Bead Gammon: A Mathematical Game Using the Rekenrek

 Bead Gammon: A Mathematical Game Using the Rekenrek

Original Game: Bead Gammon

Materials

• Danish 100-bead counting frame (Rekenrek) per player
• Two 6-sided dice per player
• Players: 2

Setup

Each player starts with all 100 beads on their counting frame in the "home" position (pushed to one side).

Objective

Be the first player to move all 100 beads from home to the opposite side of the frame.

Basic Rules

1. Taking Turns: Players alternate rolling both dice.

2. Standard Roll: Add the two dice values and move that many beads from home to the opposite side.

   • Example: Roll 3 and 5 = move 8 beads

3. Doubles Bonus: When rolling doubles, multiply the value by 4 (double the doubled amount).

   • Example: Double 6s = 6 × 4 = 24 beads moved

4. Snake Eyes Penalty (Double 1s): This is the "gotcha" moment!

   • The player who rolled snake eyes removes only 4 beads from their frame
   • Their opponent must move ALL their beads back to home position
   • This creates dramatic momentum shifts in the game

5. Winning: First player to move all 100 beads wins the game.

Mathematical Skills Developed

• Addition: Combining dice values
• Multiplication: Calculating doubles
• Subitizing: Quick recognition of bead quantities
• Number sense: Understanding magnitude and proximity to 100
• Strategic thinking: Risk assessment and probability
• Mental math: Tracking progress toward 100

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Variation 1: Target Number Bead Gammon

Changes from Original

• Players race to reach exactly 50 beads (or any target number)
• Must land exactly on the target—if a roll would exceed it, the player loses that turn
• No snake eyes penalty; instead, snake eyes allows the player to move opponent back 10 beads

Skills Enhanced

• Precise calculation
• Estimation (how close am I to the target?)
• Strategic decision-making about when to risk rolling

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Variation 2: Subtraction Bead Gammon

Setup

All beads start on the opposite side (all 100 "moved")

Objective

Be the first to move all beads back to home (essentially counting down from 100 to 0)

Rules

• Same dice rules, but subtract instead of add
• Doubles still multiply by 4 (subtract 24 for double 6s)
• Snake eyes: Player subtracts 4, opponent adds 20 back to their frame (moves away from goal)

Skills Enhanced

• Subtraction fluency
• Counting backward
• Understanding inverse operations

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Variation 3: Decade Bead Gammon (Using 10-Frame Rows)

Materials

• Standard Rekenrek (with visible rows of 10)
• Two 6-sided dice

Rules

• Players must complete entire rows of 10 before starting a new row
• When rolling, announce both the beads moved AND which decade you're in
  • Example: "I'm moving 7 beads, finishing my third ten and starting my fourth ten"
• Doubles bonus: Move double the amount AND get an extra turn
• Snake eyes: Lose your most recently completed row of 10

Skills Enhanced

• Place value understanding
• Grouping by tens
• Decomposing numbers (splitting moves across decade boundaries)
• Benchmark numbers (multiples of 10)

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Variation 4: Rounding Race

Rules

• After each roll, player must round their TOTAL bead count to the nearest 10
• Announce both actual total and rounded total
  • Example: "I have 37 beads, which rounds to 40"
• Scoring variant: Winner is determined by who has the higher rounded total after 10 rounds
• Strategic element: Sometimes it's better to have 35 beads (rounds to 40) than 34 beads (rounds to 30)

Skills Enhanced

• Rounding to nearest 10
• Understanding place value
• Strategic number positioning

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Variation 5: Partner Bead Gammon

Setup

• Two teams of 2 players each
• Each team shares ONE Rekenrek

Rules

• Partners alternate rolling dice
• On your turn, you can either:
  • Move beads forward (traditional), OR
  • Move beads backward if your partner is closer to winning than you
• Teams must communicate strategy
• First team to 100 wins

Skills Enhanced

• Collaborative problem-solving
• Communication of mathematical thinking
• Strategic planning

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Abacus-Style Variations: Place Value Bead Gammon

Setup Concept

Transform four standard 10-bead Rekenrek rows into a place value system:

• Row 1: Ones place
• Row 2: Tens place
• Row 3: Hundreds place
• Row 4: Thousands place

Each bead in a row represents its place value (1, 10, 100, or 1000).

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Abacus Variation 1: Build to 1,000

Materials

• Rekenrek configured as abacus (4 rows = ones, tens, hundreds, thousands)
• Two 6-sided dice
• Optional: Three 6-sided dice for advanced play

Rules

1. Roll dice and add the values
2. Decide which place value row to add your total to
3. When a row reaches 10 beads, it "carries over"—reset that row to zero and move one bead in the next higher place value
   • Example: You have 8 beads in ones place, roll 7. Move 7 beads in ones → causes overflow → reset ones to 5, carry 1 to tens place
4. First to reach exactly 1,000 (all 10 beads in thousands place) wins

Strategic Element

Players must decide: "Should I build up my ones to carry over, or start building tens directly?"

