Fraction Shape Puzzle is a learn fractions game in which you shade 2 of 4, 4 of 6, 6 of 8, 4 of 10, and 10 of 12 equal cells, check each result with two independent whole-number cross products, and complete all five fixed cards for exactly 1,000 points. The direct task is to connect each written target to the same share of a shape whose equal-part count changes from card to card: 1/2, 2/3, 3/4, 2/5, and 5/6. The denominator tells you how many equal cells form one whole, while the numerator tells you how many cells to shade. Because the grid deliberately uses denominators 4, 6, 8, 10, and 12, the required shaded count is not always the same as the target numerator. Open the Fraction Shape Puzzle, then use its visible cell buttons with a pointer or touch screen. Keyboard players can move the current cell with the Arrow keys, press Space to toggle shading, and press C or choose the Check shape control. Each correct card adds 200 points and opens the next fixed shape. An empty check reports incomplete without changing the score or mistakes, while a second distinct nonempty wrong mask ends the run. Completion and deadlock freeze the controls, and Restart restores the first card, an empty shape, zero score, and zero mistakes. All state stays in the browser, with no account, upload, API, model call, timer, or assessment service.
Connect the target to equal parts
OpenStax Prealgebra’s Visualize Fractions section supports the game’s basic visual model. In each rectangular shape, the equal cells together represent one whole. The denominator counts those parts, and the numerator counts the cells selected as the fraction’s share. That distinction matters because the target fraction and the visible grid do not always use the same numbers.
For example, the first card displays 1/2 but divides the whole into four equal cells. Matching the target therefore means selecting two cells, not four. The second card displays 2/3 on six parts, so it requires four shaded cells even though its numerator is 2. The interface also shows the current shaded fraction, giving you a way to inspect the selection before submitting it.
Using different visual denominators is central to the exercise. A fraction can describe the same share while using a different numerator and denominator. The game’s checks make that equivalence visible without relying on decimal estimates. For the first card, the complete cross-product check is 2 shaded cells × 2 target denominator = 1 target numerator × 4 equal cells, so 4 = 4.
The five fixed targets and their checks
Every run follows the same deterministic sequence. These are the game’s five defined values, not randomly generated examples:
| Card | Target | Equal cells | Cells to shade | Cross-product pair |
|---|---|---|---|---|
| 1 | 1/2 | 4 | 2 | 2 × 2 = 4 and 1 × 4 = 4 |
| 2 | 2/3 | 6 | 4 | 4 × 3 = 12 and 2 × 6 = 12 |
| 3 | 3/4 | 8 | 6 | 6 × 4 = 24 and 3 × 8 = 24 |
| 4 | 2/5 | 10 | 4 | 4 × 5 = 20 and 2 × 10 = 20 |
| 5 | 5/6 | 12 | 10 | 10 × 6 = 60 and 5 × 12 = 60 |
The general rule is shadedCount × targetDenominator = targetNumerator × partCount. The implementation uses integer cross products instead of floating-point comparisons. After a valid check, the interface shows both products, along with the target, current shaded fraction, level progress, distinct errors, feedback, and score.
Equal cross products mean the two fractions describe the same share of their respective wholes. That rule is consistent with the treatment of equivalent fractions in the Mathematics LibreTexts chapter on equivalent fractions and cross products. The sources support the fraction model and equivalence test; they do not endorse the game’s selected cards, scoring system, or error rules.
Complete the five-card route
- Open the first card. Confirm that it contains an empty shape divided into four equal cells and displays the target 1/2. The denominator tells you the whole contains four parts, while the target numerator tells you the selected share should be half of that whole.
- Choose an input method. With a pointer or touch screen, select the visible cell buttons to shade or unshade them. Every cell button is at least 44 pixels tall. For keyboard play, use the Arrow keys to move the current cell, Space to toggle its shaded state, and C to check the shape. The Check shape button provides the same submission action.
