Students reverse engineer a hidden system by observing dice, proposing rules, testing counterexamples, and turning their discoveries into an algorithm.
By the end of the lesson, students will be able to:
use pattern recognition to infer rules from input-output examples;
decompose one problem into smaller bear, fish, and plankton subproblems;
test a hypothesis with deliberately chosen inputs;
describe how abstraction leaves out details that do not affect an answer;
express a discovered rule as an algorithm using sequence, selection, and iteration.
Suggested 50-minute lesson
1. Hook and riddle - 5 minutes
Read the poem aloud. Tell students that the language contains clues, but do not define hole, bears, fish, or plankton. Emphasize that productive frustration is expected.
2. Partner investigation - 12 minutes
Pairs roll three to five physical dice or use the simulator. One student records observations while the other proposes a rule; then they switch roles. Ask them to keep separate hypotheses for bears, fish, and plankton.
3. Strategic testing - 10 minutes
Have pairs choose rolls that isolate one face value at a time. Ask, “What roll would prove your idea wrong?” and “Which detail changed between these examples?”
4. Class share and X-ray - 10 minutes
Collect candidate rules without immediately judging them. Use X-ray mode to color-code the visible roles and show each die's contribution. Compare the class rules with new rolls.
5. CS connection - 10 minutes
Name the thinking students already used: pattern recognition, decomposition, abstraction, algorithm design, testing, and debugging. Identify sequence, selection, and iteration in the revealed pseudocode, then trace one roll through it.
6. Exit reflection - 3 minutes
Ask students to answer: “What did your group believe at first, what evidence changed your mind, and how is that similar to debugging a program?”
Facilitation moves
Give process hints before rule hints: “Break the problem into three totals.”
Encourage controlled experiments. A single die isolates a rule better than five random dice.
Ask students to explain why a rule works for every face, not only one roll.
Normalize incorrect hypotheses as useful models that need another test.
Delay X-ray mode until groups have recorded at least one hypothesis for each category.
From the game to computer science
Pattern recognition
Students compare multiple examples and identify recurring relationships.
Decomposition
Students solve three smaller counting problems instead of one tangled problem.
Abstraction
Students represent a die by its top value, parity, and opposite value while ignoring color, orientation, and other irrelevant features.
Algorithm
Students express the rule as exact, repeatable steps: sequence orders the calculations, selection chooses the odd or even branch, and iteration applies the rule to every die.
Testing and debugging
Students compare expected and actual totals, locate a faulty assumption, and revise it.