AXIOKids

Proof and counterexample artifacts

Produce a visible example, counterexample, or short proof artifact that justifies or rejects a mathematical claim.

Surface

Children may meet this skill through task formats such as Clue-card candidate choice, Candidate elimination markboard, Violated-clue marker, Ambiguity repair clue choice, Minimal clue set choice, Grid consistency repair, List missing or duplicate repair, Parity pairing proof choice, Invariant move legal-illegal mark, Truth card verifier, Proof card evidence choice, Counterexample card build-select, Contradiction clue mark, Pigeonhole box guarantee choice, Invariant game challenge choice.

Task formats

Ambiguity repair clue choice

Ambiguity repair clue choice asks children to choose a clue action that changes an ambiguous clue set into a valid unique solution.

Child actionChoose a clue action that changes an ambiguous clue set into a valid unique solution.
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

Candidate elimination markboard

Candidate elimination markboard asks children to mark candidates eliminated by a highlighted clue or all clues.

Child actionMark candidates eliminated by a highlighted clue or all clues.
CheckComplete the candidate elimination markboard action.
UseSupport / Core / Transfer
ShowsCheck only
Age6-7 / 8-9 / 10-11

Practice focus

Word problems are confusing

Clue-card candidate choice

Clue-card candidate choice asks children to use clue cards to eliminate visible candidates and choose the single survivor.

Child actionUse clue cards to eliminate visible candidates and choose the single survivor.
CheckChoose the answer that matches the visible prompt.
UseSupport / Core / Transfer / Challenge
ShowsIndependent solve / Supported solve / Challenge ready
Age6-7 / 8-9 / 10-11

Practice focus

Word problems are confusing

Contradiction clue mark

Contradiction clue mark asks children to mark the clue, statement, or grid mark that contradicts the rest.

Child actionMark the clue, statement, or grid mark that contradicts the rest.
CheckComplete the contradiction clue mark action.
UseSupport / Core / Transfer
ShowsCheck only
Age6-7 / 8-9 / 10-11

Practice focus

Word problems are confusing

Counterexample card build-select

Counterexample card build-select asks children to select or build one valid counterexample to disprove a claim.

Child actionSelect or build one valid counterexample to disprove a claim.
CheckComplete the counterexample card build-select action.
UseSupport / Core / Transfer
ShowsCheck only
Age6-7 / 8-9 / 10-11

Practice focus

Word problems are confusing

Grid consistency repair

Grid consistency repair asks children to find and fix a wrong mark in a partially filled grid.

Child actionFind and fix a wrong mark in a partially filled grid.
CheckComplete the grid consistency repair 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

List missing or duplicate repair

List missing or duplicate repair asks children to mark duplicate, missing, or illegal cases in a list.

Child actionMark duplicate, missing, or illegal cases in a list.
CheckComplete the list missing or duplicate repair action.
UseSupport / Core / Transfer
ShowsCheck only
Age6-7 / 8-9 / 10-11

Practice focus

Word problems are confusing

Minimal clue set choice

Minimal clue set choice asks children to select the smallest sufficient clue set or mark a redundant or necessary clue.

Child actionSelect the smallest sufficient clue set or mark a redundant or necessary clue.
CheckComplete the minimal clue set choice action.
UseSupport / Core / Transfer
ShowsCheck only
Age6-7 / 8-9 / 10-11

Practice focus

Word problems are confusing

Parity pairing proof choice

Parity pairing proof choice asks children to pair objects or choose a proof card to justify even, odd, or impossible.

Child actionPair objects or choose a proof card to justify even, odd, or impossible.
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

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

Proof card evidence choice

Proof card evidence choice asks children to select the proof card that supports a visible claim.

Child actionSelect the proof card that supports a visible claim.
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

Truth card verifier

Truth card verifier asks children to mark a visible statement as true, false, or not determined and choose evidence when required.

Child actionMark a visible statement as true, false, or not determined and choose evidence when required.
CheckComplete the truth card verifier action.
UseSupport / Core / Transfer
ShowsCheck only
Age6-7 / 8-9 / 10-11

Practice focus

Word problems are confusing

Violated-clue marker

Violated-clue marker asks children to given a proposed candidate or arrangement, mark the clue it breaks.

Child actionGiven a proposed candidate or arrangement, mark the clue it breaks.
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