You've helped them one at a time. The real understanding is how the ideas CONNECT — teach that next.
Kindra (recognise the schema — spot "this is a coin problem" before solving) ×Lettie (set up the equation — name the unknowns and write the relationship)
Why does Lettie's equation come out wrong if Kindra mislabels a "legs" problem as a "money" problem?
Kindra then says: “I'll just write some equation with x and y — the problem type doesn't matter.” — is that right?
The link: recognise the type first, and the setup follows from it.
Name the kind of problem, then the equation writes itself.
Tad (simplify to a smaller case — solve a tiny version first) ×Genny (generalise — write the rule that works for any numbers)
You solved the puzzle for 2 chickens, then for 3. How do Tad and Genny turn that into a rule for 100?
Tad then says: “The small cases were just practice — they don't help me find a general rule.” — is that right?
The link: specialise to see the pattern (Tad), then generalise to state it (Genny).
Shrink it to see it, then scale it to state it.
Capstone — solve one word problem together
Chickens and rabbits: 10 heads, 28 legs. Bring in the cast member for each move.
First: recognise "this is a heads-and-legs problem". Who?
Who do you bring in?
Next: "let c = chickens, r = rabbits; c + r = 10, 2c + 4r = 28." Who?
Who do you bring in?
Finally: substitute back — does 2(6) + 4(4) = 28? Who?
Who do you bring in?
The synthesis: name the type, set up the equation, and check the answer — a word problem solved with structure, not guessing.
Recognise, set up, check — the shape of a solved problem.
