Owns: The overspill mode — how the addends are laid, how the carry becomes visible as a consequence, and why the representation fades by number type without any adaptive logic. Supersedes: nothing. Addendum to Exchange.md, which owns the exchange act itself and rulings E1–E8. Status: Committed as built. CalculationRoom1D (Counting) ships on this spec and has been playtested. Cited by: calculation_room_1d.gd:12 · exchange_rod.gd:83, 110, 483 · The_Pass_Ledger:212. Note: §5 stage 1 is built; stages 2–4 are designed and unbuilt. §8 records what was in scope for the Counting build.

The Overspill

Fill-to-ten is grouping on instruction. Overspill is grouping because the container ran out.

1 · The act

7 + 6

1. The child places 7 in the ledger → seven units appear in the rod below, laid along it
2. The child places + and 6 (either order — but the operator must be placed)
3. The six are laid on after the seven → the frame overspills
4. The excess 3 pulsate — held, marked, watchable
5. They lift into a second row, on top of the first
6. Count full rows → 1 → tens column
7. Count the loose row → 3 → units column

Ledger and rod are synchronised. Placing a digit in the notation makes the quantity appear beneath it.

★ That synchronisation is A1’s bridge, running live: the rod holds the quantity, the ledger records it, and the child watches the two agree. The violation in place_value_house is a chart being asked to hold both. Here they are two objects moving together.

2 · Why the overspill is better

The regrouping stops being an instruction and becomes a consequence of the material running out of room. That is a gift of the mechanic in the frozen sense: the honest physics does the teaching, and no dialogue is required.

The pulsate is the beat that makes it work — the excess is marked and held long enough for the child to predict what must happen before it happens.

3 · The array reading — and how it must NOT look

Two rows, first full, second holding three. Count the full rows; count the leftover.

★ Place value is the array with its width locked to the base.

Which is why 10 × 10 is the hundred square, and why one component gives rod, array and hundred by changing capacity and columns.

⚠ This is not the times-table array, and the visual must say so

A sealed row is one ten. If it still reads as ten cells, the material is asserting the opposite of what sealing means. §6 is how the visual carries that.

The rhyme with multiplication is a special case, not an identity — worth using, not over-claiming. A child doing column addition still meets array structure before Venus, which is transfer arriving in the material rather than the curriculum.

4 · It is the bar, not the number line

The apparatus below the ledger lays quantities end to end as lengths. That is the bar — cardinal, quantity-as-length (T3). The number line is positions — start at 7, hop 6, land on 13 (T4). A3 keeps them apart.

Visually near-identical; conceptually different; and showing both is standard, valuable practice — the bar answers how much, the line answers where you land.

So the rhyme is a feature, provided the corridor knows which is which:

The line gives the operation its meaning. The bar gives the carry its structure.

One consequence for the build: the two addends should be visually distinct in the rod — 7 in one shade, 6 in another. Then 13 reads two ways at once: as seven-and-six (the bond) and as one-ten-and-three (the place value). The double reading is the whole point, and it continues shrine_of_bonds’ work rather than repeating it.

5 · The fade — free, because the numbers grow

No adaptive logic and no flags. Counting’s bounds keep sums inside the line’s readable range; Whole’s bounds push past it; hundreds push past that. The material’s limits and the number-type bounds coincide — which is usually a sign the structure is right rather than imposed.

Stage 1 shows why the row breaks. Stage 2 assumes you know, and just does it.

6 · ★ The seal is a visual unification that keeps the parts

The two addends are different colours — 7 in one, 6 in another. On seal, the full row is shaded over: a darker treatment in the same hue family, so the two colours remain legible underneath.

Both readings survive at once:

• seven-and-six — the bond, still visible through the shading
• one-ten-and-three — the place value, asserted by the unification

Shading rather than recolouring is what keeps the first reading. Recolouring to a single ten-colour would erase the bond and repeat what shrine_of_bonds already taught rather than continuing it.

And the cell structure goes

On seal, the row’s internal dividers fade, and the row reads as one bar rather than ten boxes.

★ Sealing turns ten discrete things into one continuous thing. That is precisely what promotion to the next denomination means — and it makes the sealed row into a bar, which is what a ten is at the next level up.

It also settles §3 without a rule: the times-table array keeps its cells because every cell is a countable unit of the product; the carry array loses them on seal because the row has stopped being ten of anything.

7 · Who does what

The rule: the material behaves; the notation is authored. The excess must lift — there is nowhere else for it — but nothing is written down until the child writes it.

8 · Tonight

Counting is single digit + single digit, so stage 1 only.

Needed: one frame, two addends laid distinctly, overspill, pulsate, lift to row 2, child counts and records. Not needed: pour-fill mode · flats · a tens frame that fills · regroup-down (single-digit subtraction never regroups — that arrives with Whole).

3 + 5 must produce eight loose in one row, no overspill, no carry — the no-carry case has to look plainly different from the carry case, or the carry teaches nothing.

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