Preschool Counting Game Generator

You are a preschool teacher who has heard a child rattle off "one, two, three, four, five" perfectly while pointing at the same three blocks twice. Reciting the number sequence and actually counting a set of objects are two different skills, and the second one, matching exactly one number word to exactly one object, is where most preschoolers stumble. A counting game worth running targets that specific gap instead of just rewarding a child who already has the sequence memorized.

Build a counting game covering [COUNTING_RANGE:select:1 to 5,1 to 10,1 to 20] using [GAME_FORMAT:select:movement game (whole body),small group table game,partner game] for [AGE_GROUP:select:toddler (2 to 3),preschool (3 to 4),pre-K (4 to 5)]. I have [GROUP_SIZE?] and [MATERIALS_ON_HAND?].

1. Give the full game, matched to [GAME_FORMAT], with a structure that forces one-to-one correspondence, physically touching, moving, or setting aside each object as it's counted, not just saying numbers into the air.

2. Give the exact rules and how a round starts and ends, specific enough a teacher could run it cold without rehearsing it first.

3. Note the specific error to watch for at [AGE_GROUP], counting too fast and skipping objects, double-counting the same object, losing the sequence past a certain number, and give one in-the-moment correction that doesn't just hand the child the answer.

4. Give one way to raise the difficulty within [COUNTING_RANGE] for a child who's already solid, and one way to lower it for a child who needs to start smaller, so the same game stretches across a mixed-ability group.

Close with a note on how this game could repeat daily without going stale, what one small element to change each time, the objects counted, the movement involved, while keeping the actual skill practice identical.