Shake and Spill

A cup, a small handful of two-colour counters (red on one side, yellow on the other), and one question: “How many red, and how many yellow?” The child shakes, spills, and discovers a different way to break the same number into two parts every time.

  1. Count out a fixed number of counters together — start with 5. Two-sided counters are ideal, but you can colour one side of large dried beans, bottle caps, or cardboard discs with a marker.
  2. Tip them into a cup or your cupped hands. Let the child shake and gently spill them onto the table.
  3. Ask: “How many landed red? How many yellow?” Count each colour, then say the whole story: “3 red and 2 yellow — that makes 5!”
  4. Shake and spill again. A new split appears — “4 and 1,” then “1 and 4,” then “5 and none.” Treat each one as a discovery.
  5. Optional: record each split by colouring a row of five circles, or draw a number bond — the total in a circle on top, the two parts below.

Variation: once 5 feels easy, move to 6, then toward 10. Pose the challenge “Can we find all the ways to make 5?” and hunt for any missing combinations together.

Requirements

  • Space: A table, tray, or any flat surface; a few minutes is plenty
  • Surface: Hard and flat so counters settle face-up; a rimmed tray or baking sheet stops them scattering
  • Materials: 5–10 two-colour counters (or beans, caps, or discs with one side coloured), a cup or small tub; optional paper and crayons to record number bonds
  • Participants: 1 adult and 1 child; works well with 2–3 children each with their own cup
  • Supervision: Light for 5-year-olds — observe and narrate; close if a younger sibling who mouths objects is nearby

Rationale & Objective

Shake and Spill is the classic concrete route into decomposing numbers — seeing that one quantity (5) is built from smaller parts (3 and 2, 4 and 1) that combine back into the whole. This part-part-whole insight is the conceptual heart of addition and subtraction and is named directly in Common Core K.OA.3 (decompose numbers ≤ 10 into pairs in more than one way). Because the same total keeps reappearing as different splits, the child also meets conservation of number and the commutative idea that “3 and 2” and “2 and 3” make the same whole. Kathy Richardson’s Developing Number Concepts and the Erikson Institute’s Big Ideas of Early Mathematics both treat flexible part-whole decomposition as a foundational “big idea” that predicts later fluency far better than rote memorisation.

Progress Indicators

  • Early: recounts every spill from 1 as if it were brand new; doesn’t yet notice the total stays the same each time
  • Developing: counts each colour reliably and names both parts (“3 and 2”); may still need help seeing the parts rebuild the same whole
  • Proficient: states the total without recounting and names the two parts quickly; notices “I had that one already” when a split repeats
  • Advanced: predicts and hunts for missing combinations (“we still need 5-and-none!”); sees that 4-and-1 is 1-and-4 flipped; records splits as number bonds or equations

Safety Notes

  • Use counters at least 4.5 cm across if the child still mouths objects or a younger sibling is in reach — small counters and dried beans are choking hazards
  • A rimmed tray keeps counters off the floor (slip hazard) and contains the activity
  • Keep sessions short; if the child starts guessing colours instead of counting, stop while it is still fun
  • Never use known allergens (nuts, certain seeds) as counters, even briefly

Hints

  • Playfulness: give the cup a silly name and a “magic shake,” and make the spill dramatic — children love calling out the new combination like a game-show reveal
  • Sustain interest: change the counters often (buttons, painted caps, two-tone pom-poms, even crackers at snack); keep a “ways to make 5” chart on the fridge and add a mark for each new split found
  • Common mistake: jumping to 10 too soon. Master 5 first — only six combinations — so the child can experience finding all the ways before numbers get big. Resist filling in answers; let the child read the spill
  • No equipment: colour one side of any small objects with a marker, or flip coins (heads/tails). A handful of pasta works fine
  • Cross-domain: recording splits builds early writing and numeral formation; naming combinations aloud builds math language; sorting the two colours first touches classification
  • Progression: all the ways to make 5 → make 6 → make 10 → write each split as a number bond → write it as an equation (3 + 2 = 5) → cover the counters and recall the parts from memory

Sources

  • Richardson, K. (1999/2012). Developing Number Concepts, Book 2: Addition and Subtraction. Pearson
  • Clements, D. H. & Sarama, J. (2014/2021). Learning and Teaching Early Math: The Learning Trajectories Approach (3rd ed.). Routledge
  • Erikson Institute Early Math Collaborative (2014). Big Ideas of Early Mathematics. Pearson
  • Common Core K.OA.A.3 (decompose numbers into pairs in more than one way)
  • Head Start ELOF — Mathematics Development (P-MATH 6: addition and subtraction)
  • Illustrative Mathematics — “Shake and Spill” task (Kindergarten, K.OA)
  • HighScope KDI 33 (Part-whole relations — combining and separating quantities)