Choose a fresh short opportunity when it helps the actual mathematical component. Each may be drawn large, tactile, selected or adult-operated at the child’s direction. These are not advanced learner labels, homework or a compulsory extra quota. No formal multiplication/division, repeating-pattern or whole-year attainment is claimed.
Supplement 1 · Same collection, new layout
Try: Use eight new marks. Child makes pairs, then directs a new layout without adding/removing.
Look for: Four pairs/eight objects in each layout, with correspondence.
Stop/revisit: If spacing changes the claimed quantity, match marks one-to-one, then a new six-mark set.
Keep first thinking and later support separate. Use a smaller range or another format where useful; actual selected range is named.
Supplement 2 · Pause in the twos count
Try: Use six pairs. Pause after the fourth pair; child shows how many objects are included and what remains.
Look for: 8 included, two pairs/four objects remain, complete total 12.
Stop/revisit: If the final 12 is given for the pause, separate completed/uncompleted groups and recheck after a new stopping point.
Keep first thinking and later support separate. Use a smaller range or another format where useful; actual selected range is named.
Supplement 3 · An own different start
Try: Child chooses a known starting amount, then adds two objects at each of three stages.
Look for: Any explicit consistent two-object increase with matching representation is valid; no prescribed initial number.
Stop/revisit: If labels alone change, identify two actual added marks and ask for a new stage.
Keep first thinking and later support separate. Use a smaller range or another format where useful; actual selected range is named.
Supplement 4 · First unequal group
Try: Prepare five alleged pairs with member counts 2,2,1,3,2. Child finds the first break and repairs membership.
Look for: Total 10 retained; move one from 3 to 1 for five true pairs.
Stop/revisit: If only the final numeral changes, inspect actual group membership before recounting.
Keep first thinking and later support separate. Use a smaller range or another format where useful; actual selected range is named.
Supplement 5 · Two true accounts
Try: Make sixteen new marks. Child counts in pairs, then shows another supported complete grouping or one-by-one verification.
Look for: Eight pairs→16; a new valid account must cover the same sixteen once.
Stop/revisit: A total without unit/coverage support gets a new small collection and one verified group.
Keep first thinking and later support separate. Use a smaller range or another format where useful; actual selected range is named.
Supplement 6 · An incomplete five
Try: Prepare groups 5,4. Child decides to restore a full group or label actual 9.
Look for: 9 unmodified;10 after one actual new mark.
Stop/revisit: Do not call a predicted addition performed. Check the actual representation after the decision.
Keep first thinking and later support separate. Use a smaller range or another format where useful; actual selected range is named.
Supplement 7 · Make a fives start
Try: Child chooses a known starting amount and makes three increasing five-object transitions.
Look for: Any explicit consistent five-object increase and matching totals; a nonzero start is valid.
Stop/revisit: If the start disappears, retain it and add five before a fresh attempt.
Keep first thinking and later support separate. Use a smaller range or another format where useful; actual selected range is named.
Supplement 8 · Replace, do not double
Try: Use thirty marks as six fives, then three tens. Child keeps both drawings and explains the one original set.
Look for: 30 in either account; drawing both does not add thirty new original objects.
Stop/revisit: If 60 is claimed, match the actual original marks to both representations and model a new small replacement.
Keep first thinking and later support separate. Use a smaller range or another format where useful; actual selected range is named.
Supplement 9 · Audit a large account
Try: Use a teacher-selected new large collection at a suitable demonstrated range. Child selects grouping, checks one unit and all coverage.
Look for: Record actual size/count/support; no pre-filled “to 120” result.
Stop/revisit: Continue partial work later or reteach coverage on a new small collection; do not credit an unmade larger total.
Keep first thinking and later support separate. Use a smaller range or another format where useful; actual selected range is named.
Supplement 10 · Your useful count note
Try: Child creates a manageable own collection account and a new skip-count sequence; explanation can be pointed/signed/scribed.
Look for: Separate grouping/cumulative count from recognition/continuation/creation; no required audience.
Stop/revisit: Choose the next component task from the first evidence, not from neatness, speed or response mode.
Keep first thinking and later support separate. Use a smaller range or another format where useful; actual selected range is named.
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