Montessori Math

Browse by Age

Ages are readiness ranges, not deadlines — most children work across two bands at once. When in doubt, start earlier in the sequence than you think and let ease decide.

Lessons, in order

1Numbers to 10Ages 4–6 · PK–K

  1. 1The Colored Bead StairYour child builds a triangle-shaped "stair" from nine colored bead bars, counting each one from 1 to 9. It is one of the very first math works: each quantity gets its own color and length, so numbers become something you can see and hold.ages 4–6
  2. 2Cards & Counters and Odd/EvenYour child lays the numeral cards 1 through 10 in order and counts exactly 55 counters beneath them in pairs. It is the classic test of whether counting to ten is truly secure — and the doorway to odd and even numbers.ages 4–5

2Linear & Skip CountingAges 4–7 · PK–1

  1. 1Teen Board: Names of the TeensYour child learns the names and numerals of eleven through nineteen by sliding unit cards over the printed tens of the Seguin board. This is where counting past ten begins, right after the colored bead stair.ages 4–6
  2. 2Teen Board with Beads: 11–19Quantity meets symbol: beside each numeral on the board, your child lays one golden ten-bar plus the colored bead bar that matches, and discovers that 14 really is ten-and-four you can hold and count.ages 4–6
  3. 3Ten Board: Names of the TensThe Ten Board (Seguin Board B) gives the tens their names — twenty, thirty, forty, all the way to ninety — and shows that each one is simply that many ten-bars. It follows the Teen Board and opens the door to counting to 99.ages 5–7
  4. 4Counting to 99With the tens named, the child now counts through every number from 10 to 99 on the Ten Board — sliding unit cards over the zeros and adding one bead at a time, trading ten loose beads for a ten-bar at every new ten. This is where counting past twenty stops being a chant and becomes a structure.ages 5–7
  5. 5The Hundred BoardThe child places number tiles 1 to 100, in order, on a ten-by-ten board. It pulls together everything learned about counting past ten and lets the child see the whole landscape of numbers to one hundred laid out in rows of ten.ages 5–7
  6. 6Skip Counting on the Hundred BoardUsing a completed hundred board, the child counts by twos, fives, tens — eventually by every number from 2 to 10 — and marks each number they land on. The marked squares form striking visual patterns, planting the seeds of the multiplication tables.ages 5–7
  7. 7Bead Chains & Skip CountingYour child counts a chain of bead bars from end to end, labeling each stopping point — 5, 10, 15, 20, 25 — and meets the square of a number at the finish. Skip counting learned this way is the direct seed of the multiplication tables.ages 5–8
  8. 8The Long Chains: 100 and 1,000The long chains are the longest count in the primary classroom: one golden line of ten-bars that your child counts by tens, labeling every bar along the way. The hundred chain comes first — ten ten-bars ending at 100 — and then the thousand chain turns counting into a true expedition, one hundred ten-bars long with a milestone waiting at every hundred.ages 5–8

3The Decimal SystemAges 4–7 · PK–2

  1. 1Introduction to the Golden BeadsYour child meets the four sizes of the decimal system — a unit bead, a ten-bar, a hundred-square, and a thousand-cube — and learns their names by holding, counting, and comparing them. This one short lesson is the doorway to all later work with big numbers.ages 4–6
  2. 2Introduction to the Number CardsYour child has already held one golden bead and hefted a cube of one thousand; now they meet the written symbols 1, 10, 100, and 1000. This short naming lesson attaches numerals to the quantities they already know with their hands.ages 4–6
  3. 3Building Big Numbers (Formation)Quantity and symbol come together: you name a number such as 2,436, and your child fetches that many thousands, hundreds, tens, and units from the "bank," then matches the number cards to the beads. This is where a four-year-old starts reading four-digit numbers.ages 4–6
  4. 4The Bird's-Eye View: 1 to 9,000All thirty-six number cards are laid out in one grand grid so your child sees the whole decimal system at a glance — then learns the trick at its heart: stacking cards so 3,000, 200, 50, and 1 read as 3,251.ages 4–7
  5. 5Golden Bead AdditionTwo quantities are laid out on the mat, pushed together, and counted — and when a column overflows past nine, ten beads are traded at the bank for one of the next size. Your child physically performs the "carrying" that written addition only hints at.ages 5–7
  6. 6Golden Bead SubtractionYour child builds a large quantity, then gives an amount of it away — and when a column runs short, a bigger piece is traded at the bank for ten smaller ones. Borrowing stops being a trick and becomes something your child’s hands understand.ages 5–7
  7. 7Golden Bead MultiplicationYour child lays out the very same number two, three, or four times, pushes the layouts together, and exchanges — and discovers that multiplication is just addition with a beautiful secret: every addend is the same. The answer to 1,568 × 3 is found entirely by hand.ages 5–7
  8. 8Golden Bead DivisionA big quantity is shared fairly among little wooden skittles — one thousand for you, one for you, one for you — with the bank standing by to break big pieces into small ones. Whatever cannot be shared stays on the mat: your child has met the remainder.ages 5–7

