Sandpaper Numerals
Sandpaper numerals are the figures 0 to 9 cut from sandpaper and mounted on smooth boards. A child of about 3.5 to 4 traces each one with two fingers, in the direction it's written, and says its name. Montessori taught them the way she taught the letters, then had the child lay each figure on its number rod.
Sourced from the texts, not yet presented at home
| Typical age | 3.5 to 5 years |
|---|---|
| Area | Math |
| Before this | |
| Materials | |
| Direct aim | To learn the shape and the name of each numeral, 0 to 9, by touch and sight together with the spoken name. |
| Control of error | The sandpaper. A finger that slips off the numeral meets the smooth board at once. Naming mistakes are the adult's to notice; the answer is another first period on another day. |
| Leads to | |
| Time | About 5 minutes for two or three numerals (our estimate). |
| Grouping | One child |
| Parent prep | None. The boards stand in their box on the shelf. |
| Cost | Buy about $12 to $36. Make: easy to make at home. |
| Other names | Sandpaper numbers, Sandpaper figures, Tactile numerals |
What the work teaches
Direct aim. To learn the shape and the name of each numeral, 0 to 9, by touch and sight together with the spoken name.
Indirect aims, the ones you will not see at once
- Preparation for writing numerals, since the fingers trace each stroke in writing order
- Linking each numeral to a quantity the child already knows from the number rods
- A light, controlled touch, the one the sandpaper letters train
- Preparation for the spindle boxes, where the numeral comes first and the child makes the quantity
Set it out before you invite the child
Ten boards, each with one numeral cut from fine sandpaper. Current sets mount them on green boards; Alison's boards are 4 by 4.5 inches.
Montessori's 1914 box held smooth cards with the figures 1 to 9. Zero came later, with the counting boxes, as the compartment where nothing goes. Current sets add a 0 board.
Pick the print style you'll use when the child writes numbers. Montessori Outlet's set is cursive; most others are print.
A table and chair, the child beside you on the side of the writing hand. Keep the number rods within reach for the last step.
Presentation, step by step
- 1Bring two numerals that look nothing alike, such as 1 and 2, and lay them in front of the child.
- 2Trace the 1 slowly with the first two fingers of your writing hand, in the direction it's written, and say "one".
- 3Invite the child to trace it and say the name. Do the same with 2.
- 4Second period: "Show me two." "Trace one." Mix the boards and ask again.
- 5Third period: point to a numeral and ask "What is this?"
- 6On a later day, with the number rods laid out as a stair, have the child place each numeral card beside its rod.
Details that hold the child's attention
The rough numeral under two fingertips, against the smooth board.
Tracing with eyes closed and still knowing which numeral it is.
A numeral laid on its rod: the stair of rods becomes a stair of numbers.
The zero, which Montessori turned into a game about nothing.
How the child sees a mistake
The sandpaper. A finger that slips off the numeral meets the smooth board at once. Naming mistakes are the adult's to notice; the answer is another first period on another day.
The words come after the hands
| Words | Shown with |
|---|---|
| one to nine | The numeral names, two or three at a time. |
| zero | The numeral for nothing. It gets its own lesson with the spindle boxes. |
| numeral | The written sign, as against the quantity. The adult's word for now. |
| trace | Following the numeral with two fingers, the way it's written. |
The three-period lesson, scripted
You need two numerals that look different, such as 1 and 2.
| Period | What you do and say |
|---|---|
| 1. Naming | Trace the 1: "This is one." Trace the 2: "This is two." |
| 2. Recognition | "Give me one." "Give me two." |
| 3. Recall | Point to one and ask "What number is this?" |
These are Montessori's own 1912 words for the numerals. Our suggestion: keep 6 and 9 apart until both are secure.
Extensions and variations
- Placing the numeral cards on the number rods laid out as a stair, the first exercise Montessori gave once the figures were known
- Tracing with eyes closed
- Tracing a numeral, then writing it with a finger in a tray of salt
- Writing numerals on a chalkboard
- The spindle boxes, where the numeral asks for a quantity
Variations
- Cursive or print sets: use the style you'll teach for writing
Make it or buy it
| Material | Make it | Buy, approx. |
|---|---|---|
| Sandpaper Numerals | Easy | $12 to $36 |
Prices noted . Approximate US street prices for home-use versions; they vary by maker and change often, so recheck before buying.
Making it at home
Print large numerals 0 to 9, trace them onto the back of fine sandpaper in reverse, cut them out and glue each to a smooth board about 10 by 11 cm.
What to check when buying a set
Check that the sandpaper is fine and firmly glued. A box is useful but optional; some sets sell it separately.
Printables for this age
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.
- Shelf plan for age 3PDF, 1 page, 250 KBEvery work for this age on one page, in order, with a column to date each presentation.
Every printable for one age, by email
The shelf plan and the lesson printables for your child's age in one email, then three short emails on the first lesson, what to make or buy, and what comes next.
