Montessori Math

The Lesson AlbumLinear & Skip Counting · lesson 7ages 5–8grades K–2

Bead Chains & Skip Counting

Your 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.

Materials

  • The short bead chains 2–10 with their arrow labels (or the virtual Bead Chains material on this site)
  • Household substitute: pony beads threaded on pipe cleaners — make five pipe cleaners with five beads each and twist them together end to end for a chain of five; match colors if you can
  • Small slips of paper and a pencil to make your own labels (for the chain of five, write 5, 10, 15, 20, 25)
  • A rug, towel, or clear stretch of table long enough to lay the chain out straight

No materials at home? Use the virtual Bead Chains.

Before this lesson

Aims

Direct

  • Skip count by any number from 2 to 10, up to that number’s square
  • Connect each spoken multiple to its written numeral by labeling the chain
  • Discover that counting a chain of equal bars always ends at the square of the number

Indirect

  • Preparation for memorizing the multiplication tables
  • A first sensorial impression of the square of a number, preparing for later work with squares and powers
  • Practice sustaining order and attention through one long, satisfying piece of work

Presentation

  1. 1 Choose the chain of 5 on screen, or lay a real five-chain out straight on a rug with its labels nearby in a little pile. Sit beside your child.This is the chain of five. Every bar on it has five beads.
  2. 2 Run a finger slowly along the whole chain from one end to the other, so your child sees it is one long line of bars joined together.
  3. 3 Count the beads of the first bar one at a time, touching each bead as you say its number.One, two, three, four, five.
  4. 4 Find the ticket that says 5 and place it at the end of the first bar. On screen: tap the 5 ticket in the tray, then tap the empty spot at the end of the first bar.Five. This ticket marks five.
  5. 5 Count on across the second bar without starting over — six, seven, eight, nine, ten — and place the 10 ticket at its end. Invite your child to take over the counting and placing as soon as they lean in.Six, seven, eight, nine, ten. Ten.
  6. 6 Let your child continue bar by bar to the end of the chain, counting every bead and labeling each bar. Resist the urge to rush or correct — a recount settles any doubt.
  7. 7 When the last ticket, 25, goes in place, pause. It is the biggest label on the chain.Five bars of five make twenty-five. Five taken five times is twenty-five — we call it the square of five.
  8. 8 Go back to the beginning and read only the tickets, touching the end of each bar as you say its number together.Five, ten, fifteen, twenty, twenty-five.
  9. 9 On screen, tap Check if your child wants to be sure — each placed ticket is marked right or wrong, and a wrong one simply means it is time to recount that bar. Another day, invite your child to choose a different chain.

Points of interest

  • Each chain wears the same color as its bead-stair bar — the chain of 5 is light blue, and the chain of 10 is golden
  • The last ticket on every chain is larger than the rest: the square
  • The rhythm of the numbers — after a few rounds children start chanting the sequence before their finger gets there
  • The chains grow visibly longer as the numbers grow: the chain of 10 has one hundred beads

Control of error

  • The beads themselves: recounting a bar shows whether the ticket at its end is right
  • The tickets form one fixed set — a ticket left over, or a gap with no ticket that fits, shows something is off
  • On screen, the Check button marks each placed ticket right or wrong without giving away the answer

Vocabulary

  • chain
  • bar
  • ticket (arrow label)
  • skip counting
  • square of a number

Variations

  • Let your child pick the chain — a favorite color is a fine reason to count by sevens
  • Count backward from the square once the chain is labeled: 25, 20, 15, 10, 5
  • Play the whisper game: whisper the in-between numbers and say the ticket numbers out loud

Extensions

  • Fold a real chain bar by bar into a solid square to see with your eyes why 25 is called the square of five
  • Find every ticket number on the hundred board and notice the pattern the multiples make
  • Skip count past the square on paper: keep the sequence going — 30, 35, 40 — as far as your child can

Follow-up work (pencil & paper)

  • Print a skip-counting worksheet for the chain your child just worked with, and let them fill in the missing multiples in pencil.Printable: Skip Counting
  • Ask your child to write one chain’s sequence from memory on paper — 5, 10, 15, 20, 25 — then lay out the chain and check it against the tickets.
  • Count real things in groups and write the running totals down: eggs by twos or sixes in a carton, muffin-tin cups by threes or fours, fingers by fives and tens.

What comes next

One grand adventure remains in this strand: the long chains. The hundred chain and the great thousand chain stretch skip counting by tens all the way to 1,000 — see the next lesson, The Long Chains. After that, the path leads into the Memorization strand, where the Snake Game turns counting into addition facts.

Next in this strand: The Long Chains: 100 and 1,000