A short structured activity using a printed ten-frame — a 2×5 grid of squares — that the child fills with counters to show a quantity. The frame externalises the base-10 structure of our number system and makes 5 and 10 visible as benchmark quantities.
- Print or draw a ten-frame: a 2 × 5 grid (5 squares on top, 5 on bottom, 10 squares total) on cardstock. Make several copies. Each square should be about 4 × 4 cm.
- Provide counters: dried beans, buttons, plastic chips, two-colour counters (red on one side, yellow on the other), cereal pieces, or small stones.
- Call out a number 1–10. “Show me 6.” The child fills 6 squares. Convention: start top-left, fill left-to-right, top row first, then bottom row.
- Ask: “How many filled? How many empty?” This builds the complement to 10 (“6 and 4 make 10”) — quietly preparing the ground for early operations.
- Next, call “Show me 8.” The child can either start over or add 2 more to the 6. Either is valid; “add two more” is faster and starts to feel like operations naturally.
- Mix in “How many?” tasks — place counters in a pattern (e.g., 5 on top, 2 on bottom — 7 total) and flash for one second. Child says “7.” This trains conceptual subitizing against the structured frame.
- Aim for 5–10 numbers per session, 10 minutes max.
Variation: two-colour counters to show decompositions — “show 6 as 4 red and 2 yellow; now show another way: 3 and 3; now another: 5 and 1.” Two ten-frames to build numbers 11–20. Blank-frame challenge — adult fills the frame partly, child answers “how many to make 10?” (early subtraction sense). Race to fill — two children take turns rolling a 1–6 die and adding that many counters; first to fill the frame wins.
Requirements
- Space: A small table or any flat surface
- Surface: Hard, flat (table or floor)
- Materials: Printed or drawn ten-frame on cardstock (a few copies); 20–30 small counters (dried beans, buttons, two-colour counters, cereal, stones); optional die for race variant; optional numeral cards 0–10
- Participants: 1 adult + 1 child; works well with 2 children playing the race variant
- Supervision: Light to moderate — adult sits alongside, models, asks the questions, and lets the child fill
Rationale & Objective
The ten-frame is the central manipulative in early-numeracy curricula worldwide — Singapore Math, TERC’s Investigations, Bridges in Mathematics, Eureka Math, JUMP Math, and Clements & Sarama’s Building Blocks. It externalises the base-10 structure of our number system and supports subitizing of 5 and 10 as benchmark quantities. Clements & Sarama (2014) place “five-frame and ten-frame quantification” at a key step in the counting and subitizing learning trajectories. Research on visual-quantitative scaffolds (Bobis, 1996, 2008; Van de Walle, Karp & Bay-Williams, 2018) shows that children who use ten-frames develop stronger mental imagery for quantities and faster fact retrieval. The structure also seeds early decomposition — “6 is 5 and 1,” “8 is 5 and 3” — which is the bridge into addition and subtraction.
Progress Indicators
- Early: places counters randomly across the frame; can’t tell how many filled vs. empty without recounting both; treats the frame as just a place to put things
- Developing: fills left-to-right, top-row-first with reminders; counts every counter to confirm; recognises a full top row as “5”
- Proficient: fills the frame conventionally without reminders; sees and names the quantity at a glance for 1–10; spontaneously says “5 and 1 make 6” or “8 is 5 and 3”
- Advanced: builds two-digit numbers across two ten-frames (12 = full frame + 2); shows multiple decompositions of the same number (“6 is 5+1, or 4+2, or 3+3”); answers “how many more to make 10?” without counting
Safety Notes
- Choose counters larger than 4.5 cm if a younger sibling is in reach (no dried beans, no marbles, no small beads)
- Avoid candy-like counters (M&Ms, Skittles) unless the child can manage not to eat them mid-game; it’s a recipe for distraction
- Watch for frustration if the child is rigid about left-to-right filling — let them choose at first; introduce the convention gently over time
- Keep the activity short (10 minutes) — structured frames demand more attention than free counting
- Wash hands afterwards if using natural counters (stones, acorns)
Hints
- Playfulness: call counters “passengers boarding the airplane,” “eggs in the carton,” or “pirates climbing into the boat.” Decorate the frame with a theme — bus seats, parking spaces, hotel rooms. Children love when the structure has a story
- Sustain interest: rotate counter type — beans Monday, buttons Tuesday, mini erasers Wednesday, two-colour counters Thursday. Add a die for randomised challenges. Make a small “Ten-Frame Folder” where the child draws each filled frame to keep a record
- Common mistake: always asking for the same easy numbers (5, 10). Push into 7, 8, 9 — the harder ones for subitizing. Also: skipping the “how many empty?” question. The complement (10 − n) is what makes the frame work as a number-sense tool
- Limited space: print a ten-frame on a single sheet of paper; counters are anything (cereal pieces, coins, pebbles, paperclips). Travel-friendly in a Ziploc bag
- Cross-domain: sort counters by colour before placing (classification); read the numeral that goes with each filled frame (numeral recognition); compare two filled frames (more/fewer); record results on a chart over days (data and early writing)
- Progression: show 1–5 → show 6–10 → “how many empty?” → “how many to make 10?” → “show 6 two different ways” → two-frame numbers 11–20 → ten-frames replaced by mental imagery alone (“close your eyes — picture 8 in the ten-frame”)
Sources
- Clements, D. H. & Sarama, J. (2014/2021). *Learning and Teaching Early Math: The Learning Trajectories Approach* (3rd ed.). Routledge
- Bobis, J. (1996). "Visualisation and the development of number sense with kindergarten children." In *Children's Number Learning*. MERGA
- Bobis, J. (2008). "Early spatial thinking and the development of number sense." Australian Primary Mathematics Classroom, 13(3), 4–9
- Van de Walle, J. A., Karp, K. S. & Bay-Williams, J. M. (2018). *Elementary and Middle School Mathematics: Teaching Developmentally* (10th ed.). Pearson
- TERC (2017). *Investigations in Number, Data, and Space* (3rd ed.). Pearson
- Singapore Ministry of Education. *Nurturing Early Learners* (NEL) Mathematics framework
- National Research Council (2009). *Mathematics Learning in Early Childhood: Paths Toward Excellence and Equity*. National Academies Press
- Common Core K.OA.A.4 (decomposing 10), K.NBT.A.1 (place value foundations)
- Head Start ELOF — Mathematics Development (P-MATH 1, 2, 3)
- Teaching Strategies GOLD Objective 20 (counting)
- HighScope KDI 35 (Comparing quantities), KDI 36 (Whole-number addition and subtraction)