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.

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
The Great Race — Linear Number Board Game

A simple, linear (not circular) number board game played with a small spinner or low-numbered die. The child moves a token one square at a time and says the numeral on each square as they land. Modeled on Siegler & Ramani’s research-validated intervention.

  1. Make or print a linear board with squares labelled 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 in order, left to right. Each square should be the same size, and the layout strictly linear — not curving, not in a spiral. A strip of paper 30–50 cm long works.
  2. Make a spinner with the numbers 1 and 2 (so the child moves either 1 or 2 squares per turn) — or use a tetrahedral die showing only 1 and 2. A regular die can be re-marked with stickers.
  3. Each player gets a token (a coin, a small toy figure, a button). Tokens start on a “start” line just before square 1.
  4. On each turn the child spins, then moves their token one square at a time, naming each square as they go. “I got a 2 — one… two!” They say the numeral printed on each square they land on, not just count moves.
  5. First to reach square 10 wins. Play 2–3 rounds.
  6. As skill grows, expand to a 0–20 board with a 1–6 die.

Variation: redesign the board with the child every few weeks — pirate map (1–10 islands), space mission (1–10 planets), candy run (1–10 stops). The numerals stay; the theme rotates. Avoid chutes / ladders / shortcuts at this age — they break the linear magnitude structure that makes the activity work (Siegler & Ramani, 2009).

Requirements

  • Space: A small table or any flat surface 30–50 cm wide
  • Surface: Hard, level (table or floor)
  • Materials: A linear 1–10 board (homemade strip of paper / printed sheet / DIY card), a 1–2 spinner OR a die with only 1s and 2s, two tokens (coins, mini-figures, buttons)
  • Participants: 2 players (adult + child, or two children); 3 players also fine
  • Supervision: Light — sit alongside, model the first round, then play together

Rationale & Objective

This is the single most well-replicated early-numeracy intervention in the research literature. Siegler and Ramani’s “The Great Race” (2008, 2009) showed that 4-year-olds who played a linear number board game for just four 15-minute sessions improved their numerical magnitude estimation, numeral identification, and counting — and that gains persisted 9+ weeks later. The intervention closes a substantial portion of the SES gap in early math by age 5. Critical detail: the board must be linear, with equal-sized squares, with numerals visible — Siegler & Ramani (2009) showed directly that circular boards (like Candy Land) do not produce the same gains because they don’t reinforce linear magnitude structure. The verbal naming of the numeral on each square is essential — that’s what builds the symbol-to-magnitude link.

Progress Indicators

  • Early: doesn’t say the numeral on each square as they move; counts spaces (“one, two”) but ignores the printed numerals; treats the board as just a path
  • Developing: says some numerals on landing squares with reminders; counts moves correctly; begins to anticipate “I need a 3 to win”
  • Proficient: names every numeral they pass over without prompting; predicts how many more spaces to win (“I’m on 7, I need to reach 10, so 3 more”); compares positions (“I’m ahead, you’re at 4 and I’m at 6”)
  • Advanced: estimates magnitude without counting (“7 is closer to 10 than to 0”); plays comfortably on a 0–20 or 0–100 board; transfers the linear sense to other contexts (calendar, ruler, number line in books)

Safety Notes

  • Tabletop game with no physical risk
  • Use tokens larger than 4.5 cm if a younger sibling is nearby (choking hazard with small coins or mini-figures)
  • Watch for losing-aversion meltdowns — for some children, switch to a collaborative version where both players advance the same token until tolerance for losing develops
  • No screens needed — keep it on paper; physical movement of the token reinforces the linear sense

