VectorPaint abacus place-value cards: map one-five and four-one beads, including zero columns

English translation of the Chinese original, translated on 2026-11-08. Original publication dates, attribution, code and version notes are retained.

Adding every visible bead can misread an abacus diagram. This exercise explicitly uses one upper bead worth five and four lower beads worth one per column, counted only when engaged toward the beam, to make three-digit cards. Use static graphics and external arithmetic, without an assumed abacus widget, traditional procedure instruction or physical-operation training.

Fix column order and the counting convention

Create a landscape card with hundreds, tens and units from left to right, each heading aligned to its rod. Add a beam, one upper bead and four lower beads on each column, retaining all fifteen beads in every state. Explain that the upper bead counts five toward the beam, each lower bead counts one toward it, and away beads do not count. Colour is supplementary rather than the sole active-state signal. The upper bead moves down toward the beam; lower beads move up. Record a maximum column value of nine, five plus four ones, rather than treating the upper section as five physical beads.

Draw all beads in the zero state

Begin with all three columns at zero: upper beads away from the beam and every lower bead at the away end, with consistent bead/rod relationships. Leave a clear beam-side gap; a lower bead must not touch the beam while labelled inactive. Ellipses or simplified beads should have consistent size, without deleting zero columns or shortening their rods. Reduced views must still distinguish sections and columns. Preserve this zero-state baseline for duplication: it is not an empty canvas and distinguishes a genuine zero from an unknown state caused by missing beads.

Encode 305 column by column

Duplicate zero. Engage three lower beads in the hundreds column, leaving its upper bead inactive; keep tens zero; engage only the upper units bead, with all four lower units beads away. Write 3 times 100 plus 0 times 10 plus 5 times 1 equals 305. An upper bead’s five is not automatically five hundred: calculate its column digit, then apply place value. Enlarge each column to inspect positions for both engaged and away beads, with no disappearing inactive beads. Keep value text outside the card so it does not obscure beam-side gaps.

A 350 comparison requires bead changes too

Duplicate a 350 state: retain hundreds three, engage the upper tens bead for five and reset units to zero. Compare it with 305; both tens and units positions change, not merely the two printed digits. Read left to right as three-zero-five or three-five-zero before reading the whole integer. Mirroring a card affects column order and is not an arbitrary decorative transformation. Retain the same frame, beam height and bead count so differences arise from counting positions rather than simultaneous layout changes.

Separate 308 and 309 by one lower bead

From 305, create 308 by engaging three lower units beads in addition to the upper five, giving five plus three. For 309, engage the fourth lower bead as well, giving five plus four. Other columns stay identical, and each still has one upper/four lower beads; do not invent a fifth lower bead to represent ten. List active beads for eight and nine beside the views, calculating textually before matching the drawing. If lower beads are widely separated, make the engaged beam-side region unambiguous rather than leaving each bead’s status to guesswork.

Reset units and increase tens for the carry state

For the external arithmetic example 309 plus one, the result is 310. Retain hundreds three, engage one lower tens bead and move the upper and all four lower units beads away. Show both changed columns explicitly, without a ten-valued units bead or an improvised extra units rod. Display 308,309,310 in sequence if desired, but arrows describe static relationships rather than app-executed addition. This does not teach a physical finger sequence; use appropriate separate instruction for real bead manipulation instead of inferring operation standards from graphical displacement.

Hide printed answers when checking output

Save the source and export a PNG. Open it, conceal printed answers temporarily and read each three-column card independently before checking text. Count fifteen beads on every card, including five on a zero tens column. At viewing size, inspect upper-away gaps and lower-engaged positions, enlarging sections if necessary rather than using colour alone to compensate for ambiguous placement. Correct stacking if backgrounds or strokes obscure rods, then inspect every column again. Deliver the convention, column headings and complete values, without letting printed answers substitute for readable bead positions.

Troubleshoot bead state, place value and zero columns

If 305 reads as 350, inspect column headings and placement rather than changing the printed answer. If eight reads as three, check the upper bead’s engagement. If nine becomes ten, check an extra lower bead. If the carry still resembles 309, verify that units fully reset. Repair one column at a time and independently reread the whole number. The checklist contains five states: 305,350,308,309,310, all under one convention. Reconstructing their numbers establishes clear encoding, not calculation speed, mental-arithmetic ability or an interactive app abacus.