Numbercade looks like an arcade, but the cabinets are in an order. This page shows the whole route: what each game teaches, world by world, which Common Core standards that content covers, and where your kid should probably start.
We could have shipped forty shallow games and called it a curriculum. We picked eight topics instead, and the choice was not casual. When the U.S. Department of Education convened the National Mathematics Advisory Panel to ask what kids must own before algebra, its 2008 report named three Critical Foundations of Algebra: fluency with whole numbers, fluency with fractions (decimals and percents included), and particular aspects of geometry and measurement, notably the similar triangles that slope stands on. The panel also flagged fractions as the most underdeveloped skill of all. That report is expert panel consensus, not a trial, and we label it that way. Our games are those foundations plus the bridge they exist to hold up: equations, slope, and their kin.
These topics are also precisely where kids' documented errors pile up. Kids treat a fraction as two whole numbers stapled together (whole-number bias; Ni & Zhou 2005). They add when a problem needs multiplying (the additive trap; Hart 1981). They peel the minus sign off its number and lose it (the detached minus sign; Linchevski & Livneh 1999). Each of those errors has a descriptive research literature behind it, and each one is a named villain in a specific game.
Uncorrected, they do not fade; they settle in for years. Hart's team tracked the additive error in thousands of students in England and found it alive across ages 11 to 16. And a 2025 study of adults found only about one in six fully understood the order of operations (Eaves, Attridge & Gilmore 2025).
The stakes run long. Kids' fraction and division knowledge at age 10 predicts their algebra and overall math achievement at 16, controlling for IQ and family income (Siegler et al. 2012). How far a student climbs in high school math is the strongest coursework predictor of finishing a college degree (Adelman 1999). Both findings are correlational: predicts, not causes, and we say so.
So, eight deep games rather than forty shallow ones. Our bet, stated as a bet: mastery of the foundations transfers; coverage does not.
The sequence follows how the math itself builds. Order of operations and the structure of expressions come first, because everything downstream is written in that language. Proportional reasoning comes second, because it is the single biggest idea of the middle grades. Equations come third, and they use both. Slope is the capstone that turns equations into pictures. The last three games are parallel branches: geometry, roots and exponents, and probability each lean on games 1 to 3, but not on each other.
We audited the actual lessons and challenges in each game (not the marketing copy) and mapped each world to the Common Core State Standards its content covers. Depth is our honesty column: core means the world teaches and practices the standard's central skill; partial means it covers part of the standard; enrichment means the content goes beyond the grades 4-8 standards (we mark the nearest high school code); review is a boss world that mixes the earlier worlds. Scroll the table sideways on a phone.
| Game | World | Concepts taught | Common Core standard(s) | Grades | Depth |
|---|---|---|---|---|---|
| 1. Number Forge | 1. The Anvil | Multiplication and division facts to 12 times 12; fact families; automaticity | 3.OA.C.7 (fluency maintained) | 4-6 | core |
| 2. The Smelter | Prime vs composite; prime factorization; factors and multiples; GCF and LCM; divisibility rules for 2, 3, 4, 5, 6, 9 and 10 | 4.OA.B.4, 6.NS.B.4 | 4-6 | core | |
| 3. The Tricksmith | Mental-math strategies (times 5, 11, 25, 9; friendly products) | supports 3.OA.B.5 | 4-6 | partial | |
| 4. The Scales | Quantitative comparison (A / B / equal / cannot be determined), including the x below zero squaring trick and the two-roots trap | test-style reasoning | 5-8 | enrichment | |
| 5. The Ice House | Negative numbers on the below-zero number line; ordering integers; adding and subtracting with negatives; the two meanings of the minus sign; multiplying and dividing with negatives (sign rules) | 6.NS.C.5, 6.NS.C.6a, 6.NS.C.7, 7.NS.A.1, 7.NS.A.2 | 5-7 | core | |
| 6. The Gauntlet | Boss: mixed review of stations 1 to 5 | review of the above | 4-8 | review | |
| 2. Order Up! | 1. Prep Station | Order of operations without parentheses; multiply and divide before add and subtract; left to right within a rank; reordering with the signs attached | 6.EE.A.2c | 5-6 | partial |
| 2. Parentheses Pantry | Grouping symbols; nested parentheses evaluated inside out; whole-number exponents in expressions | 5.OA.A.1, 6.EE.A.1 | 5-6 | core | |
