The challenge starts with 132 and accepts a split only when two whole factors greater than 1 multiply to a current composite leaf. It keeps an accepted-move ledger and displays all leaf occurrences. Two worked routes end at 2, 2, 3, 11; keeping both 2s is essential to preserving 132.
Give a legal move a precise meaning
Choose a current composite leaf, enter two factors and check their product. Replacing 132 with 6 and 22 is legal because 6 × 22 = 132 and both factors are greater than 1. A proposed 6 × 20 gives 120 and must leave the accepted tree unchanged. The feedback explains the mismatch without adding an invalid move to the history.
OpenStax's factor-tree explanation continues composite branches until every branch ends with a prime. This fixed-target activity adopts that principle with original 132 routes. Prime leaves remain; 1 is not prime, and 1 × 132 is excluded because it would not progress to smaller nontrivial factors. Blank, zero, negative and decimal factors are also rejected.
Finish the first route
Route A starts 132 = 6 × 22. Split 6 into 2 × 3 and the leaves are 2, 3, 22. Their product is still 132, but 22 remains composite. Ask which branch needs another move before offering the final key. The product check verifies the target while the primality check identifies unfinished work.
Split 22 into 2 × 11. Now every leaf is prime, and the final product is 2 × 3 × 2 × 11 = 132. Sorting for comparison gives 2, 2, 3, 11. The challenge counts three accepted splits, not every press of the check button. An invalid attempt or a repeated request to split a leaf that is no longer current cannot inflate that count.
Compare a different starting pair
Reset and try Route B: 132 = 11 × 12, 12 = 3 × 4, then 4 = 2 × 2. The intermediate 11, 3, 4 stage still has a composite 4. Only the final 11, 3, 2, 2 leaves complete the prime tree. Their sorted values match Route A, despite the different branches.
The teacher reference expresses the result as 2² × 3 × 11. Two leaves valued 2 are two factors to keep, not duplicate records to merge. Removing one makes 2 × 3 × 11 = 66. A tree rendering should give each occurrence its own node, while the text ledger states each parent-to-children change for inspection without relying on the diagram.
Ask for a reason after the split
Have learners explain why 2, 3, 22 is unfinished, why 11 and 12 is a valid start and what changes when one 2 is removed. Keep their written explanation separate from the teacher sample. The local checker handles factor products and primality; it does not decide whether a prose explanation demonstrates understanding.
The page begins with empty pair inputs and a blank reasoning area. A separate teacher-route reveal lets an instructor inspect the two references. Editing a pair clears its old feedback, and Reset restores the lone 132 root, empty move history and blank explanation. No learner grade or saved progress is created.
Carry the branch evidence into discussion
The current-leaf display and accepted ledger should agree after every legal move. If a reader chooses a prime or a value absent from the current leaves, the tree stays intact and the message asks for a current composite. The fixed root keeps the activity bounded; it is not an arbitrary-number factoring service.
Prepare a blank paper tree and the three reasoning questions alongside the digital view. Use the point where a composite remains to discuss what completion means. Finishing this 132 tree provides evidence about this example only; it is not proof of broad mastery or that the game improved learning.
Copy this prompt
Create a complete original HTML example in US English for this task: Prime factorization games for the classroom. Return one self-contained HTML file. Include all styles, data and JavaScript in the file. Use no remote dependencies. Return the working page, not an outline.
Fixed root 132. Route A 132 = 6 × 22, 6 = 2 × 3, 22 = 2 × 11. Route B 132 = 11 × 12, 12 = 3 × 4, 4 = 2 × 2. Both final sorted leaves 2, 2, 3, 11 give 132; removing one 2 gives 66. Composite 22 or 4 means unfinished despite product 132. Invalid 6 × 20 gives 120. One is not prime; 1 × 132 disallowed.
Build an original leaf diagram and equivalent text accepted-move ledger. Inputs choose a current leaf and two factors; Accept split validates whole factors greater than 1, parent present and composite, product equal. Invalid moves preserve all state. Preserve distinct node IDs for repeated 2 leaves. Recompute current product, unfinished composites and accepted-move count after each legal split. Completion requires all leaves prime, never product alone. Offer deliberate teacher-route reveal, blank explanation and Reset restoring root 132, empty ledger/answers/reveal. Do not offer arbitrary targets, scores, automated prose assessment, persistence or a classroom-outcome promise. Clear stale feedback when pair inputs change.
Use a page design suited to this particular task, readable text at least 16 px, generous spacing, visible keyboard focus and explicit labels. At 360 px, stack the content without page-level horizontal scrolling. Use type="button" click handlers for actions. Keep source facts and sample results distinct from actual observations. Leave unknown details visible rather than inventing them. Controls update only this temporary page; distinguish local changes from actual records. Provide concise task-specific feedback and a reset that clears entered answers and stale results.
Check every leaf in both routes
Place the two completed trees side by side. The HTML tree and move ledger can be rendered in NOS when a teaching colleague needs to inspect the two routes before the lesson. Ask a learner to multiply 2 × 2 × 3 × 11, then remove one 2 and explain why the product becomes 66. For the next tree, have the learner justify both checks: the product is preserved and each remaining leaf is prime.