4Memorization of FactsAges 5–9 · K–3

  1. 1The Positive Snake GameThe child lays colored bead bars into a long "snake," then counts it out ten beads at a time, trading each ten for a golden ten-bar until the colorful snake has turned to gold. It is the playful doorway into memorizing addition facts — especially the pairs that make ten.ages 5–7
  2. 2The Addition Strip BoardThe addition strip board lets a child work every addition fact with addends 1 through 9, laying a blue strip and a red strip end-to-end and reading the sum from the numbers across the top. After the snake game has made adding small numbers familiar, this board gives fast, tidy repetition — the road to knowing the facts by heart.ages 5–7
  3. 3The Subtraction Strip BoardThe subtraction strip board gives your child a way to work — and eventually memorize — every subtraction fact with answers from 1 to 17. A wooden cover strip hides the numbers you do not need, a blue strip takes away, and the answer is simply the number left showing.ages 6–8
  4. 4The Multiplication Bead BoardYour child builds each multiplication table bead by bead on a 10 × 10 board, counting the total after every column and writing the fact down. All that placing, counting, and writing is exactly how the times tables move from understanding into memory.ages 6–9
  5. 5The Unit Division BoardDivision becomes a game of sharing fairly: your child deals a pile of green beads out to little skittle "people" one round at a time, then reads the answer straight off the board. Repeated over weeks, this is how the division facts up to 81 ÷ 9 are discovered and gradually memorized.ages 6–9
  6. 6The Addition ChartsThe addition charts come after the strip board, when your child can build any fact but does not yet know them all by heart. Reading answers off the control chart, discovering the half chart, and finally rebuilding the whole table from memory with answer tiles carries the facts the last mile toward full abstraction.ages 5–8
  7. 7The Multiplication ChartsThe multiplication charts come after the bead board, when your child has built the tables by hand and is ready to own them. Looking up products on the control chart, discovering the half chart, and rebuilding the whole table from memory with answer tiles turns table-building into true recall.ages 6–9

5Passage to AbstractionAges 6–11 · 1–5

  1. 1Introduction to the Stamp GameThe stamp game carries everything your child knows from the golden beads onto identical little tiles that differ only in color and printed number. It is the first deliberate step away from bulky quantity toward symbols — a tile the size of a fingernail now stands for a whole thousand.ages 5–7
  2. 2Stamp Game AdditionAdding with the stamp game tells the same story as golden bead addition — build both numbers, slide them together, trade tens — but now in symbols. Start with sums that need no trading, then move to the exciting ones that do.ages 5–8
  3. 3Stamp Game SubtractionSubtraction with stamps means building only the starting number and taking stamps away — trading a bigger stamp down into ten smaller ones whenever a column runs short. This is where borrowing, even across a zero, becomes something the hands understand.ages 6–8
  4. 4Stamp Game MultiplicationWith stamps, multiplying means building the very same number several times and sliding the rows together. The child discovers that multiplication is just addition in a hurry — the same addend over and over.ages 6–8
  5. 5Stamp Game DivisionDivision with the stamp game is fair sharing: the stamps are dealt out to skittles, one round at a time, biggest stamps first, trading down whenever a fair round is impossible. The answer is what one skittle receives — and whatever cannot be shared fairly is the remainder.ages 6–8
  6. 6Introduction to the Small Bead FrameThe small bead frame is a beautiful abacus with four wires: ten green unit beads, ten blue tens, ten red hundreds, and ten green thousands. It is a big step toward abstraction — with the golden beads a thousand was a heavy cube of a thousand beads, but here one single bead stands for a thousand because of the wire it sits on.ages 6–8
  7. 7Small Bead Frame AdditionThe frame now earns its keep: four-digit addition where every carry is a real event — a wire fills up, ten beads slide back, and one bead comes forward on the wire below. This is the bridge between the stamp game and column addition done entirely on paper.ages 6–8

6FractionsAges 6–10 · 1–4

  1. 1Introduction to FractionsYour child discovers that a whole can be cut into equal parts, and that each family of parts has its own name: halves, thirds, fourths, on up to tenths. The fraction circles make this concrete — every piece is a real, holdable part of the same red circle.ages 6–8

Virtual materials

Worksheets