Content atlas · Common Core State Standards for Mathematics 2010

Construct viable arguments and critique the reasoning of others.

CCSS.MATH.PRACTICE.MP3

12 published problems

1. The Machine That Repeats Forever — Follow Rook's multiplication machine through any positive number of passes, then use reversibility to determine its hidden whole-number multiplier.
2. The Infinite Factorization Glitch — Stretch Rook's unfinished factor label without limit, then enter the integers and decide how sign-changed irreducible factors should be compared.
3. One Step Past Omega — Join infinite ordered rows, then decide what changes when one extra position moves from the beginning to the end.
4. Action Between Frames — Test a motion score against better and better camera measurements, repair it, and watch a sum turn into an integral.
5. Pairing Packets — Find every packet total in a short range that can be paired with none left over.
6. One Knob, Infinitely Many Histories — Turn one parameter to bend an entire motion, reduce infinitely many histories to one action function, and find where that action is stationary.
7. 404: The Address That Survived — Recover a vanished four-letter address from four one-letter-away suggestions, then decide how few clues still prove it.
8. Four Ways Back to One — Complete Rook's split-dial record to uncover every position whose square returns to 1 on a fifteen-position dial.
9. Can There Be Two Ones? — Follow Jules's four return tests, then use Vivian's definition to decide whether any operation could have two different identities.
10. Everything Points Here — Begin with functions into a one-point set, then use the definition of terminal object to prove how any two such objects must compare.
11. Two Kinds of One — Keep the category of sets fixed, change how sets combine, and determine which object acts like one in each sense.
12. The Truth Inside One — Build a complete two-stage presheaf, study the subobjects of its terminal object, and discover how its compatible global truth values behave.