Childhood Map

Discover the amazing things 5-year-olds are learning — from climbing and jumping to friendships, feelings, and first words on a page. Each skill comes with fun activities you can try together.

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by Robert Pankowecki
Mathematical Thinking

Number sense, operations, spatial reasoning, measurement, and pattern recognition that form the foundation for mathematical literacy.

Sources (6)
  • Head Start ELOF (Mathematics Development)
  • UK EYFS (Mathematics)
  • US Common Core (Math-K)
  • Montessori (Mathematics Area)
  • HighScope
  • E.D. Hirsch
5 Subdomains
Number Sense & Counting9 › Operations (Early Addition & Subtraction) › Geometry & Spatial Sense › Measurement & Comparison › Patterns & Classification ›
Number Sense & Counting

Understanding quantities, counting with meaning, and recognizing written numerals.

Examples & Achievements

  • Rote counts to 20 or beyond
  • Counts objects with one-to-one correspondence up to 10-20
  • Understands that the last number counted tells "how many" (cardinality)
  • Recognizes written numerals 0-10
  • Subitizes (instantly recognizes) small quantities (1-5) without counting
  • Compares groups and tells which has more, fewer, or the same

How to Measure

  • Accurately counts a set of 15 objects with one-to-one correspondence
  • Names written numerals 0-10
  • Answers "how many?" correctly after counting (demonstrates cardinality)
  • Subitizes quantities of 1-4 on dot cards without counting
  • Correctly compares two groups (more/fewer) for sets up to 10
Sources (4)
  • Common Core K
  • Montessori
  • Head Start ELOF
  • CDC/AAP
9 Exercises
Counting Collections › Quick-Look Subitizing Cards › Numeral Hunt — The Number Detective › Sand-Tray Numeral Tracing › Counting Songs and Finger Rhymes › More, Fewer, Same — Card Battle › The Great Race — Linear Number Board Game › Set the Table — Helper Math › Ten-Frame Builder ›
Counting Songs and Finger Rhymes

The traditional musical route into number — singing classic counting songs while showing the matching quantity on fingers, toys, or body movements. Daily, varied exposure builds the stable order of number words and primes early decomposition (“5 minus 1 is 4”).

  1. Choose a song. Reliable favourites for ages 3–6:

    • Five Little Monkeys Jumping on the Bed (counts down from 5)
    • Five Little Ducks Went Out One Day (counts down)
    • Five Green and Speckled Frogs (counts down)
    • Ten in the Bed (counts down from 10)
    • One, Two, Buckle My Shoe (counts up to 10)
    • The Ants Go Marching (counts up to 10)
    • This Old Man (counts up to 10)
    • Five Little Pumpkins (counts up to 5)

  2. Sit facing the child. Sing slowly. Show the count on your fingers as each number arrives.

  3. Encourage the child to sing along and show the matching number on their own fingers.

  4. After several repetitions, pause before each number and let the child fill it in: “Five little monkeys, jumping on the bed, one fell off and bumped his head, mama called the doctor and the doctor said: no more monkeys jumping on the ____”

  5. Add a body action — bounce on the count, stomp for each marching ant, hold up the matching number of fingers, or remove one finger as monkeys “fall off.”

  6. Over weeks, layer in songs that go to 10 and beyond, and songs that count by 2s (“Two, four, six, eight, who do we appreciate?”) or by 5s (“Five, ten, fifteen, twenty…”).

Variation: act the song out with stuffed animals or finger puppets — child removes one each verse. Record the child singing and play it back. Make a homemade counting book in which the child draws each verse on its own page.

Requirements

  • Space: Anywhere — bed, bath, car, kitchen, waiting room
  • Surface: None required
  • Materials: Optional finger puppets, stuffed animals, small instrument (shaker, drum); a screen with the song video for new songs the adult doesn't yet know
  • Participants: 1 adult + 1 child; sibling group works beautifully
  • Supervision: Light — sing along; no risk

Rationale & Objective

Counting songs are the most ancient and universal way humans transmit the stable order principle — that number words come in a fixed sequence (Gelman & Gallistel, 1978). Geist & Geist (2008) and Geist, Geist & Kuznik (2012) document gains in rote-counting fluency from regular musical engagement. Beyond just sequence, songs that count down (Five Little Monkeys, Ten in the Bed) provide an early decomposition experience — “5 minus 1 is 4” — preparing the ground for operations. Movement-paired songs activate embodied cognition: pairing number words with physical movement (fingers, claps, hops) produces stronger memory than passive listening, and the finger count provides a concrete “manipulative” the child carries with them everywhere.

