Cards and counters is the Montessori material where a child discovers odd and even numbers alone. Ten number cards, 55 red counters, and a simple rule for laying them out. Nobody has to explain the pattern. The child sees it.
This guide covers what the material is, when to introduce it, the step-by-step presentation, what to watch for, the extensions, and a free printable version you can make at home tonight.
At a Glance
- Age. Usually around 4, roughly between 3½ and 5.
- Direct aim. Match loose numerals to loose quantities, and discover odd and even.
- Indirect aims. Number order, one-to-one counting, concentration, self-correction.
- Ready when. Your child orders numerals 1 to 10, has worked with the spindle box and counts loose objects reliably.
- Next. Teen boards, the short bead stair, the hundred board.
What Are Montessori Cards and Counters?
The material is a box with wooden number cards from 1 to 10 and 55 small red counters. The child lays the cards in order across a mat, then places the right number of counters under each card, in pairs, with any extra counter centered below the last pair.
That arrangement is the point. Some numbers end with a counter that has a partner. Others end with a counter standing alone. The ones with a lone counter are odd. The child sees this in their own work before anyone names it.
Why exactly 55 counters? Because 1 + 2 + 3 + … + 10 = 55. If counters are left over, or run out before 10, something was miscounted. The total is the control of error, so the child finds the mistake without an adult.
Where It Fits in the Math Sequence
| Material | Numerals | Quantities |
|---|---|---|
| Number rods | Sandpaper numerals, separate | Fixed in wood |
| Spindle box | Fixed in the box | Loose spindles, plus zero |
| Cards and counters | Loose | Loose |
With cards and counters, both the numerals and the quantities are loose for the first time. Nothing guides the child except what they know. It brings together everything from the two materials before it. See the full order in our Montessori math materials guide.
When to Introduce It
Most classrooms present cards and counters around age 4, after the spindle box. The material assumes the child already knows that a numeral stands for a quantity. It asks whether they can show it with nothing fixed to lean on.
| Readiness sign | Why it matters |
|---|---|
| Completes the spindle box correctly and alone | The link between a numeral and its quantity is solid |
| Orders numerals 1 to 10 without the number rods | The first step is ordering loose cards |
| Counts loose objects reliably up to 10 | One miscounted group throws off every group after it |
| Notices and compares quantities on their own | A child who asks “why does nine have one left over?” is ready for odd and even |
How to Present Cards and Counters
Use a floor mat. The full layout of ten cards and 55 counters needs space. The presentation shows the setup and the pairing. The child works out the rest.
- Carry the box to the mat with two hands. Place it at the top edge and invite your child to sit beside you.
- Order the cards. Scatter the number cards. Ask your child to find 1 and place it at the top left, then ask what comes next, until all ten are in a row, a hand-width apart.
- Place one counter under 1. Centered, counting aloud, “one.”
- Place two counters under 2, side by side. Count as each one goes down.
- Place three under 3. A pair first, then the third counter centered just below it.
- Keep the pattern. Always pairs first, with any extra counter centered below the last pair.
- Hand it over. After a few numbers, invite your child to continue. Step back and watch.
What not to do in the first presentation. Don’t explain odd and even. Don’t point to the lone counters and name them. Don’t correct a non-standard arrangement in early sessions. Show the pairing again another day if needed. The discovery has to come from your child’s own observation.
What to Observe
Stay close and quiet. What your child does tells you where they are.
Signs it’s going well
- Orders all ten cards before placing counters
- Counts aloud or under their breath
- Pauses after a lone counter and looks back at the layout
- Compares odd and even numbers without being asked
- Counts back through each group at the end
Signs to step back
- Runs out of counters before 10, or has counters left over
- Places counters without pairing them
- Skips cards in the sequence
- Loses interest after a few numbers
Running short or having extras usually means a counting slip earlier in the row. If it happens every time, go back to the spindle box for a week or two. If cards get skipped, return to the number rods first.
Extensions and What Comes Next
The Finger Slide
When the layout is complete, show your child how to slide one finger down the middle of each column. For even numbers the finger passes between the pairs all the way down. For odd numbers the lone counter blocks it.
Your child feels the difference before hearing the words. Only then introduce them. “Numbers where your finger slides all the way through are called even. Numbers where a counter is in the way are called odd.”
A Three-Period Lesson
Once the words are known, use a three-period lesson. First name them (“this is odd, this is even”), then ask your child to show one (“show me an even number”), then to recall (“what kind of number is this?”).
Sorting From Memory
Write “odd” and “even” on two cards (they are in the printable). Mix the number cards and invite your child to sort them without counters, then check with the counters and the finger slide.
New Counters, Same Idea
Any 55 identical objects work. Pebbles, acorns, shells, dried beans or glass nuggets bring children back to the activity when the red counters have lost their novelty. Avoid small objects if a younger sibling is around.
After Cards and Counters
The next steps are the teen boards for 11 to 19, the short bead stair, and then the decimal system with the golden beads. See our Montessori math beads guide.
My Child Says “One-Zero” for Ten
This is very common. The card for 10 looks like two numbers, a 1 and a 0, and young children read what they see. It’s a sign they know their numerals, not a mistake to worry about.
- Quantity first. Count out ten counters together and say “ten” while touching the card.
- Bundle ten. Put ten counters in a small cup or tie ten sticks with a rubber band. “This is one ten.”
- Give it time. The idea that 1 in 10 means “one group of ten” comes later, with the golden beads and teen boards. See our Montessori math beads guide.
Free Printable Cards and Counters
Cards and Counters Printable
Three pages. Number cards 1 to 10, 55 counters to cut out, odd and even labels and the layout guide. Print on card stock, US Letter.
Prefer the wooden version? Compare current sets on Amazon (affiliate link). Montessori Theory may earn a small commission at no extra cost to you.
Questions Parents Ask
Can I Make My Own Cards and Counters at Home?
Yes, it is one of the easiest Montessori math materials to make. Print or write the numerals 1 to 10 on card stock and gather 55 identical objects. Keep the counters all the same so the child isn’t distracted by color or shape.
My Child Keeps Running Out of Counters. Is That a Problem?
It usually means the material came a little early. Go back to the spindle box for a week or two. Cards and counters needs reliable counting of loose objects up to 10.
When Do I Introduce the Words Odd and Even?
After your child has done the finger slide and noticed that some numbers let the finger through and some don’t. The words follow the experience.
Where Does This Fit in the Montessori Math Sequence?
It is the third of the first number materials, after the number rods and the spindle box, and before the teen boards and the golden beads.
Sources
- Laski, E. V., Jor’dan, J. R., Daoust, C. and Murray, A. K. (2015). What Makes Mathematics Manipulatives Effective? Lessons From Cognitive Science and Montessori Education. SAGE Open, 5(2). doi:10.1177/2158244015589588.
- Pires, A. C. et al. (2019). Building Blocks of Mathematical Learning: Virtual and Tangible Manipulatives Lead to Different Strategies in Number Composition. Frontiers in Education, 4, 81. doi:10.3389/feduc.2019.00081.
- Montessori, M. The Discovery of the Child (1948), on the arithmetic materials.
- Diagram and printable by Montessori Theory. Photo from Pexels (free licence).