Challenge library
Choose by grade, math area, story, time, or reasoning level. Most worksheets use one printable page.
Ideas that branch and reconnect
Follow a recommended route, explore a focused branch, and see how earlier ideas combine in a capstone.
Worksheet arc · 5 problems · 4 stages · 2 routes
A worksheet arc that branches from recurrence into complex-orbit and safe-zone reasoning, then reunites those ideas in two exact Mandelbrot arguments.
Start: Rook’s Halfway SignalFinish: How Far East Can the Mandelbrot Set Go?
Worksheet arc · 3 problems · 3 stages · 1 route
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
One complete catalog
Every filter and detail is available to everyone: visual themes, readiness, skills, time, reasoning, workload, and curriculum mappings. Switch to a compact list whenever that is easier to scan.
Grade 11 · Uses HS PRE math · 25–50 minutes
Find what two linear transformations erase, then prove why looking only at zero detects every possible collision.
Practices: Systems and linear algebra
Rating evidence
Topics: Systems and linear algebra
Grade 6 · Uses Middle Grade 7 math · 6–13 minutes
Follow Rook's multiplication machine through any positive number of passes, then use reversibility to determine its hidden whole-number multiplier.
Practices: Transformations, composition, and inverses
Rating evidence
Grade 3 · Uses Late Grade 3 math · 2–6 minutes
Decode a repeating jewel necklace and count what appears before the clasp.
Practices: Cycles and invariants
Rating evidence
Topics: Cycles and invariants
Grade 5 · Uses Middle Grade 5 math · 2.5–6.5 minutes
Measure Steve’s cube-shaped dig and make sense of the amount of coal expected inside.
Practices: Volume and surface area · Fractions as numbers
Rating evidence
Topics: Volume and surface areaFractions as numbersProbability and expected value
Grade 3 · Uses Middle Grade 3 math · 3–7 minutes
Track an 18-piece order across six equal supply chests and decide where Alex stops.
Practices: Multiplication and division · Addition and subtraction
Rating evidence
Grade 3 · Uses Late Grade 3 math · 2–6 minutes
Plan a Minecraft wheat farm, mark its gate, and decide whether the available fence is enough.
Practices: Area and perimeter · Addition and subtraction
Rating evidence
Grade 3 · Uses Middle Grade 3 math · 2–6 minutes
Finish a stained-glass color plan by connecting a fraction’s two numbers to the eight panes.
Practices: Fractions as numbers · Addition and subtraction
Rating evidence
Grade 3 · Uses Middle Grade 3 math · 3–7 minutes
Race a two-stage Minecraft shelter build against a sunset finish line.
Practices: Length, time, money, mass, and capacity
Rating evidence
Grade 3 · Uses Late Grade 3 math · 2.5–7 minutes
Read a Minecraft ore graph, move one cartload, and update the comparison.
Practices: Early data and displays · Multiplication and division
Rating evidence
Topics: Early data and displaysMultiplication and divisionAddition and subtraction
Grade 2 · Uses Late Grade 2 math · 6–15 minutes
Find Nurse Joy’s one packing plan that satisfies both container clues.
Practices: Place value and numeration · Addition and subtraction
Rating evidence
Grade 2 · Uses Middle Grade 2 math · 4–12 minutes
Find Rotom’s hidden rectangle numbers and explain the pattern that always appears.
Practices: Place value and numeration · Addition and subtraction
Rating evidence
Grade 8 · Uses Late Grade 8 math · 8–18 minutes
Stretch Rook's unfinished factor label without limit, then enter the integers and decide how sign-changed irreducible factors should be compared.
Practices: Number theory
Rating evidence
Topics: Number theory
Grade 2 · Uses Middle Grade 2 math · 6–15 minutes
Use equal jumps to locate the Ironclad’s hidden Rest Site on the Spire.
