The activity highlights the five ordered pairs making 8 and the two making 3 out of 36. Its fictional four-trial sample gives 8 twice, or 2/4, while the model remains 5/36. A separate manual trial log begins empty and calculates observed frequency only after a reader records a pair.
Declare the dice model
Use distinguishable six-sided dice D1 and D2. The theoretical comparison assumes fair dice and independent results, giving 36 equally likely ordered pairs. The University of Hawaiʻi's two-dice reference explains that counting basis. A physical set of dice has not been checked for fairness merely because this model is useful in class.
Ask first, “Which sum is more likely, 8 or 3, and why?” Keep the learner's prediction blank until supplied. The eleven possible sum labels 2 through 12 are not eleven equally likely outcomes. Each cell of the six-by-six grid is one ordered pair, with D1 setting its row and D2 its column.
Count the favorable cells
For 8, mark (2, 6), (3, 5), (4, 4), (5, 3) and (6, 2). Five cells give 5/36. For 3, mark (1, 2) and (2, 1). Two cells give 2/36. The denominators match, so the five-cell event is more likely under the stated model.
The highlight controls change the target event and the visible fraction together. The text list of pairs remains available beside the grid. Ask the learner to finish, “There are ___ favorable ordered pairs out of ___ equally likely pairs.” Reversing the dice matters: (1, 2) and (2, 1) occupy different cells even though both sums are 3. Keep the teacher reference separate from the actual explanation.
Explain the four-trial sample
The fictional worked trials are F1 (2, 6), F2 (1, 2), F3 (4, 4) and F4 (6, 1), with sums 8, 3, 8 and 7. Sum 8 appears 2 times out of 4, so its sample frequency is 1/2. Sum 3 appears 1 time out of 4, giving 1/4. The final 7 belongs in the denominator despite meeting neither target event.
Four trials use a denominator of 4, not 36. Those observed fractions do not replace the model's 5/36 and 2/36. They neither prove fairness nor show that a small class sample must contain more 8s than 3s. Label the sample fictional rather than calling it a simulation or an actual classroom experiment.
Record a fresh experiment in a separate place
The local trial-entry panel accepts D1 and D2 as whole faces 1 through 6, computes their sum and adds one row. It does not roll a physical die or generate random sums. That makes every entered trial inspectable and lets the teacher use actual classroom results in the appropriate record later.
Before the first pair, frequency is undefined. After one recorded (2, 6), the 8 frequency is 1/1. After adding (1, 2), it is 1/2, and the 3 frequency is 1/2. The page updates event counts and total trials together. Blank, decimal or out-of-range faces are rejected without adding a row.
Reset clears the temporary trial log and prediction field while retaining the original theoretical grid and separately labeled worked sample. Keep the model identifier and dice assumptions with a real experiment, and start another log if the model changes. Record the learner's reasoning in the maintained packet; the page provides no saved assessment or learning-effect claim.
Copy this prompt
Create a complete original HTML example in US English for this task: Probability dice 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.
Two distinguishable fair independent six-sided dice, 36 ordered pairs. Sum 8:(2, 6), (3, 5), (4, 4), (5, 3), (6, 2) gives 5/36. Sum 3:(1, 2), (2, 1) gives 2/36. Fictional worked sample F1 (2, 6), F2 (1, 2), F3 (4, 4), F4 (6, 1): sums 8, 3, 8, 7, sample 8 frequency 2/4 and 3 frequency 1/4. Separate manual log starts with zero trials, frequency undefined.
Build an original responsive 6-by-6 pair grid, event 8/event 3 highlight buttons and accompanying favorable-pair text. Keep theoretical fractions separate from the fictional sample and from a new manual log. Provide D1/D2 inputs and an Add trial button that validates whole faces 1–6, computes the sum and updates both event counts and the full trial denominator. Do not generate a uniform random sum or claim physical dice were rolled. Invalid input adds nothing; zero trials is undefined. Add a blank prediction/reason area, separate teacher explanation and reset. No rewards, scores, persistence or automatic mastery.
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.
Compare the two denominators
Ask learners to point to all five sum-8 cells, then to the four fictional trials. A co-teacher preparing this discussion can render the HTML pair grid and trial comparison together in NOS. Have learners explain why 5/36 describes the model while 2/4 describes that sample. Use the class’s separate trial log for the next comparison, counting every recorded trial, including sums other than 8 or 3.