How is this different from the Red Rods?
The Number Rods are physically similar to the Red Rods but pedagogically different. The Red Rods are visual-sensorial; they train the eye to discriminate length. The Number Rods are the first maths material; they give the child quantity.
The Red Rods are a uniform red. The Number Rods alternate red and blue in 10cm segments. The shortest rod is 10cm long, one segment. The second is 20cm, two alternating segments (red 10cm, blue 10cm). The tenth is 100cm, ten segments. The child can count the segments on each rod to establish "how many" is in it.
The Red Rods come first in the sensorial area at around three and a half. The Number Rods come next in the maths area at around four. A child who has consolidated Red Rods will recognise the Number Rods immediately as the "same shapes, different colours, with countable segments".
The Number Rods, in detail
The presentation begins with three rods: one, two and three. The child learns to associate the spoken number with a rod length.
Invite the child. Carry the three rods to the work rug. Lay them in order, shortest at the top. Point to the shortest rod. Count its single segment: "one." Point to the middle rod. Count its two segments: "one, two." Point to the longest. "One, two, three."
Return the rods to the shelf. Invite the child to try. Step back.
Over several sessions, add rods up to ten. The child learns to count the segments on each rod in turn and to associate the word (one, two, three) with the rod. By the end of this phase, the child can lay out the full series of ten Number Rods and count them from "one" to "ten".
The Sandpaper Numerals
The ten digits 0 to 9, cut from sandpaper and mounted on thin wooden boards (traditionally green; sometimes deep red). They parallel the Sandpaper Letters for language but use the same material for a different subject area.
The presentation mirrors the Sandpaper Letters: trace each numeral with two fingers in writing direction while saying the number name. "One." "Two." "Three." Introduce two or three at a time via the three-period lesson. Do not introduce all ten at once.
The direct aim is the written symbol: the child learns the shape of each digit by tracing it, with the phonic-style association of name-to-shape built through the fingers. The indirect aim is writing: the muscle memory of tracing the numerals supports forming them later with a pencil.
A good UK set costs £20-50 new. Unlike the Sandpaper Letters, DIY versions for the numerals are easier because there are only ten; a careful parent can cut them from fine sandpaper and mount them on bought wooden boards for around £15.
Associating rods and numerals
The third step. Both rods and numerals must be consolidated separately first.
Lay the Number Rods out in order on the work rug. Place the Sandpaper Numerals 1 to 10 in a jumble on a second rug. Pick up the "1" numeral, trace it, say "one", place it next to the shortest rod. Pick up "2", trace, say "two", place next to the two-segment rod. Continue.
The child then replicates the work independently. The rod-numeral association is usually firm within a few sessions for a child who has mastered both sides separately.
Subsequent work: lay out the rods jumbled rather than in order; the child places numerals correctly and then reorders the rods. Lay out numerals; the child fetches the correct rod for each. The rod-numeral pair is the child's concrete-to-symbol bridge.
The Spindle Boxes: meeting zero
A wooden box with ten compartments labelled 0 to 9. A basket of forty-five small wooden spindles (thin rods).
The child counts the correct number of spindles into each compartment. One spindle in compartment "1". Two in "2". Three in "3". And so on to nine in "9".
The "0" compartment gets no spindles. It stays empty.
This is the child's first formal encounter with zero as a quantity (specifically, as no quantity). The empty compartment is the definition of zero in physical form. Children often find this moment satisfying and sometimes strange; a compartment that is meant to be empty is a new kind of quantity.
The Spindle Boxes also introduce the idea of loose quantities for the first time. The Number Rods give fixed, connected quantities (a rod of three is always a rod of three). The spindles are separate; three spindles is a count that the child can verify by recounting. This is a move toward the decimal system that will come next.
Spindle Box counting should be done in compartment order (0, 1, 2, 3, ..., 9) the first times, so the child encounters zero at the start. Once confident, the child works freely.
A commercial Spindle Box set costs £15-35 in the UK. DIY is possible with a stationery box and wooden dowels cut to size.
