lets the students come to the generalizations under their own power.

This has the secondary effect of making math fun, as it's hands-on, critical thinking instead of lecturing and repeating.

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This is not a one-person job. The development of these generalizations should include everyone in the department. A mix of ideas will help everyone write better generalizations!

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If scaffolding works so well for your students, why wouldn't it work for you? Take the time to revisit and revise your generalizations as you get more practice writing them.

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is, are, have, impacts, affects, influences

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What is the significance or effect of this generalization? Where might students find examples of it?

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How/why will they understand the generalization?

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Students will Understand that.... (concept)