Hints

  • Playfulness: racing-themed — cars, horses, dragons, snails. Adult plays a “slow tortoise”; child plays a “speedy hare.” Cheer landed numerals dramatically (“SEVEN!” with a fist pump)
  • Sustain interest: redesign the board every few weeks with the child — pirate islands, space planets, candy stops. Same 1–10 numerals; new theme keeps it fresh. Laminate a favourite and reuse
  • Common mistake: using a circular Candy Land or Snakes-and-Ladders board — research shows linear boards produce gains, circular ones don’t. Also: not requiring the child to say the numeral on each square — verbal naming is the active ingredient, not the rolling and moving
  • Limited space: a strip of paper, a die, two coins. Plays on a café table, an aeroplane tray, or the floor of a waiting room. Pocket-portable
  • Cross-domain: read the spinner / die (subitizing); count the moves (one-to-one); compare positions (“you have more, I have fewer” — comparison); discuss fairness (“we both got the same, it’s a tie” — social reasoning); take turns (executive function)
  • Progression: 1–10 linear board with 1-or-2 spinner → 1–10 with 1–3 spinner → 1–20 with 1–6 die → 0–100 strip with 1–10 die → number-line jumps without a board (“if I’m on 7 and I jump 3, where am I?”)

Sources

  • Ramani, G. B. & Siegler, R. S. (2008). "Promoting broad and stable improvements in low-income children's numerical knowledge through playing number board games." Child Development, 79(2), 375–394
  • Siegler, R. S. & Ramani, G. B. (2009). "Playing linear number board games — but not circular ones — improves low-income preschoolers' numerical understanding." Journal of Educational Psychology, 101(3), 545–560
  • Ramani, G. B., Siegler, R. S. & Hitti, A. (2012). "Taking it to the classroom: Number board games as a small group learning activity." Journal of Educational Psychology, 104(3), 661–672
  • Siegler, R. S. & Booth, J. L. (2004). "Development of numerical estimation in young children." Child Development, 75(2), 428–444
  • Laski, E. V. & Siegler, R. S. (2014). "Learning from number board games: You learn what you encode." Developmental Psychology, 50(3), 853–864
  • National Research Council (2009). *Mathematics Learning in Early Childhood: Paths Toward Excellence and Equity*. National Academies Press
  • Common Core K.CC.A.1 (count to 100 by ones), K.CC.A.3 (numeral recognition)
  • Head Start ELOF — Mathematics Development (P-MATH 1, 2, 4)
  • HighScope KDI 32 (Number words and symbols), KDI 33 (Counting)

Childhood MapMathematical ThinkingNumber Sense & Counting

The Great Race — Linear Number Board Game

A simple, linear (not circular) number board game played with a small spinner or low-numbered die. The child moves a token one square at a time and says the numeral on each square as they land. Modeled on Siegler & Ramani’s research-validated intervention.

  1. Make or print a linear board with squares labelled 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 in order, left to right. Each square should be the same size, and the layout strictly linear — not curving, not in a spiral. A strip of paper 30–50 cm long works.
  2. Make a spinner with the numbers 1 and 2 (so the child moves either 1 or 2 squares per turn) — or use a tetrahedral die showing only 1 and 2. A regular die can be re-marked with stickers.
  3. Each player gets a token (a coin, a small toy figure, a button). Tokens start on a “start” line just before square 1.
  4. On each turn the child spins, then moves their token one square at a time, naming each square as they go. “I got a 2 — one… two!” They say the numeral printed on each square they land on, not just count moves.
  5. First to reach square 10 wins. Play 2–3 rounds.
  6. As skill grows, expand to a 0–20 board with a 1–6 die.

Variation: redesign the board with the child every few weeks — pirate map (1–10 islands), space mission (1–10 planets), candy run (1–10 stops). The numerals stay; the theme rotates. Avoid chutes / ladders / shortcuts at this age — they break the linear magnitude structure that makes the activity work (Siegler & Ramani, 2009).

This is the single most well-replicated early-numeracy intervention in the research literature. Siegler and Ramani’s “The Great Race” (2008, 2009) showed that 4-year-olds who played a linear number board game for just four 15-minute sessions improved their numerical magnitude estimation, numeral identification, and counting — and that gains persisted 9+ weeks later. The intervention closes a substantial portion of the SES gap in early math by age 5. Critical detail: the board must be linear, with equal-sized squares, with numerals visible — Siegler & Ramani (2009) showed directly that circular boards (like Candy Land) do not produce the same gains because they don’t reinforce linear magnitude structure. The verbal naming of the numeral on each square is essential — that’s what builds the symbol-to-magnitude link.