Short Bead Chains (Squaring Chains)

Direct aim. To count to 100 in a line, and then to count by each number up to its square.

Indirect aims, the ones you will not see at once

The hundred chain: ten golden ten bars joined end to end, about 70 cm long in Montessori's 1917 material. Nienhuis sells it on its own.

The short chains: for each number, as many bars as beads on a bar, joined end to end, with a bead square of the same color. Montessori's 1917 squares run 2 green, 3 pink, 4 yellow, 5 pale blue, 6 gray, 7 white, 8 lavender, 9 dark blue and 10 orange.

Labels: one small card or arrow per bar, marked with the running count, 10, 20, 30 to 100 for the hundred chain. Montessori's 1917 children matched cards marked 10, 20 and so on to ten bars; printed arrows are the later form.

A strip of floor or a long table, so the chain lies straight.

1. 1Lay the hundred chain out straight, with the golden hundred square at its top end.Silent Straighten the chain so every bar shows.
2. 2Count the first bar bead by bead with the child, one to ten. Set the 10 label at the tenth bead.Say Count together, touching each bead: "one, two" up to "ten".
3. 3Count on, eleven to twenty, and set down the 20 label. Carry on to 100.Say "Eleven, twelve..." Keep counting; set each label down without a word.
4. 4Read the labels back: ten, twenty, thirty, up to a hundred.Say "Ten, twenty, thirty..." Point to each label as you read it.
5. 5Fold the chain at each bar so the bars lie side by side, and lay the hundred square beside it: the same beads, in a square.Silent Fold slowly and let the square appear.
6. 6On later days, give the short chains one at a time, from the smallest, counting each by its own number.Say "This is the four chain." Count "four, eight, twelve, sixteen."

Folding the chain into a square that matches the hundred square exactly.

The row of labels along the floor, a number line made by the child.

The 2 chain, four beads, lying next to the hundred chain.

The discovery Montessori recorded: "The hundred chain has ten ten-bead bars!"

The labels and the square. The last label on each chain must read its number squared, 100 on the hundred chain, and the folded chain must match the bead square of the same color.

Montessori’s name for this check is the control of error.

• Counting the hundred chain backward, 100 down to 1
• Skip counting each short chain without the labels
• Writing the running count on a paper strip as long as the chain
• Writing the squares, 5² = 25, as Montessori's 1917 children did
• The thousand chain: ten hundred chains, about 7 m long, counted in a hallway over several days
• The long chains, one for the cube of each number, folded from square chains

Variations

This work needs only the material, so it has no printable of its own. The shelf plan below places it among the other works for the same age.

Free to print for your family, no email needed. Print at 100%, not “fit to page”, so the drawings keep their scale. Every printable on the site is listed on the printables page.

Ready for the first presentation

Ready for the next lesson

Beads on a homemade chain need strong cord and secure knots. A loose bead is a choking hazard.

Keep chains out of a toddler's reach. A long chain can wrap around a neck.

We have not bought the paid homeschool curricula, so they are not listed here.

1. Maria Montessori, The Montessori Elementary Material (1917)

   Part III, Tens, Hundreds, and Thousands

   Ten ten-bead bars joined end to end make the hundred chain, about seventy centimeters long, and ten hundred chains joined by flexible links make the thousand chain, about seven meters.

   Children counted bead by bead from 1 to 100, and a child counting the thousand chain stopped at seven hundred to mark the place and come back the next day.

   Children cried out that the thousand chain has ten hundred chains and that the hundred chain has ten ten-bead bars.

   Part III, Numbers 1 to 10

   Small cards marked 10, 20 and so on are matched by putting together the number of ten-bead bars each card calls for.

   Part III, Square and Cube of Numbers

   For each number there are as many bars as beads, joined in a chain or laid side by side as a square, in the counting colors: pink for 3, yellow for 4, pale blue for 5, gray for 6, white for 7, lavender for 8, dark blue for 9, orange for 10.

   The ten bars of the square of ten placed end to end make the hundred chain; the 5 × 5 chain holds the same 25 beads as its square, and the child writes 5 squared = 25.

   The square material is offered beginning with the smaller numbers, and the child is left free to work the idea into his consciousness.

   The chain of the cube of a number is made of chains of the square joined by links so that it can be folded into squares.

Lesson text and the scope and sequence are CC BY 4.0: reuse them with credit to Owen Wren, Homeschool Montessori, and a link. Photos and illustrations are all rights reserved. Terms.