Practices: Place value and numeration · Multiplication and division
Rating evidence
Topics: Place value and numerationMultiplication and division
Grade 3 · Uses Early Grade 3 math · 13–30 minutes
Test Lakitu’s hidden boost setting and prove where every later checkpoint becomes reachable.
Practices: Place value and numeration · Number theory
Rating evidence
Topics: Place value and numerationNumber theoryMultiplication and divisionAddition and subtraction
Grade 5 · Uses Late Kindergarten math · 12–30 minutes
Investigate every shortest way the fire and frost dragons can swap sides of the bridge.
Practices: Counting, cardinality, and numerals · Place value and numeration
Rating evidence
Topics: Counting, cardinality, and numeralsPlace value and numerationOperation foundationsShapes and spatial reasoning
Kindergarten · Uses Late Kindergarten math · 1–3 minutes
Count four glowing jars, circle the jar with five fireflies, and finish another jar to make five.
Practices: Counting, cardinality, and numerals · Place value and numeration
Rating evidence
Topics: Counting, cardinality, and numeralsPlace value and numerationOperation foundations
Grade 3 · Uses Middle Grade 3 math · 2–6 minutes
Draw a split through the corner courtyard and use two rectangles to find its area.
Practices: Area and perimeter
Rating evidence
Topics: Area and perimeter
Grade 3 · Uses Early Grade 3 math · 2–6 minutes
Choose which Slay the Spire attack Pen Nib should double first and explain the better order.
Practices: Multiplication and division
Rating evidence
Topics: Multiplication and division
Grade 3 · Uses Early Grade 3 math · 3–8 minutes
Follow the Defect’s three-Orb queue and predict which Orb leaves on the 100th channel.
Practices: Cycles and invariants
Rating evidence
Topics: Cycles and invariants
Grade 3 · Uses Middle Grade 2 math · 2–7 minutes
Circle one Slay the Spire hand that disproves Neow’s claim about every hand.
Practices: Addition and subtraction
Rating evidence
Topics: Addition and subtraction
Grade 5 · Uses Early Grade 5 math · 2.5–7 minutes
Apply Jar Jar’s one-tenth movie rule and decide whether changing two words changes the count.
Practices: Fractions as numbers
Rating evidence
Topics: Fractions as numbers
Grade 2 · Uses Middle Kindergarten math · 4–11 minutes
Use Grogu’s four clues to arrange floating objects, then test whether one clue is necessary.
Practices: Shapes and spatial reasoning
Rating evidence
Topics: Shapes and spatial reasoning
Grade 4 · Uses Middle Grade 4 math · 6–13 minutes
Build a knight-move-count map for one outlined quarter of a chessboard and discover which counts never occur anywhere on the board.
Practices: Combinatorics
Rating evidence
Topics: Combinatorics
Grade 6 · Uses Late Grade 5 math · 18–48 minutes
Track a knight through a cube of 512 rooms and find a way to classify every possible move number without checking the rooms one at a time.
Practices: Combinatorics
Rating evidence
Topics: Combinatorics
Grade 10 · Uses HS DISC math · 9–24 minutes
Join infinite ordered rows, then decide what changes when one extra position moves from the beginning to the end.
Practices: Algebraic structures
Rating evidence
Topics: Algebraic structures
Grade 7 · Uses Middle Grade 6 math · 8–16 minutes
Compare four timed puck histories with a new physics score, then use the results to describe the motion nature selects.
Practices: Expressions and symbolic structure
Rating evidence
Grade 9 · Uses HS DISC math · 9–23 minutes
Tune an observatory signal by following a rule that creates each new reading from the one before it, then find a shortcut to a faraway step.
Practices: Algorithms and recursion
Rating evidence
Topics: Algorithms and recursion
Grade 10 · Uses HS A2 math · 11–28 minutes
Learn how to square and plot complex numbers, then follow one short Mandelbrot orbit until it reveals a repeating loop.
Practices: Complex numbers and vectors
Rating evidence
Topics: Complex numbers and vectors
Grade 9 · Uses HS DISC math · 11–28 minutes
Test whether one interval can trap every future value of a recurrence, then find a smaller interval that almost works but fails at an endpoint.