Progress Indicators

  • Early: hums along but skips numbers; finger gestures don’t match the count; needs many repetitions to remember the song
  • Developing: sings most number words in correct sequence with adult support; finger count usually matches; can fill in the last number of a verse
  • Proficient: sings whole songs independently with correct number sequence; finger count matches every verse; introduces own variations (“ten little ladybugs!”)
  • Advanced: counts up to 20 or beyond in songs; makes up own counting songs and verses; recognises the pattern of counting down (5, 4, 3, 2, 1) as repeated subtraction; teaches the song to a sibling

Safety Notes

  • No physical risks
  • Watch volume of recorded music — for headphones, follow the audiologist guideline of 60% volume / 60 minutes max per day for young children
  • Some children with sensory sensitivities dislike loud singing; sing softly and let them choose to join in
  • “Five Little Monkeys” includes “bumped his head” — for very literal children, reframe gently (“the monkey is fine, just bouncy”)
  • Avoid bouncing on actual beds during the song with under-5s — children often act it out and falls happen

Hints

  • Playfulness: dramatise each verse with a different voice or face. Use small finger puppets for a “monkey-bed-doctor” stage. Take turns being “the doctor” who scolds the monkeys
  • Sustain interest: rotate songs across the week — Monkey Monday, Frog Friday. Add an instrument (shaker, drum) for the count. Build a small song-card deck the child picks from to choose the day’s song
  • Common mistake: singing too fast — the count word and the action have to line up exactly. Slow it down so the child can match fingers to words. Also: only ever singing songs that count down. Mix in counting-up songs to support both directions
  • Limited space: zero materials, anywhere — bath, car, waiting room, bedtime. Travel-perfect
  • Cross-domain: clap the rhythm (music & rhythm); act out the verses (dramatic play); draw a picture of each verse (visual arts); read picture-book versions of the songs (literacy bridge)
  • Progression: sing along with adult → fill in last word of each verse → sing alone → finger-count matches every verse → introduce songs that go to 10 → invent own verses → count by 2s, 5s, 10s in songs → connect song count to written numerals

Sources

  • Geist, K. & Geist, E. A. (2008). "Do re mi, 1-2-3: That's how easy math can be — Using music to support emergent mathematics." Young Children, 63(2), 20–25
  • Geist, E. A., Geist, K. & Kuznik, K. (2012). "The patterns of music: Young children learning mathematics through beat, rhythm, and melody." Young Children, 67(1), 74–79
  • Pouw, W. T. J. L., van Gog, T. & Paas, F. (2014). "An embedded and embodied cognition review of instructional manipulatives." Educational Psychology Review, 26, 51–72
  • Gelman, R. & Gallistel, C. R. (1978). *The Child's Understanding of Number* — stable order principle. Harvard University Press
  • Head Start ELOF — Mathematics Development (P-MATH 1: counts in sequence)
  • Common Core K.CC.A.1 (count to 100 by ones and by tens)
  • HighScope KDI 33 (Counting; rote count)
  • UK EYFS — Mathematics: Number ELG (verbally count beyond 20)
  • Teaching Strategies GOLD Objective 20a (verbally counts)

Childhood Map › Mathematical Thinking › Number Sense & Counting

Counting Songs and Finger Rhymes

The traditional musical route into number — singing classic counting songs while showing the matching quantity on fingers, toys, or body movements. Daily, varied exposure builds the stable order of number words and primes early decomposition (“5 minus 1 is 4”).

  1. Choose a song. Reliable favourites for ages 3–6:

    • Five Little Monkeys Jumping on the Bed (counts down from 5)
    • Five Little Ducks Went Out One Day (counts down)
    • Five Green and Speckled Frogs (counts down)
    • Ten in the Bed (counts down from 10)
    • One, Two, Buckle My Shoe (counts up to 10)
    • The Ants Go Marching (counts up to 10)
    • This Old Man (counts up to 10)
    • Five Little Pumpkins (counts up to 5)

  2. Sit facing the child. Sing slowly. Show the count on your fingers as each number arrives.

  3. Encourage the child to sing along and show the matching number on their own fingers.

  4. After several repetitions, pause before each number and let the child fill it in: “Five little monkeys, jumping on the bed, one fell off and bumped his head, mama called the doctor and the doctor said: no more monkeys jumping on the ____”

  5. Add a body action — bounce on the count, stomp for each marching ant, hold up the matching number of fingers, or remove one finger as monkeys “fall off.”

  6. Over weeks, layer in songs that go to 10 and beyond, and songs that count by 2s (“Two, four, six, eight, who do we appreciate?”) or by 5s (“Five, ten, fifteen, twenty…”).

Variation: act the song out with stuffed animals or finger puppets — child removes one each verse. Record the child singing and play it back. Make a homemade counting book in which the child draws each verse on its own page.

Requirements

Rationale & Objective

Counting songs are the most ancient and universal way humans transmit the stable order principle — that number words come in a fixed sequence (Gelman & Gallistel, 1978). Geist & Geist (2008) and Geist, Geist & Kuznik (2012) document gains in rote-counting fluency from regular musical engagement. Beyond just sequence, songs that count down (Five Little Monkeys, Ten in the Bed) provide an early decomposition experience — “5 minus 1 is 4” — preparing the ground for operations. Movement-paired songs activate embodied cognition: pairing number words with physical movement (fingers, claps, hops) produces stronger memory than passive listening, and the finger count provides a concrete “manipulative” the child carries with them everywhere.

Progress Indicators

Safety Notes

Hints

Sources