Exercise 1: Walking Through a Real Article V Amendment — Possible Solution
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Article V lays out two stages, and only one real-world combination of
methods has ever actually succeeded (Congress proposes, state
legislatures ratify), so that's the one worth walking through
concretely.

STAGE ONE — PROPOSAL
A new amendment would first need to pass both chambers of Congress,
not by an ordinary simple majority the way most legislation does, but
by a two-thirds supermajority in each chamber separately.

  - House of Representatives: with 435 voting members, two-thirds
    means at least 290 representatives voting in favor.
  - Senate: with 100 members, two-thirds means at least 67 senators
    voting in favor.

Both thresholds have to be cleared independently - a 290-vote House
majority does not carry the Senate, and vice versa. Given that party
control of Congress rarely produces a two-thirds majority for either
party alone, this stage in practice requires genuine support that
crosses party lines, not just party-line control of one chamber.

STAGE TWO — RATIFICATION
Once proposed, the amendment goes to the 50 state legislatures. It
becomes part of the Constitution only once three-fourths of them
approve it.

  - With 50 states, three-fourths means at least 38 state
    legislatures would need to ratify.
  - Each state legislature typically needs to pass the ratification
    in both of its own two chambers (all states except Nebraska have
    a bicameral legislature), so this stage really means clearing a
    majority vote in roughly 75 separate state legislative chambers.

There is no fixed deadline built into Article V itself, though
Congress has sometimes attached a ratification time limit (commonly
seven years) to specific amendments it proposes.

WHY THIS IS GENUINELY HARD
Clearing 290 House votes, 67 Senate votes, and then 38 separate state
legislatures - all without a single overriding deadline - requires a
level of broad, geographically and politically diverse consensus that
a simple 51% national majority could never deliver on its own. That is
exactly the outcome Article V was built to produce: fundamental
constitutional change has to survive far more veto points than
ordinary legislation does.

ANSWER: Reaching a real Article V amendment today would require at
least 290 of 435 House votes and 67 of 100 Senate votes to propose it,
followed by ratification from at least 38 of the 50 state
legislatures (typically both chambers in each) to adopt it - a
deliberately high, multi-stage supermajority threshold that no single
party or narrow national majority can clear alone.

WHY THIS WORKS AS AN ANSWER
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It translates Article V's abstract "two-thirds of Congress, three-
fourths of the states" language into concrete, real vote counts (290
House votes, 67 Senate votes, 38 state legislatures) using the actual
current size of Congress and the real 50-state total, showing exactly
why the threshold is a genuine structural barrier rather than a
formality.