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Deductive proof and geometric reasoning
Can do: Writes a valid proof where every step has a justification, and spots an invalid step in someone else's.
Why it matters
Proof is the point of geometry. It is the first sustained training in constructing an argument where each step must be defensible.
What it looks like when it's wobbly
Writes what's obviously true rather than what follows from the given, and cites reasons that don't apply.
⏱️ Two-minute check
Give a two-column proof with one wrong justification. "Find the invalid step."
Solid looks like: Finds it and explains why that reason doesn't hold.
The full activity for this topic · 30 minutes
Justify Every Line
- 1Write the given and the goal at the top and bottom before anything else.
- 2Work backwards from the goal: what would be enough to prove it?
- 3Write each step with its reason, and refuse any step whose reason is "it looks like it".
- 4Have them explain the proof aloud to you — gaps become audible immediately.
- 5Then find a flawed proof and identify exactly where it breaks.
If it's too hard
Fill in the missing reasons in a given proof.
If it's too easy
Prove a statement two different ways, and prove one false statement is false with a counterexample.
Say this
"It looks true isn't a reason. What theorem lets you write that line?"