| 3. Tray Service | Distributive property, numeric (6 x 102 in your head) and symbolic (3(x + 4)); factoring out a common factor | 6.EE.A.3, 6.NS.B.4, 7.EE.A.1 | 6-7 | core | |
| 4. Mix and Match | Commutative and associative properties; when swapping breaks (subtraction, division); strategic regrouping for mental math; equivalent expressions | 6.EE.A.3, 6.EE.A.4 | 5-6 | core | |
| 5. The Critic's Table | Boss: mixed review of worlds 1 to 4 | review of the above | 5-6 | review | |
| 3. Slime Lab | 1. Starter Dish | A fraction as one number (equal cuts, equal parts); fraction OF a number (divide by the bottom, times the top) | 4.NF.B.4, 5.NF.B.4a | 4-5 | core |
| 2. The Goo Vat | Equivalent fractions (same amount, different cuts); simplifying to plainest form | 4.NF.A.1 | 4-5 | core | |
| 3. Splash Tank | Comparing fractions: the benchmark half, cross-multiplying, and why the WHOLE matters | 4.NF.A.2 | 4-5 | core | |
| 4. The Goo Press | Fraction times a whole number (including fractions greater than 1); improper and mixed conversions; adding mixed numbers with unlike denominators; dividing a fraction by a fraction (keep-change-flip) | 4.NF.B.3, 4.NF.B.4, 5.NF.A.1, 6.NS.A.1 | 4-5 | core | |
| 5. The Magma Pen | Ratio language ("for every"); scaling batches; unit rate as the value of ONE; comparing travel times; two-rate totals (per-day plus per-mile costs); combined work rates (add the rates, never the times) | 6.RP.A.1, 6.RP.A.2, 6.RP.A.3b, 6.RP.A.3d | 6 | core | |
| 6. Nebula Chamber | Percent as per 100; the benchmark keys (10%, 25%, 50%); percent of a number; part-to-percent; successive discounts (multiply, never add the percents) | 6.RP.A.3c, 7.RP.A.3 | 6 | core | |
| 7. The Morph Tank | Fraction to decimal to percent conversion in all six directions; the benchmark chart; ordering numbers written in different forms | 4.NF.C.6, 6.RP.A.3c | 4-6 | core | |
| 8. Throne Room | Boss: mixed review of all seven stations (the Overgrown Gloop) | review of the above | 4-6 | review | |
| 4. Equation Pirates | 1. Harbor Cove | The unknown as x; one-step add and subtract equations; inverse operations; keeping both sides equal; substituting to check; tape diagrams | 6.EE.B.5, 6.EE.B.7 | 6 | core |
| 2. Barrel Bay | One-step multiply and divide equations (3x = 21, x/4 = 5); the invisible multiplication sign; comparing strategies | 6.EE.B.7 | 6 | core | |
| 3. Gull Isle | Two-step equations; which operation to undo first; checking solutions; function notation f(x) and the f(2) + f(3) trap; setting up equations from words, incl. consecutive-integer sums, perimeter setups, and missing-score mean problems | 7.EE.B.4a, 8.F.A.1, 6.EE.B.6 | 7 | core | |
| 4. The Sea Galley | Variables on both sides; parentheses via the distributive property; multi-step solving; setting up both-sides equations from words | 8.EE.C.7b, 7.EE.B.4a | 7-8 | core | |
| 5. Blackfin Reef | Boss: test strategies; evaluating expressions by structure instead of solving; cross-multiplying proportions; rereading what the question asks | review + HS A-SSE.A.2 | 7-8 | enrichment | |
| 5. Slope Quest | 1. The Ramp Builder | Slope as rise over run; reading slope from a graph; positive, negative, zero, and undefined slope; comparing steepness | 8.EE.B.5 | 7-8 | partial |
| 2. The Mine Shaft | Slope formula from two points; negative coordinates; finding a missing coordinate from a known slope | 8.EE.B.6, 8.F.B.4 | 8 | partial | |
| 3. The Crystal Bridge | y = mx + b; identifying slope and y-intercept; matching equations to graphs; writing the equation of a line | 8.EE.B.6, 8.F.A.3 | 8 | core | |
| 4. Diamond Summit | Mixed test-style review: slope from points, steepness comparison, slope in context, writing equations | review of worlds 1 to 3 | 8 | review | |
| 5. Nether Fortress | Boss: converting standard form Ax + By = C to slope-intercept form; reading the slope out of standard form | HS A-CED.A.4 (nearest) | 8+ | enrichment | |
| 6. Master Builder | 1. Highland Ranch | Area and perimeter of rectangles (blocks that cover vs the fence around); composite rectangular builds | 3.MD.C.7, 3.MD.D.8, 6.G.A.1 | 4-6 | core |
| 2. Wool Wrapping | Surface area of rectangular prisms via nets and the formula; cube shortcut; surface area vs volume | 6.G.A.4, 7.G.B.6 | 6-7 | core | |
| 3. Statue Scaling | Similar triangles; scale factor; corresponding sides; cross-multiplying to find a missing side | 7.G.A.1, 8.G.A.4 | 7-8 | partial | |
| 4. Angle Anvil | Triangle angle sum; angles on a straight line; corresponding angles in similar triangles; algebraic angle problems; Pythagorean theorem and rectangle diagonals with the 3-4-5 / 5-12-13 / 8-15-17 triples and compare-without-computing reasoning; triangle families (equilateral, isosceles, scalene); complementary vs supplementary; regular polygon interior angles | 7.G.B.5, 8.G.A.5, 8.G.B.7 | 7-8 | core | |
