AXIOKids

Combinatorics Counting List

Combinatorics Counting List practice with visual examples, common slips, and next-step routes.

Surface

Children may meet this skill through task formats such as Systematic list tray build, List missing or duplicate repair, Tree diagram branch read-build, Casework cover board.

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

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

Systematic list tray build

Systematic list tray build asks children to build an organized list of all valid cases using cards or chips.

Child actionBuild an organized list of all valid cases using cards or chips.
CheckComplete the systematic list tray build action.
UseSupport / Core / Transfer
ShowsCheck only
Age6-7 / 8-9 / 10-11

Practice focus

Word problems are confusing

Tree diagram branch read-build

Tree diagram branch read-build asks children to read or build branches representing all choices in order.

Child actionRead or build branches representing all choices in order.
CheckComplete the tree diagram branch read-build action.
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