These ratio games use three rounds with labeled counter collections. The first checks an ordered comparison, the second doubles both parts, and the third tests unequal scaling. Each result explains what the numbers count, while an optional reason field lets a teacher inspect the learner's own explanation.
Keep the collection beside the question
The original bag has 3 Red and 5 Blue counters, total 8. Red to blue is 3:5. Red to all is 3:8 because all includes both groups. Blue to red is 5:3. OpenStax presents ratios as ordered comparisons; this activity uses quantities in the same unit rather than rates.
Every colored counter has a word label and each collection has visible counts. The activity therefore remains readable without relying on color. The counts are fictional game material, not observations about a real class. Keep the named question next to the answer choices so a bare ratio cannot appear correct under the wrong comparison.
Use the wrong choices to ask better questions
Round 1 asks red to blue and offers 3:5, 3:8, and 5:3. Choose 3:8 and inspect the explanation: the eight counts all counters, not blue counters. Choose 5:3 and the explanation identifies blue first, which reverses the requested order. The target is 3:5, with red first and blue second.
Before checking, ask the learner what each number describes. The check can identify the fixed choice, but the teacher still needs the learner's reason. An empty selection stays unanswered. Repeating a check remains work on Round 1 rather than increasing a completion count.
Double both parts, then inspect the total
Round 2 uses 6 Red and 10 Blue counters, total 16. The red-to-blue ratio 6:10 reduces to 3:5 because both original parts doubled. The red-to-all ratio 6:16 reduces to 3:8 and answers a different question. Use the named group labels to see why sixteen cannot be the blue count.
Equivalent ratio does not mean unchanged collection size. The valid doubled bag contains sixteen counters instead of eight. Changing rounds refreshes red, blue, total, question, choices, and explanation together. The previous response is cleared, so a Round 1 answer cannot carry an old correctness message into a different question.
Reject unequal scaling for the right reason
Round 3 shows 6 Red and 8 Blue, total 14. Its red-to-blue ratio is 6:8, or 3:4, rather than 3:5. Red doubled from three to six, but blue would need to reach ten to double from five. The mismatch concerns the relationship between the named parts, not merely the changed total.
Choose whether this competing bag preserves the original red-to-blue ratio, then check the explanation. A larger total alone does not decide equivalence; the valid doubled bag changed its total too. Use the separate teacher reference for all three rounds and leave actual learner records blank until attempted. Reset restores Round 1 and clears reasons and feedback. The fixed positive-count activity does not need an arbitrary ratio calculator, zero-denominator path, or automatic evaluation of free reasoning.
Copy this prompt to adapt the example
Design a ratio practice page that keeps quantities and their order visible, shows each comparison in context, and explains why a selected answer works. Return one self-contained HTML file with embedded styling and working interactions. Use readable type, strong contrast, clearly labeled keyboard controls, and a layout that flows on a narrow phone. Identify the supplied data as a fictional example.
Make a complete three-round ordered-ratio activity with labeled Red/Blue counters and text-equivalent counts. Round 1 bag 3 Red, 5 Blue, total 8; ask red to blue, choices 3:5, 3:8, 5:3. Explain that 3:8 is red to all and 5:3 reverses the order. Round 2 bag 6 Red, 10 Blue, total 16; ask the red-to-blue label, choices 6:10 and 6:16. Key 6:10 = 3:5; 6:16 is red to all. Round 3 competing bag 6 Red, 8 Blue, total 14; ask whether it preserves original red:blue. Key No; 6:8 = 3:4 because both parts did not double.
Provide round buttons, explicit labeled answer buttons with visible selected state, Check answer, optional free reason, reset, and separate teacher reasoning. Every round change updates quantities, total, question, choices, and counter labels, clearing previous response and feedback. Editing a choice clears feedback. Empty is unanswered. Track exactly three unique rounds without counting repeat checks as more work. Reset returns Round 1 and clears reason. Do not grade free reasoning, invent learners/results, use color-only meaning, offer unsupported arbitrary inputs, send, or save work.
Before choosing another collection, ask the learner to name the two quantities in order. An HTML view in NOS brings the group counts and explanations together while you prepare that discussion. If the learner compared part to whole when the question asked part to part, change the next question's labels first; a larger set of objects will not by itself resolve that confusion.