The Teachers Move the Goalposts
Ender's GameBattle School and Command School are deliberately unbalanced tests, and Ender's response is to break the rules outright.
increasing
Bearing strength in each event
decreasing
Unfair Stars

Unfair Stars
Graff orders Major Anderson to create battle scenarios with impossible star arrangements and imbalanced forces. Anderson protests that it will destroy the integrity of the game.
Context
Graff needs Ender to face situations that exceed any known rules because real war will be unfair.
Significance
Ender's victories in these rigged battles prove his genius but also begin to isolate him from the other commanders.
Seven Battles in Seven Days

Seven Battles in Seven Days
Dragon Army is ordered to fight every day for a week, a pace that has never been permitted before. Ender wins all seven but nearly exhausts his soldiers.
Context
Graff has told Anderson to 'bring Ender along' with an intelligent progression, but the progression is impossibly fast.
Significance
Ender's ability to sustain the pace makes him a living legend, but it also sets him up for the final break.
Two Armies at Once

Two Armies at Once
Ender is ordered to fight Griffin and Tiger armies simultaneously, with the battleroom's view blocked by stars. He wins by sending a formation to touch the enemy's gate while most of his army is destroyed.
Context
The teachers have changed the rules to make victory nearly impossible. Ender finds a loophole in the victory ritual itself.
Significance
His success enrages the teachers and makes them revise the rules again, proving that their 'fair' game is anything but fair.
Impossible Final Exam

Impossible Final Exam
Mazer presents Ender with a battle against a force that outnumbers him a thousand to one, surrounding a planet. Ender initially despairs, then decides to break the rules.
Context
Mazer is testing whether Ender can improvise against overwhelmingly superior forces. He has no expectation that Ender will survive a conventional fight.
Significance
The exam is actually the final battle of the Third Invasion, and Ender's rule-breaking wins the war.
Destruction of the Rules

Destruction of the Rules
Instead of fighting the enemy fleet, Ender orders his ships to fire on the planet itself. The planet explodes and takes the entire bugger fleet with it.
Context
No human commander has ever considered using Dr. Device on a world. Ender does it because the enemy has left him no other strategy.
Significance
The death of the rules is also the death of five billion buggers, and Ender will spend the rest of his life paying for it.
when Graff orders Anderson to rig the game
after Ender becomes Dragon commander
the day after Bonzo's attack
Ender's last simulated battle
climax of the final exam