Signs the child is ready, and signs it is done
Ready for the first presentation
- Names all ten number rods in order.
- Traces sandpaper letters with a light touch.
- Counts ten objects accurately.
- Asks what the numbers on clocks and doors say.
Ready for the next lesson
- Names any numeral 0 to 9 on sight.
- Traces each in the writing direction without being shown.
- Puts the numeral cards 1 to 10 on the right rods.
- Writes a few numerals on paper, unprompted.
Fitting it into a home, not a classroom
| If you have | Do this |
|---|---|
| A tight budget | Cut numerals from fine sandpaper using a printed template and glue them to card or thin board. The material page has the steps. |
| Sandpaper letters already on the shelf | Present the numerals the same way. Montessori used one method for both, so the child already knows the routine. |
| A child who writes some numerals backward | Go back to tracing those numerals in the writing direction. Leave the written ones uncorrected for now. |
| Two children | The older names a numeral and the younger fetches the rod with that many sections. |
When it does not go to plan
| When | Try this |
|---|---|
| The child traces in the wrong direction. | Trace it again yourself, slowly, beside them. The direction matters because the hand is learning to write. |
| 6 and 9 get mixed up. | Give them in different sessions until each is secure on its own. |
| The child counts well but can't name the numerals. | That's expected. The quantity came first with the rods; the symbol is a new step. Two numerals per session. |
| The child wants all ten at once. | Let them trace all ten, but name only two or three in the three periods. |
Hazards to check before each session
On homemade boards, glue the sandpaper flat and seal the edges so a corner can't lift and scratch.
There are no small parts here. The boards are safe around younger children.
Where other sequences and standards place it
We have not bought the paid homeschool curricula, so they are not listed here.
| Framework | Where it sits |
|---|---|
| This site's Math sequence | Lesson 2 of 12 published, after Number Rods and Sandpaper Letters, before Spindle Boxes: Counting 0 to 9. Checked in: the scope and sequence |
| Montessori, The Montessori Method (1912) | Teaching of numeration: once the child names the rods, and if he can already write, the sandpaper figures come with the same three periods as the letters. Checked in: Chapter XIX, Teaching of Numeration |
| Montessori, Dr. Montessori's Own Handbook (1914) | Arithmetic: a box of sandpaper figures 1 to 9, traced in the writing direction and then placed on the rods. Checked in: Arithmetic |
| Common Core, Kindergarten math | K.CC.A.3: write numbers from 0 to 20; represent a number of objects with a written numeral 0 to 20, with 0 for a count of no objects. Checked in: tasks.illustrativemathematics.org |
| Head Start Early Learning Outcomes Framework, preschool | P-MATH 3: the child understands the relationship between numbers and quantities. Checked in: www.in.gov |
Sandpaper Numerals: questions parents ask
What are sandpaper numerals in Montessori?
The numerals 0 to 9 cut from sandpaper on smooth boards. The child traces each with two fingers in the direction it's written and says its name, so hand, eye and ear learn the figure together. They work exactly like the sandpaper letters.
What age are sandpaper numerals for?
About 3.5 to 4, once the child names the number rods in order, and on this site up to 5. Montessori's 1912 book adds a condition: give the sandpaper figures once the child already knows how to write.
Should numerals come before the number rods?
No. Montessori's order is quantity first: the child names the rods, then meets the figure, then lays it on the rod. The numeral then names something the child has already carried.
Do sandpaper numerals need a zero?
Current sets include one. Montessori's 1914 box held 1 to 9, and zero came with the counting boxes, as the compartment where nothing goes. Present it then.
Sources cited by book and chapter
- Maria Montessori, The Montessori Method (1912)
Chapter XIX, Teaching of Numeration
If the child already knows how to write, the figures cut in sandpaper and mounted on cards are presented with the same method as the letters, This is one, Give me two, What number is this, and the child traces them with his finger.
Chapter XX, Sequence of Exercises
The child places the corresponding figures beside the number of blue and red sections on each rod of the long stair.
- Maria Montessori, Dr. Montessori's Own Handbook (1914)
Arithmetic
A box of smooth cards with the figures one to nine cut out in sandpaper, like the sandpaper letters; the child touches each figure in the direction in which it is written and names it.
The child is shown how to place each figure on the corresponding rod, and placing the number cards on the rods arranged in gradation is one of the first exercises.
The figure is a graphic sign that can be substituted for the concrete rods and permits unlimited progress in arithmetic.
In the box containing the pegs one compartment is marked 0, inside which nothing must be put, and then we begin with one.
Reviewed by
What to offer next
Once the child chooses this work unprompted and finishes it without help, the next lesson to prepare is Spindle Boxes: Counting 0 to 9.
- Number Rods3.5 to 5 years
- Sandpaper Numerals3.5 to 5 years
- Golden beads4 to 5.5 years
- Spindle boxes4 to 5.5 years
- Teen boards4 to 6 years