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Fraction Shape Puzzle

Shade equal parts to match five target fractions and verify every answer by independent cross products on the way to 1,000.

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How to use

  1. 1.Read the target fraction and the number of equal cells, then shade cells with pointer controls or Arrow keys and Space.
  2. 2.Press Check shape. The game compares shaded/parts with the target by cross products, and an identical wrong mask cannot count twice.
  3. 3.Shade 2 of 4, 4 of 6, 6 of 8, 4 of 10, and 10 of 12 cells to solve all five cards for exactly 1,000 points.

About Fraction Shape Puzzle

Fraction Shape Puzzle is a five-card browser game about equal parts and equivalent fractions. Each card displays a rectangular shape divided into equal cells, a target fraction, and a current shaded fraction. The visual model follows the standard meaning of a fraction: the denominator counts equal parts in the whole, and the numerator counts selected parts. OpenStax Prealgebra supports that model, while an independent Mathematics LibreTexts textbook states the cross-product test used for equivalence.

The five cards deliberately use different visual denominators. The first asks for one half on a four-part shape, so two cells must be shaded. The second asks for two thirds on six parts, so four cells are needed. The third asks for three quarters on eight parts, which requires six cells. The fourth asks for two fifths on ten parts, which requires four. The fifth asks for five sixths on twelve parts, which requires ten shaded cells.

A submission is correct when the shaded count divided by the number of equal parts is equivalent to the target numerator divided by its denominator. The implementation avoids floating-point comparisons. It checks shadedCount × targetDenominator against targetNumerator × partCount. Equal cross products mean the two fractions describe the same share of the whole.

Use the visible cell buttons with a pointer or touch screen. Keyboard players move the current cell with the Arrow keys, press Space to toggle shading, and press C to check the shape. Every cell is at least 44 pixels tall. The interface shows the target, current shaded fraction, both cross products after a valid check, level progress, distinct errors, feedback, and score.

A correct card awards 200 points and opens the next fixed shape. Five approvals therefore produce exactly 1,000. An empty shape is treated as incomplete and does not spend an error. A nonmatching nonempty shaded set creates one recoverable mistake. Rechecking the identical level-and-shaded-mask signature is deduplicated. A different wrong shading creates the second distinct mistake and closes the run.

Unknown, negative, out-of-range, or fractional cell indexes are atomic no-ops. A zero target denominator, impossible part count, or unsafe cross-product boundary is rejected rather than producing a misleading result. Completion and deadlock freeze cell toggles, cursor movement, and checks. Restart restores the first card, empty shape, zero score, and zero mistakes. The standard Boss Key remains available through the shared game shell.

Evidence includes eleven literal external and product goldens. Independent tests restate all five part counts, target fractions, shaded answers, and cross products without asking the reducer to generate expected values. They cover equivalent and nonequivalent pairs, a zero denominator, empty submission, overflow protection, repeated wrong masks, a second distinct wrong mask, all five 200-point approvals, keyboard boundaries, restart, and terminal freezing.

All state stays in the browser. There is no account, upload, API, model call, timer, assessment service, or new dependency. This is educational entertainment, not a graded test, placement decision, tutoring guarantee, or cognitive assessment. The citations support fraction visualization and equivalence only; they do not endorse the product's cards, scoring, or error rules.

Methodology & sources

Represent each original card by an equal part count, target numerator, and nonzero denominator. Toggle unique cell indexes, reject unsafe or invalid input atomically, and test equivalence with shadedCount times targetDenominator equals targetNumerator times partCount. Award 200 per correct card and exactly 1,000 after five; treat empty submission as incomplete, deduplicate a level-and-shaded-mask error signature, deadlock on the second distinct wrong mask, and freeze terminal states. Independently restate five answers and at least eight literal cross-product vectors.

Frequently asked questions

Why can different shaded counts match the target fraction?
Equivalent fractions describe the same share. The game verifies equivalence with equal cross products rather than decimal rounding.
Does an empty shape count as a mistake?
No. Checking with no shaded cells shows an incomplete message and does not change score or error count.
What sources support the fraction rule?
OpenStax supports the equal-part visual model, and an independent LibreTexts textbook supports the cross-product equivalence test.

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