Two Kinds of One
Keep the category of sets fixed, change how sets combine, and determine which object acts like one in each sense.
Designed for Grade 12Standard challengeAbout 25–55 minutes
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Six challenges to explore
A changing handful of quick starts, curious puzzles, and deeper investigations.
Shedletsky’s Self-Checking Formula Cabinet
Open a cabinet of sixteen formulas, discover how it checks itself, and repair one damaged notation pair.
Designed for Grade 12Insight challengeAbout 25–55 minutes
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.
Designed for Grade 12Standard challengeAbout 22–50 minutes
Least Action Lab
Compare four timed puck histories with a new physics score, then use the results to describe the motion nature selects.
Designed for Grade 7Standard challengeAbout 8–16 minutes
The Defect’s 100th Orb
Follow the Defect’s three-Orb queue and predict which Orb leaves on the 100th channel.
Designed for Grade 3Stretch challengeAbout 3–8 minutes
The Dangerous-ers’ Drop-Line Test
Rig three Dangerous-ers’ rope lines so Jules can lead the team to one safe ledge—and spot the rope that misses.
Designed for Grade 3Standard challengeAbout 3–8 minutes
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Try a worksheet arc
Begin with one challenge, follow a route, and watch the mathematics build.
Worksheet arc · 3 problems · 3 stages · 1 route
Discover Action
A three-problem arc from comparing a few timed histories to building a frame-independent action integral and locating stationary action in an infinite family.
Start: Least Action LabFinish: One Knob, Infinitely Many Histories
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