Meet the frame.

Before moving a bead, identify its rod, its counting area and the decimal boundary. Then ask what its movement means.

Optional read-aloud uses your browser’s voice.

Photograph of the wooden prototype showing positive whole and fractional places — Original photograph from page 24. This is the positive portion of the prototype, not the complete signed frame. Open full size

Question

If one bead looks larger than another, does its size alone tell you its numerical value?

Count and place work together

Each decimal digit position uses nine movable beads and an empty count for zero. Rod labels identify place value. Bead diameters provide visual and tactile cues; they are not proportional measures of numerical value.

The cut bicone profile reflects the designer’s attention to touch and movement. A contrasting fifth bead is a grouping cue: moving it alone still counts as one bead of that rod’s value.

Original diagram labelling rods, bead store, counting area, zero line, decimal boundary and movement directions — Original page 18 diagram. Labels are preserved. Open full size to examine the details. Open full size

Full signed layout with positive and negative stores and whole and fractional places — Original page 19. The dot column marks the decimal boundary; the zero line separates sign areas. Open full size

Movement needs context

Area	Activate beads	Return to storage
Positive, store above	Move down: increase positive magnitude	Move up: decrease positive magnitude
Negative, store below	Move up: increase negative magnitude	Move down: decrease negative magnitude

Why “add a bead” can be ambiguous

Activating another negative unit changes −3 to −4. Adding positive one to −3 gives −2 and removes one negative unit. Always state the sign and starting value before describing movement.

Try it

Activate one more negative unit from −3. What is the new value?

Choose an answer when you are ready.

Explore the four layouts

Positive whole places

Original positive whole-number rods, store and movement arrows — Original page 20. Stored beads initially give an empty count. Open full size

Negative whole places

Original negative whole-number rods, lower store and arrows — Original page 21. Activating negative beads moves them upward. Open full size

Positive fractional places

Original positive fractional rods and decimal-boundary markers — Original page 22. Each place right is one tenth of the preceding place. Open full size

Negative fractional places

Original negative fractional rods, lower store and decimal markers — Original page 23. Read the whole fractional magnitude with one negative sign. Open full size

Reflect

How can the same upward direction have different meanings in the positive and negative areas?

Shifting is re-entering counts

Recreate a digit pattern one rod left to multiply by ten or one rod right to divide by ten. Beads slide vertically on fixed rods; they do not slide sideways between rods. The destination places must exist.

Explore this on the interactive frame