Practices: Algorithms and recursion
Rating evidence
Topics: Algorithms and recursion
Grade 10 · Uses HS A1 math · 14–34 minutes
Use a safe zone and a guaranteed step-by-step increase to prove the exact last point of the Mandelbrot set on the positive real axis.
Practices: Expressions and symbolic structure
Rating evidence
Grade 11 · Uses HS A2 math · 20–44 minutes
Trap one nonreal orbit to prove the Mandelbrot set reaches surprisingly far east, then use the second iterate to build a wall it cannot cross.
Practices: Complex numbers and vectors · Expressions and symbolic structure
Rating evidence
Topics: Complex numbers and vectorsExpressions and symbolic structure
Grade 4 · Uses Middle Grade 4 math · 5–12 minutes
Turn 2gether’s famous title equation into a digit puzzle and find every screen that works.
Practices: Combinatorics
Rating evidence
Topics: Combinatorics
Grade 12 · Uses HS CALC math · 12–24 minutes
Test a motion score against better and better camera measurements, repair it, and watch a sum turn into an integral.
Practices: Integrals and the Fundamental Theorem · Limits and continuity
Rating evidence
Topics: Integrals and the Fundamental TheoremLimits and continuity
Grade 3 · Uses Middle Grade 3 math · 4–11 minutes
Test pairs of glowing tile trays and choose the fullest pair that the Gallery case can safely hold.
Practices: Addition and subtraction · Place value and numeration
Rating evidence
Grade 2 · Uses Middle Grade 2 math · 5–12 minutes
Read six short Gallery notes and write equations that say exactly what each note says.
Practices: Addition and subtraction · Algebraic foundations and generalization
Rating evidence
Topics: Addition and subtractionAlgebraic foundations and generalization
Grade 4 · Uses Early Grade 5 math · 6–15 minutes
Build one Workshop story into larger and larger numerical equations, then repair an almost-right expression.
Practices: Expressions and symbolic structure
Rating evidence
Grade 10 · Uses HS A2 math · 11–28 minutes
Turn a three-stage signal story into compositions, then run the pipeline backward with inverse functions.
Practices: Transformations, composition, and inverses
Rating evidence
Grade 3 · Uses Middle Grade 3 math · 5–12 minutes
Choose how many museum cases receive sapphires so the finished collection can be shared into equal trays.
Practices: Multiplication and division · Addition and subtraction
Rating evidence
Grade 2 · Uses Late Grade 2 math · 2–6 minutes
Find every packet total in a short range that can be paired with none left over.
Practices: Number theory
Rating evidence
Topics: Number theory
Grade 2 · Uses Late Grade 2 math · 12–28 minutes
Track three Pokémon berry piles through a passing circle and prove the smallest possible start.
Practices: Multiplication and division · Number theory
Rating evidence
Topics: Multiplication and divisionNumber theoryAddition and subtraction
Grade 12 · Uses HS CALC math · 13–27 minutes
Turn one parameter to bend an entire motion, reduce infinitely many histories to one action function, and find where that action is stationary.
Practices: Derivatives · Integrals and the Fundamental Theorem
Rating evidence
Grade 3 · Uses Middle Grade 2 math · 3–8 minutes
Rig three Dangerous-ers’ rope lines so Jules can lead the team to one safe ledge—and spot the rope that misses.
Practices: Addition and subtraction
Rating evidence
Topics: Addition and subtraction
Grade 3 · Uses Early Grade 4 math · 6–17 minutes
Move one square panel to straighten Jules’s shadow screen, then explain why its area stays put while its perimeter shrinks.
Practices: Area and perimeter
Rating evidence
Topics: Area and perimeter
Grade 5 · Uses Middle Grade 5 math · 7–18 minutes
Use a real Minecraft chest, 64-block stacks, and cube dimensions to prove a surprising volume match and plan a hollow build.
