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What is the Casa maths sequence and why does it matter?
The Casa maths sequence (Casa meaning the Montessori 3-6 classroom, also called Children's House) is the order in which presentations (short, adult-led demonstrations of a specific concept or material) are traditionally given to children in Plane 1 (roughly birth to six, the period of the absorbent mind). It runs from concrete, hands-on counting all the way through to the four operations and early place-value work.
The order is not arbitrary. Each presentation builds a specific sensory or cognitive foundation that the next one depends on. Number rods (ten graduated wooden rods, alternating red and blue, representing quantities 1-10 as physical length) come before sandpaper numerals (individual digits cut from fine-grade sandpaper, traced with the fingertips) because a child needs to feel quantity before attaching a written symbol to it.
You do not need to have studied the full AMI Casa maths album (the detailed teacher's lesson-plan guide) to use this sequence at home. What you need is the order, the materials list, and an observational eye for when your child is ready to move on.
Pace by the child, not the calendar
This is the single most important thing to hold in mind. The 12-24 month range on the printable is the typical Casa classroom span. Some children move through the whole sequence in 9 months. Others take 30 months. Neither is ahead or behind.
Your child is ready for the next presentation when you observe mastery of the current one, not when a calendar says it is time. The "ready when" markers on the printable are observational cues, not pass/fail tests. They describe what you might notice when your child has internalised the concept. If you are not seeing those signs yet, stay where you are. The material will do its work in its own time.
If you are a single parent or shift worker with limited windows for presentations, that is fine. A presentation takes 5-10 minutes. The child's independent repetition afterward (which is where the real learning happens) does not require you to be sitting there. You can present once and let them return to the work across the week.
The printable: 12-24 month Montessori maths sequence
Band 1: Months 1-12 (numeration and introduction to quantity)
| # | Presentation | Materials needed | DIY? | Ready when... |
|---|---|---|---|---|
| 1 | Number rods | Ten graduated rods (alternating red/blue), 10cm increments | Commercial recommended (precision matters) | Child names quantities 1-10 by pointing to the correct rod without hesitation |
| 2 | Sandpaper numerals | Cards with digits 0-9 in fine sandpaper | Commercial recommended (tactile quality matters) | Child traces and names all digits 0-9 from memory |
| 3 | Spindle box (a partitioned box with compartments labelled 0-9, into which loose spindles are counted) | Box with 10 compartments, 45 spindles or similar small objects | DIY acceptable (ice-cube trays, egg boxes, craft sticks) | Child counts the correct number of objects into each compartment, including zero |
| 4 | Cards-and-counters (numeral cards laid in order with counters placed beneath, revealing odd and even) | Numeral cards 1-10, 55 identical counters | DIY acceptable (cut card, dried beans or buttons) | Child lays out independently, can identify which numbers are odd and which are even |
| 5 | Golden bead introduction (the entry point to the decimal system, using physical beads to represent units, tens, hundreds, thousands) | Unit beads, ten-bars, hundred-squares, thousand-cube | Commercial essential (uniformity of bead size is load-bearing) | Child names "unit, ten, hundred, thousand" while pointing to the correct bead material |
Band 2: Months 12-24 (operations and exchange)
Multiplication follows addition here because it is presented to the child as repeated addition, with the addition work still concretely fresh. Subtraction then comes in as the inverse of addition, and division as the inverse of multiplication.
| # | Presentation | Materials needed | DIY? | Ready when... |
|---|---|---|---|---|
| 6 | Static addition (combining two quantities with golden beads where no carrying is needed) | Golden bead material, large number cards (symbol cards showing 1-9000), felt mat | Same golden bead set as step 5 | Child combines two quantities, counts the result and lays the matching number cards without prompting |
| 7 | Static multiplication (repeating a quantity several times and counting the total) | Golden bead material, large number cards, felt mat | Same set | Child sets out the same quantity multiple times and counts the combined total |
| 8 | Static subtraction (removing a smaller quantity from a larger one, no exchanging) | Golden bead material, large number cards, felt mat | Same set | Child removes beads confidently and reads the result with number cards |
| 9 | Static division (sharing a quantity equally among skittles or small figures) | Golden bead material, large number cards, 2-3 skittles | Same set + 2-3 small identical figures | Child distributes beads equally, names the share each figure receives |
| 10 | Exchange game (the bridge to dynamic operations, where ten units are traded for one ten-bar and vice versa) | Golden bead material | Same set | Child spontaneously reaches for a ten-bar when they have ten loose units and names the exchange unprompted |
| 11 | Introduction to the bead frame (representing larger numbers on a frame rather than with loose beads, opening the door to Plane 2 work) | Small bead frame (4-wire, one wire per place value, colour-coded) | Commercial essential (precision of bead movement matters) | Child reads and builds 4-digit numbers on the frame. Note: this presentation opens Plane 2 maths; it is introduced here but not concluded at Casa level |
A real example
Maya is four and lives with her mum, Priya, in a Cardiff terrace. Priya works three days a week in NHS admin and does maths presentations on the other two mornings, usually around 9:15 once Maya's younger brother is settled with a basket of toys.