| 5. Redstone Grid | Translations, reflections, and 90-degree rotations with coordinates; identifying which transformation maps one shape to another | 8.G.A.3, 8.G.A.1, 8.G.A.2 | 8 | core | |
| 6. The Storehouse | Volume of rectangular prisms (l x w x h); unit cubes filling a box; volume vs surface area | 5.MD.C.5, 6.G.A.2 | 5-6 | core | |
| 7. The Round Pen | Radius and diameter; circumference; area of a circle with pi about 3.14 | 7.G.B.4 | 7 | core | |
| 8. The Ender Build | Boss: mixed review of area, surface area, similarity, angles, transformations, volume, and circles | review of worlds 1 to 7 | 6-8 | review | |
| 7. Crystal Caverns | 1. Torchlight Tunnel | Squaring; square roots of perfect squares; recognizing perfect squares; the root-is-not-halving trap; the area-and-side model | 8.EE.A.2, 6.EE.A.1 | 6-8 | partial |
| 2. Echo Chasm | Estimating irrational square roots by trapping them between perfect squares; placing roots on a number line | 8.NS.A.2 | 8 | core | |
| 3. Geode Grotto | Evaluating powers; the product rule for same-base powers; missing exponents; comparing powers; negative bases (odd power keeps the minus, even erases it); two-power combos evaluated power-first | 6.EE.A.1, 8.EE.A.1, 7.NS.A.2 | 6-8 | partial | |
| 4. Crystal Forge | Simplifying radicals (the square root of 8 becomes 2 times the square root of 2); radical equivalence | HS N-RN.A.2 (nearest) | 8+ | enrichment | |
| 5. The Deep Dark | Boss: order of operations with roots and powers; distributing over radical expressions; why the root of a sum is not the sum of the roots | 8.EE.A.2 + 6.EE.A.2c applied | 8 | core | |
| 8. Loot Lab | 1. Spawn Zone | Probability of a simple event as favorable over total; marbles, dice, and spinners; probability as a number from 0 to 1 | 7.SP.C.5, 7.SP.C.7a | 7 | core |
| 2. Trade Plaza | Complements: P(not A) = 1 minus P(A); certain and impossible events | 7.SP.C.5, 7.SP.C.7a | 7 | core | |
| 3. Obby of Independence | Independent compound events by multiplying; coin-and-die combos; draws with replacement; combined-choice sample spaces | 7.SP.C.8a-b; HS S-CP.A.2 | 7-8 | partial | |
| 4. No-Replacement Nexus | Dependent events without replacement ("the bag shrinks"); step-by-step conditional reasoning; with vs without replacement | HS S-CP.A.3/S-CP.B.6 (nearest) | 8+ | enrichment | |
| 5. Tycoon Tower | Boss: mixed review including the sum of two spinners (a true sample-space count) and without-replacement draws | 7.SP.C.8b + review | 7-8 | core |
Rows marked partial or enrichment are deliberate honesty, not gaps we are hiding: where a world covers part of a standard we say which part, and where the games run past grade 8 (simplifying radicals, standard-form conversions, without-replacement probability) we name the nearest high school code instead of stretching a middle school one. The audit notes live in our repo's curriculum map and get updated whenever a game's worlds change.
The arcade has a grade picker that highlights the same recommendations; here they are in words.
Start with Number Forge (the arcade's START HERE cabinet: it builds the fact fluency every other game leans on), then Order Up! and Slime Lab. Slime Lab's first station is fraction foundations with a slime you literally cut into equal parts, which meets a fourth grader exactly where the cliff starts, and Order Up! builds the operation-order habits everything else assumes.
Start with Slime Lab (ratios and percents are the heart of grade 6) and Equation Pirates (one-step equations are on the menu this year). Visit Order Up! first if order of operations still wobbles.
Start with Equation Pirates (two-step equations are the grade 7 main event) and add Loot Lab, since probability is the grade 7 topic most schools sprint past. Master Builder and Crystal Caverns are natural next stops.
Start with Slope Quest and Crystal Caverns: slope, linear equations, roots, and exponent rules are the core of grade 8. Jump back to Equation Pirates first if solving equations is the wobble.
What this alignment does and does not claim. The table above describes content coverage: which standards the games' lessons and problems address. It is not a claim that playing Numbercade causes mastery of those standards, and no standards alignment from any company is. Numbercade has not itself been tested in an efficacy study; in the federal ESSA evidence tiers we are Tier 4, Demonstrates a Rationale, and we say so plainly.
What we can show you is the research behind the design choices, mechanic by mechanic, with citations: that lives on our why it works page and on each game's "The Research" screen.
Every game is free. Pick your grade on the arcade page and it will point at the right cabinet.
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