How Close to 100?¶

Strategy · All strategies
Evidence · 1 claim (1 for) · 3 studies (2 review, 1 causal), q2–q3 · 0 of 3 report an effect size

Description¶

A game played in partners where children roll two dice to determine the dimensions of an array to draw on a 100 grid, aiming to fill the grid as much as possible. Each roll produces two factors; the player draws the corresponding array anywhere it fits on the grid and writes the number sentence (e.g., 4 × 6 = 24). Play ends when neither partner can place an array; the winner is the player whose grid is more completely filled. The game was popularized by Jo Boaler's youCubed as a low-floor, high-ceiling fluency task.

Design Implications¶

The game converts multiplication fact practice from rote recall into spatial-compositional reasoning: children must decompose the remaining space, estimate which factor pairs fit, and connect symbolic number sentences to visual area models. This dual symbolic–pictorial encoding supports fact fluency grounded in conceptual understanding rather than memorization alone [~M]. Because each roll forces a decision under constraints (what fits, where), the game embeds strategic thinking and adaptive choice of facts rather than isolated drill [~M].

Context¶

Requirements¶

• Two dice and a printed or drawn 100 grid per player
• Pencils or colored markers for drawing arrays
• A recording convention for number sentences (e.g., 4 × 6 = 24 written inside or beside each array)
• A partner or small group; the game also works solo

Constraints¶

• Limited to multiplication facts with products within 100 (two dice, 1–6); does not by itself extend to larger factors or division
• If grids fill with random placement, the strategic element collapses into mere drawing — the teacher must prompt "where will this fit best?" to preserve the reasoning demand
• Children with weak array/area-model understanding may place arrays without connecting them to the multiplication structure; brief modeling of the first turn is needed [-W]
• Competitive scoring can shift attention from reasoning to winning for some learners; cooperative variants (fill one shared grid together) reduce this [~W]

Implementation Variability¶

• Grid size: use a 50 grid, 144 grid, or blank grid to adjust difficulty
• Dice: use 1–10 dice, two-digit dice, or three dice (choose two of three rolled numbers) to widen the factor range and add decomposition decisions
• Solo mode: one player tries to beat their own previous fill score, supporting Adaptive Difficulty
• Reflection add-on: after play, ask which rolls were hardest to place and why, surfacing factor-pair reasoning

Target Learners¶

• Primary school children (roughly ages 7–11) building multiplication fact fluency
• Learners who benefit from concrete–representational links between symbols and area models [~M]
• Mixed-ability pairs: the open placement decision gives stronger students strategic depth while weaker students still practice facts at their own pace
• Less suitable for learners who have not yet encountered arrays or the area meaning of multiplication — they need prior Practice with drawing arrays from a given fact

Target Learning Goals¶

• Multiplication fact fluency through repeated, meaningful retrieval
• Conceptual understanding of multiplication as area / rows-and-columns structure
• Spatial reasoning and decomposition of rectangular space
• Strategic decision-making: choosing among factor pairs under constraints

Instructions¶

1. Model one turn aloud: roll two dice (e.g., 4 and 6), state the product, draw a 4×6 array on the grid, and write 4 × 6 = 24 — making the fact-to-array connection explicit (Demonstration)
2. Players take turns rolling, drawing an array that fits in remaining space, and recording the number sentence (Practice)
3. If a rolled pair cannot fit anywhere, the player skips that turn
4. When neither player can place an array, count filled squares; the player closer to 100 wins
5. Debrief with questions such as "Which roll was hardest to place, and what would have helped?" (Check-In)

Related Strategies¶

• Arrays and area-model tasks — the same representational basis applied in instruction rather than game form
• Fact-fluency games — other retrieval-practice games; this one adds a spatial constraint that most drill games lack
• Integrate math into game play and strategy rather than treating it as an add-on

Related Elements¶

• Practice — each turn is a spaced, meaningful retrieval of a multiplication fact
• Demonstration — the teacher's modeled first turn establishes the fact–array connection
• Check-In — post-game discussion consolidates the strategic reasoning

Patterns That Use This Strategy¶

• CGI for Math — shares the commitment to children's own strategies and spatial reasoning over taught procedures
• Cognitive Load Theory — the grid externalizes the "remaining space" so working memory is spent on factor reasoning, not tracking state Chunking reduces working memory load. [+M]

Examples¶

• Partner rolls a 4 and a 6 to make a 4×6 array on the grid, then writes 4 × 6 = 24.
• A class uses a 144 grid with 1–12 dice, extending play to the full times table.
• A solo variant: a child plays three rounds alone, graphing how close to 100 they get each time to track their own strategic improvement.

Key Sources¶

• Boaler, J. (2016). Mathematical Mindsets: Unleashing Students' Potential through Creative Math, Inspiring Messages and Innovative Teaching. Jossey-Bass.
• Baroody, A. J. (2003). The development of adaptive expertise and flexibility: The integration of conceptual and procedural knowledge. In A. J. Baroody & A. Dowker (Eds.), The Development of Arithmetic Concepts and Skills (pp. 1–33). Lawrence Erlbaum.
• Clark, R. C., & Mayer, R. E. (2016). E-Learning and the Science of Instruction (4th ed.). Wiley. doi:10.1002/9781119239086