They started with number rods in January. Maya loved them immediately and was naming quantities within a fortnight. Sandpaper numerals took longer. She could trace but kept mixing up 6 and 9, so Priya stayed on step 2 for about six weeks, presenting just those two numerals side by side. No rush.
By March they had reached the spindle box. Priya made one from an old egg box (12 compartments, tape over two) and a jar of wooden pegs from a charity shop. It cost nothing and worked perfectly.
The golden beads arrived in April. Priya bought a second-hand set from a home-ed Facebook group for £35. She could not have DIY'd them (the bead uniformity matters for the child to feel the ten-ness of a bar), but she was glad she waited for a second-hand set rather than buying new.
Six months in, Maya is on static addition with the golden beads. She can build numbers with the large symbol cards (large numeral cards showing units, tens, hundreds and thousands in different colours) and combine two small quantities. Priya has not touched multiplication yet. The printable is still on the cupboard door. The "ready when" marker for step 7 is what she is watching for.
If Priya were working full-time shifts, the same sequence would work. The presentations themselves take under ten minutes. She could present on a Saturday morning and let Maya return to the material across the week independently.
What about DIY vs commercial materials?
Some materials in this sequence need to be commercially made. Sandpaper numerals need consistent grit and precise letter-formation. Golden beads need uniform size so that ten units genuinely equal one ten-bar in weight and feel. The bead frame needs smooth, colour-coded beads that slide accurately.
Others are perfectly fine as DIY. The spindle box can be an egg carton. Cards-and-counters can be hand-cut card and dried beans. The number rods can be painted dowels if you have a saw and patience (though most families find a second-hand set easier).
If money is tight and you cannot currently stretch to golden beads, you can work through steps 1-4 while saving or watching second-hand groups. This is one of the more cost-effective aspects of homeschool Montessori maths: the numeration foundation is largely DIY-friendly. Steps 1-4 alone cover several months of meaningful maths work. You are not stalling; you are building a solid numeration foundation that the operations depend on.
What comes after the exchange game?
The bead frame (step 11) is the final presentation in this sequence, but it is an opening rather than a conclusion. It bridges into Plane 2 maths work (roughly ages 6-12, the period of the reasoning mind) where the child moves toward abstraction, larger numbers and more complex operations.
This printable does not cover Plane 2 territory. If your child reaches the bead frame and thrives, the next steps include the stamp game (a Casa-level dynamic-operations material your child may already be using alongside the bead frame), the dot game, and eventually the bead-frame operations for long multiplication and division. Those are a different article for a different stage.
Frequently asked.
- Does my child need to complete the whole sequence before age six?
- No. The 12-24 month range is a typical Casa span, not a target. Some children move through it in 9 months, others in 30. Both are normal.
- Can I skip presentations my child already seems to understand?
- Each presentation builds a specific skill the next one relies on. If your child seems ready, you can move quickly through a step, but presenting it briefly still matters.
- Do I need to buy commercial Montessori materials for every step?
- Not every step. Some materials (sandpaper numerals, golden beads) work best as commercial products because precision matters. Others (spindle box, cards-and-counters) are perfectly fine as DIY.
- What if we only have 20 minutes a day for maths?
- Twenty minutes of focused work is plenty at this age. A presentation itself takes 5-10 minutes. The child practises independently afterward. That practice is the real learning.
- My child loves the golden beads but refuses the number rods. Is that a problem?
- It is common. The number rods build a sense of quantity-as-length that the golden beads build on. You might try shorter sessions with the rods or revisit them alongside the beads rather than forcing a strict sequence.
- What is the difference between static and dynamic operations?
- Static means no carrying or borrowing is needed (e.g. 23 + 14 = 37). Dynamic means you need to exchange (e.g. 27 + 15 = 42, where the 12 units become 1 ten and 2 units). This sequence covers static first; the exchange game bridges into dynamic.