Cards and Counters: odd and even, discovered
A set of cards for the numerals 1 to 10, and a basket of fifty-five small counters (traditionally red circular tiles or glass beads). The child lays the cards in order and places the correct number of counters under each, arranged in a specific layout.
The layout matters. For even numbers, the counters are laid in pairs (for 2: two counters side by side; for 4: two pairs; for 6: three pairs). For odd numbers, the counters are laid in pairs with one left over in the middle (for 3: one pair plus one below; for 5: two pairs plus one below; for 7: three pairs plus one below).
The child, after laying out all the cards and counters, can see that the even numbers have all paired counters and no leftover, while the odd numbers each have a single unpaired counter. The word "odd" and the word "even" are introduced after the layout is stable.
Odd and even are therefore not taught as definitions. They are discovered as visible features of the physical arrangement. Children often sit and stare at the completed layout for some time, noticing the pattern. The moment of discovery is common enough that Montessori guides plan for it.
A typical first month of formal maths
A sequence that works for most four-year-olds who have consolidated the sensorial materials.
Week one. Number Rods 1 to 3. Presentation, several sessions of practice with the child counting segments. Introduce Sandpaper Numerals 1 and 2 in the same week via a separate presentation.
Week two. Number Rods 4 to 7. Sandpaper Numerals 3 and 4. Both materials are being used in alternate sessions; the child has not yet associated them.
Week three. Number Rods 8 to 10. Sandpaper Numerals 5 and 6. The full set of Number Rods is now on the shelf.
Week four. Sandpaper Numerals 7 to 9 (and 0, introduced last). The child has both sets consolidated separately.
Week five to eight. Association work. Rod and numeral matched. Spindle Boxes introduced in the middle of this range. Cards and Counters at the end.
By the end of the first two months, the child can count reliably to ten, recognise and trace each digit, associate each digit with its quantity, understand zero as an empty compartment and see odd and even as physical patterns. The decimal system work (Golden Beads, the next major material) begins after this foundation is stable.
Common home mistakes
Skipping the segment counting on the Number Rods. Counting "one, two, three" on the third rod matters; it is not optional. Presenting the rod by length alone loses the quantity association.
Presenting too many rods or numerals at once. Three at a time is the Montessori norm. Ten at once is overwhelming.
Introducing zero late or implicitly. Zero is a real number. The Spindle Boxes introduce it as an empty compartment; this is a moment the child should experience deliberately, not by default.
Using counters that do not lay out in pairs. Buttons, beads, natural stones: any small counter works if the child can arrange them in pairs on a flat surface. Large counters or ones that roll do not work for Cards and Counters.
Rushing to Golden Beads. The decimal system is the next major material, but it is much more demanding and depends on the 0-10 work being rock-solid. Do not skip ahead; the pink/blue/green-style progression applies here too.
A real family's first month of formal maths
A dad we will call Femi introduced the Number Rods to his son when he was four years and two months. He had bought a combined Number Rods / Sandpaper Numerals / Spindle Boxes set second-hand for £60.
Week one: Number Rods 1 to 3, presented on a Monday. His son counted the three rods with him and then laid out all ten rods, with Femi guiding the counting on each new rod. Within three days the son was counting to ten independently on the rods.
Week two: Sandpaper Numerals 1 and 2 introduced. Third period recall on day three was reliable.
By week four all numerals were consolidated. Week five: association. His son placed the "3" numeral next to the three-segment rod on the first try without prompting, and looked up for confirmation.
Week six: Spindle Boxes. The empty "0" compartment got a sustained look; his son said "there's none" and Femi said "that's right, that's zero". The new word was added to their spoken vocabulary.
Week eight: Cards and Counters. His son arranged the counters correctly under cards 1 to 10 on the first go, sat back and noticed the pattern. He said "some have an extra one and some don't". Femi introduced "odd" and "even" at that point.
Two months from Number Rods to Cards and Counters. Femi's son was ready for Golden Beads. Total spent: £60 on the combined set.