Bigger/Smaller/Equal¶

Strategy · All strategies
Evidence · 2 claims (2 for) · 7 studies (4 quant-synthesis, 1 causal, 1 associational, 1 theoretical), q2–q4 · 3 of 7 report an effect size

Description¶

The teacher calls out a number. If it is greater than 10, students expand their bodies to take up as much space as possible (feet planted, no running); if less than 10, they shrink to occupy minimal space; if exactly 10, they hold neutral and form an equals sign with their arms. Once students master the rules, the teacher advances to sums and differences ("12 − 5"), requiring students to compute before responding with their bodies.

Design Implications¶

The strategy converts an abstract symbolic comparison (magnitude relative to a benchmark) into a whole-body spatial representation, consistent with embodied cognition accounts in which action and gesture ground numerical concepts Embodied training of numerical concepts improves number-line estimation and comparison. [+M]. The benchmark of 10 also leverages the base-ten structure of the number system, anchoring later place-value work. Because responses are fast and public, the game functions as brief, repeated Practice with immediate feedback — students see peers' postures and can self-correct.

Context¶

Requirements¶

• An open space where all students can move freely and be seen by the teacher
• A teacher able to call out numbers, then sums and differences, at a brisk pace
• An initial Demonstration of each posture (big, small, equal) before play begins

Constraints¶

• Students who have not yet grasped magnitude comparison may guess postures randomly, and the game's speed can mask their confusion rather than reveal it [-M]
• Students with mobility limitations or self-consciousness about public movement may be excluded or disengaged; offer an arm-gesture-only variant
• The binary big/small response does not by itself teach how much bigger or smaller — magnitude precision requires a follow-up such as a number-line activity [~W]
• Overuse turns novelty into routine; short sessions (3–5 minutes) as a warm-up preserve engagement

Implementation Variability¶

• Change the benchmark number (e.g., 20, 100) as fluency grows
• Advance from single numbers to sums and differences, then to two-step expressions
• Have students lead the calling, which adds production practice and Self-Explanation [+W] opportunities when the leader must justify a peer's response
• Seated variant: arm spans wide, folded, or crossed as an equals sign for restricted spaces

Target Learners¶

• K–2 students building initial magnitude comparison and benchmark-of-10 fluency; adaptable through upper elementary for computation warm-ups
• Students who benefit from movement and multimodal encoding over purely symbolic drill Embodied training of numerical concepts improves number-line estimation and comparison. [+M]
• Less suitable as an introduction for students with no prior exposure to comparison language — pre-teach "greater than," "less than," "equal to" first

Target Learning Goals¶

• Magnitude comparison relative to a benchmark (greater than, less than, equal to)
• Fluency with sums and differences within 20, framed as comparison decisions
• Procedural fluency through high-frequency, low-stakes retrieval Active learning improves exam performance. [+S]

Instructions¶

1. Model the three postures (big, small, equals-sign) and rehearse each once — Demonstration
2. Call single numbers near 10 (e.g., 8, 11, 10) at a pace that forces quick decisions — Practice
3. Call numbers farther from 10, then sums and differences ("9 + 4", "15 − 7"), pausing briefly so students must compute rather than pattern-match
4. After each round, briefly Provide guidance: ask one student to justify a posture ("Why did you shrink for 7?") before the next call
5. Increase the benchmark or expression complexity once most students respond correctly and immediately

Related Strategies¶

• Act It Out — the broader family of dramatization strategies this game belongs to
• Activating Prior Knowledge — a fast round works as a lesson warm-up that surfaces comparison fluency before new content

Related Elements¶

• Practice — the game is distributed, repeated retrieval practice with immediate observable feedback
• Demonstration — the teacher must model postures before students can respond correctly
• Provide guidance — brief justifications between rounds convert physical response into verbal reasoning

Patterns That Use This Strategy¶

• Cognitively Guided Instruction (CGI) for Math — grounding number operations in students' informal, embodied understandings before symbolic work
• Direct Instruction — the model–practice–feedback cycle within each round

Examples¶

• Teacher calls "15": students stretch wide and tall. Teacher calls "7": students crouch compactly. Teacher calls "10": students stand neutral with arms crossed as an equals sign. Later, "12 − 5" sends the class shrinking; "8 + 3" sends them expanding.
• A grade 2 teacher uses a 3-minute round as a transition warm-up before a place-value lesson, with the benchmark raised to 20 for students who have mastered 10.

Key Sources¶

• Link, T., Moeller, K., Huber, S., Fischer, U., & Nuerk, H.-C. (2013). Walk the number line – An embodied training of numerical concepts. Trends in Neuroscience and Education, 2(2), 74–84. doi:10.1016/j.tine.2013.06.005
• Wilson, M. (2002). Six views of embodied cognition. Psychonomic Bulletin & Review, 9(4), 625–636. doi:10.3758/BF03196322
• Duijzer, C., Shayan, S., Bakker, A., van der Schaaf, M., & Abrahamson, D. (2017). Touchscreen tablets: Coordinating action and perception for mathematical cognition. Frontiers in Psychology, 8, 144. doi:10.3389/fpsyg.2017.00144
• Freeman, S., et al. (2014). Active learning increases student performance in science, engineering, and mathematics. PNAS, 111(23), 8410–8415. doi:10.1073/pnas.1319030111