Practices: Volume and surface area · Multiplication and division
Rating evidence
Topics: Volume and surface areaMultiplication and divisionMulti-operation computation
Grade 11 · Uses HS DISC math · 40–95 minutes
At an orchard ruin in Avelwythe, an ouroboros binding sends a never-ending menagerie through the lake mist. Determine whether its exact instruction point can ever repeat.
Practices: Algorithms and recursion · Number theory
Rating evidence
Grade 5 · Uses Early Grade 5 math · 8–18 minutes
Students evaluate a plain expression, then make one version that follows a calculation plan by inserting one pair each of parentheses, brackets, and braces.
Practices: Expressions and symbolic structure
Rating evidence
Grade 6 · Uses Middle Grade 6 math · 7–17 minutes
A river hollow reflects midnight at noon. Join Luna in Moorhaunt to test the lockkeeper's remedy and decide what his sign can truthfully say.
Practices: Algebraic foundations and generalization · Percent
Rating evidence
Topics: Algebraic foundations and generalizationPercentFractions as numbers
Grade 8 · Uses Late Grade 8 math · 12–28 minutes
Follow Luna's product record to its missing zero rung, then trace the same boundary through exponent notation and a product containing no factors.
Practices: Exponents and magnitude notation
Rating evidence
Topics: Exponents and magnitude notation
Grade 12 · Uses HS CALC math · 25–55 minutes
Open a cabinet of sixteen formulas, discover how it checks itself, and repair one damaged notation pair.
Practices: Systems and linear algebra · Complex numbers and vectors
Rating evidence
Topics: Systems and linear algebraComplex numbers and vectorsFunction familiesDerivativesCombinatoricsIntegrals and the Fundamental TheoremUnits, scale, and conversionProbability and expected valueLimits and continuityCycles and invariants
Grade 5 · Uses Middle Grade 3 math · 5–13 minutes
Recover a vanished four-letter address from four one-letter-away suggestions, then decide how few clues still prove it.
Practices: Logic and discrete proof
Rating evidence
Topics: Logic and discrete proof
Grade 8 · Uses HS DISC math · 12–28 minutes
Inspect three Gallery plates as the display shrinks from two seals to none, then follow the empty arrangement through factorials and identity permutations.
Practices: Combinatorics
Rating evidence
Topics: Combinatorics
Grade 9 · Uses HS DISC math · 8–18 minutes
Complete Rook's split-dial record to uncover every position whose square returns to 1 on a fifteen-position dial.
Practices: Number theory
Rating evidence
Topics: Number theory
Grade 9 · Uses HS DISC math · 8–20 minutes
Follow Jules's four return tests, then use Vivian's definition to decide whether any operation could have two different identities.
Practices: Algebraic structures
Rating evidence
Topics: Algebraic structures
Grade 11 · Uses HS DISC math · 18–40 minutes
Join Luna at a sixfold Observatory window, turn multiplication into motion, and discover which roots can generate the entire circle.
Practices: Complex numbers and vectors · Algebraic structures
Rating evidence
Grade 11 · Uses HS PRE math · 20–45 minutes
Carry one familiar equation through three coherent folds of the Manyfold and discover which proof step depends on the surrounding mathematics.
Practices: Systems and linear algebra · Number theory
Rating evidence
Grade 11 · Uses UG CAT math · 17–39 minutes
Begin with functions into a one-point set, then use the definition of terminal object to prove how any two such objects must compare.
Practices: Category theory and universal properties
Rating evidence
Grade 12 · Uses UG CAT math · 25–55 minutes
Keep the category of sets fixed, change how sets combine, and determine which object acts like one in each sense.
Practices: Category theory and universal properties
Rating evidence
Grade 12 · Uses GR TOPOS math · 22–50 minutes
Build a complete two-stage presheaf, study the subobjects of its terminal object, and discover how its compatible global truth values behave.
Practices: Categorical and intuitionistic logic
Rating evidence
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