495: Pythagorean anti-Triples?

Ask your class if there are any Pythagorean anti-Triples: $\dfrac{1}{a^2} + \dfrac{1}{b^2} = \dfrac{1}{c^2}$ ?



If a, b, c are integers, the question seems harder, since 1/3, 1/4, 1/5 would be (to me) obvious answers - leading to the rules for Pythagorean triples and just using their reciprocals.

Source:

Are there any Pythagorean anti-triples: 1/(a^2) + 1/(b^2) = 1/(c^2) ?

— James Tanton (@jamestanton) October 11, 2015

446: ASN - Geometry

Always, Sometimes, Never?

389: Talking Points - Fractions and Decimals

Always, Sometimes, Never?

Source.

326: ASN - Quadrilaterals

source

an image from there:

325: ASN - Another Algebra Set

Always True, Sometimes True, Never True?

Once again ... The why is the important part.

source, with lesson plans and materials.

324: ASN - Algebra

Always True, Sometimes True, or Never True?

Cut out the cards and have students sort them into one of the three categories.
In each case, students need to say WHY its always true or NEVER true, or give an example and a counterexample for when it is SOMETIMES true.

source: lesson plan and handouts.