Invariants, casework, and pigeonhole readiness

Use elementary olympiad-style methods such as invariant tracking, organized cases, and guarantee reasoning in visible puzzle settings.

Surface

Children may meet this skill through task formats such as Invariant move legal-illegal mark, Pigeonhole box guarantee choice, Casework cover board, Invariant game challenge choice.

Task formats

Casework cover board

Casework cover board asks children to cover all cases with chips and mark missing, duplicate, or impossible cases.

Child actionCover all cases with chips and mark missing, duplicate, or impossible cases.

CheckComplete the casework cover board action.

UseSupport / Core / Transfer

ShowsCheck only

Age6-7 / 8-9 / 10-11

Practice focus

Word problems are confusing

Invariant game challenge choice

Invariant game challenge choice asks children to predict possible or impossible final state in a constrained move game using an invariant proof card.

Child actionPredict possible or impossible final state in a constrained move game using an invariant proof card.

CheckChoose the answer that matches the visible prompt.

UseSupport / Core / Transfer

ShowsCheck only

Age6-7 / 8-9 / 10-11

Practice focus

Word problems are confusing

Invariant move legal-illegal mark

Invariant move legal-illegal mark asks children to mark whether a proposed move preserves a named invariant.

Child actionMark whether a proposed move preserves a named invariant.

CheckComplete the invariant move legal-illegal mark action.

UseSupport / Core / Transfer

ShowsCheck only

Age6-7 / 8-9 / 10-11

Practice focus

Word problems are confusing

Pigeonhole box guarantee choice

Pigeonhole box guarantee choice asks children to choose the guaranteed conclusion from objects and boxes or capacities.

Child actionChoose the guaranteed conclusion from objects and boxes or capacities.

CheckChoose the answer that matches the visible prompt.

UseSupport / Core / Transfer

ShowsCheck only

Age6-7 / 8-9 / 10-11

Practice focus

Word problems are confusing

Selection

Fresh independent work can move the child toward Core, Transfer, or Challenge routes; help use or confusion keeps support visible.

Help

Hints keep the child oriented to the visible structure; reveals show the path without counting as independent evidence.

Age

Age changes presentation, reading load, and dignity of the screen. Practice focus can bias compatible work without breaking prerequisites or story fit.

Story fit

story beats with visible logic state, manipulable evidence, and a bounded child action