- Solve the 1/2 card. Shade exactly 2 of the 4 equal cells. Press Check shape or C. A valid result shows the matching cross products, adds 200 points, records the card as complete, and opens the second fixed shape.
- Solve the 2/3 card. The new rectangle has 6 equal cells and the target 2/3. Shade 4 cells. The left product is 4 × 3, and the right product is 2 × 6; both equal 12.
- Solve the 3/4 card. On the 8-cell shape, shade 6 cells. The two products are 6 × 4 = 24 and 3 × 8 = 24. Once the check is approved, the next card opens with its own empty shape.
- Solve the 2/5 card. Count 10 equal cells before shading any. Select 4 cells to represent two fifths. A valid check gives 4 × 5 = 20 and 2 × 10 = 20, awarding another 200 points.
- Solve the 5/6 card and finish. The final rectangle has 12 equal cells, so shade 10 of them. The valid products are 10 × 6 = 60 and 5 × 12 = 60. Five correct cards produce 5 × 200 = 1,000 points, and the completion state freezes cell toggles, cursor movement, and checks.
Restart provides a clean route after completion or deadlock. It restores the first card, an empty shape, zero score, and zero mistakes. No answer has to be copied from a timer or outside account because the fixed targets and all game state are presented in the browser.
Recover from feedback without wasting mistakes
The feedback system distinguishes an empty submission from an incorrect set of shaded cells. A level-and-shaded-mask signature also determines whether a repeated wrong arrangement is the same mistake again.
- Empty shape: The check reports that the shape is incomplete. It does not spend an error, change the score, or open the next card. Shade at least one cell before checking again.
- Repeated wrong mask: If a nonempty arrangement is wrong and you submit that same arrangement again on the same level, the identical mask cannot count as a second distinct error. The first recoverable mistake remains active.
- Different wrong mask: If the first mistake is recoverable, you can correct the arrangement and reach the correct solution. Changing to another nonempty wrong arrangement creates the second distinct mistake and closes the run.
When a run enters deadlock after that second distinct mistake, toggles, cursor movement, and checks no longer change the terminal state. The same restriction applies after all five cards are approved. Use Restart to return to the initial state rather than continuing to press controls that the game deliberately ignores.
Use a repeatable fraction-checking routine
A short verbal routine can turn each card into a clear practice step rather than a guess-and-click exercise. Before submitting, identify the target, count the whole, predict the number of selected cells, and explain why the two cross products should match.
- Read the target fraction and the current shaded fraction.
- Count the equal cells that form the complete rectangle.
- Use the target denominator as the total number of parts.
- Calculate the required numerator mentally and shade that many cells.
- Check the displayed target and shaded values before confirming.
- Read both cross products and explain whether they are equal.
This routine works on every fixed card because the rule does not change. You do not need to reduce one fraction first: the game compares the exact whole-number products. If the products are unequal, the current shaded count does not represent the target share. If they are equal, the two fractions are equivalent even when their numerators and denominators differ.
The changing cell counts are useful for that distinction. A child or other learner is not merely matching 1/2, 2/3, 3/4, 2/5, and 5/6 to familiar numerals. The game asks the player to translate each target into a visible part of a whole, then supplies a mathematical check for the result.
Set clear expectations about the activity
Fraction Shape Puzzle is educational entertainment, not a graded test, placement decision, tutoring guarantee, or cognitive assessment. Its five targets, 200-point awards, run rules, and terminal states are fixed game features. Nothing in the activity should be interpreted as a measure of intelligence, academic level, or future performance.
All state remains in the browser. There is no account, upload, API, model call, timer, or external assessment service. That makes the game suitable for a private, repeatable practice activity, but it does not create a claim about learning outcomes. The references cited by the product support equal-part visualization and fraction equivalence only; they do not validate the particular sequence of five cards, the score, or the mistake-signature rules.
For a focused session, play one complete five-card route without skipping checks, then Restart and explain each answer aloud using the target, denominator, shaded count, and two products. That gives the fixed game a clear educational structure while preserving its exact deterministic route and 1,000-point finish.
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