Skills Enhanced

• Place value understanding (what each position represents)
• Regrouping/carrying
• Addition with place value
• Base-10 system comprehension

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Abacus Variation 2: Subtraction from 9,999

Setup

Start with all rows full (representing 9,999 or using a modified 10-bead per row system)

Rules

1. Roll dice, add values
2. Choose which place value to subtract from
3. If you don't have enough beads in that row, must "borrow" from the next higher place value
4. First player to reach 0 wins

Skills Enhanced

• Subtraction with borrowing/regrouping
• Place value in subtraction
• Strategic thinking about efficient subtraction paths

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Abacus Variation 3: Place Value War

Setup

• Each player has their own Rekenrek abacus
• Two 6-sided dice shared

Rules

1. Both players roll dice simultaneously
2. Winner of the roll (higher sum) places their sum's value on their abacus in ANY place value configuration they choose
   • Example: Roll 7 → could place 7 in ones, or carry over to make it 0 ones + 1 ten (with 3 ones borrowed back), etc.
3. After 15 rounds, player with the highest total number wins
4. Strategic twist: You can "block" place values—if you fill a row completely (10 beads), opponent cannot use that place value for their next turn

Skills Enhanced

• Quick addition
• Place value flexibility
• Strategic mathematical thinking
• Number composition and decomposition

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Abacus Variation 4: Rounding Challenge

Rules

1. Roll dice and build any number on your abacus using the place values
2. After building, must round your number to the nearest hundred
3. Score points based on the rounded value
4. Play continues for 10 rounds, highest score wins
5. Twist: You can "bank" your current rounded number OR risk adding more, which might round down

Example

• Player has 379 on abacus (rounds to 400 = 400 points)
• Rolls 8: Could add to ones (387, still rounds to 400) or add to tens (379 + 80 = 459, rounds to 500)
• Risk: If they get too high, might round to the next hundred and go over a target

Skills Enhanced

• Rounding to various place values
• Risk assessment
• Understanding rounding rules and boundaries (350 vs 349)
• Place value addition

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Abacus Variation 5: Race to Target Numbers

Materials

• Rekenrek abacus
• Target number cards (e.g., 247, 582, 1,350)
• Two 6-sided dice

Rules

1. Draw a target number card
2. Players take turns rolling and building their number on the abacus
3. First player to match the target number exactly wins that round
4. Cannot exceed the target—if a roll would cause you to go over, lose that turn
5. Play best of 5 rounds

Advanced Version

• Use three dice for faster play
• Allow subtraction moves (roll and subtract from a place value)
• Include "wild" turns where you can reorganize your beads across place values

Skills Enhanced

• Goal-oriented calculation
• Multi-step problem solving
• Place value construction
• Estimation and planning

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Tips for Classroom Implementation

Differentiation Strategies

For Struggling Learners:

• Use only the basic Bead Gammon game with single 6-sided dice
• Reduce target from 100 to 50 beads
• Remove snake eyes penalty initially
• Use visual charts for doubles calculation

For Advanced Learners:

• Use 10-sided or 12-sided dice for larger numbers
• Add multiplication rules (multiply dice instead of adding)
• Introduce negative numbers (can move beads backward)
• Play Abacus variations with 4-digit numbers
• Create custom penalty/bonus cards

Classroom Management

1. Partner Play: Students work in pairs, promoting mathematical discourse
2. Station Rotation: Set up different Bead Gammon variations as math stations
3. Tournament Style: Class-wide tournament with brackets
4. Reflection Component: After each game, students write one mathematical strategy they used
5. Modified Rules: Create "house rules" as a class to address specific learning objectives

Assessment Opportunities

• Observation: Watch for counting strategies, error correction, and place value understanding
• Math Journals: Students explain their strategy for winning
• Exit Tickets: "What is the probability of rolling doubles?" or "How many moves would it take to reach 100 if you rolled 7 every time?"

Extensions

1. Probability Study: Track frequency of snake eyes over multiple games
2. Data Collection: Graph wins/losses, average beads per turn
3. Fractions: "What fraction of your beads have you moved?" after each turn
4. Algebraic Thinking: "If you need 42 more beads, what combinations of rolls could get you there in 3 turns?"

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Benefits of Bead Gammon for Mathematical Development

1. Concrete-Pictorial-Abstract Progression: The physical beads provide concrete manipulation, supporting conceptual understanding before abstract calculation

2. Number Sense: Students develop intuition about number magnitude, relationships, and operations

3. Mental Math Practice: The game format encourages quick calculation without paper

4. Engagement Through Competition: Game structure motivates repeated practice

5. Low Floor, High Ceiling: Accessible to all learners while offering depth for advancement

6. Mathematical Discourse: Partners and opponents discuss strategies, defending their thinking

7. Growth Mindset: The comeback mechanism (snake eyes) teaches that games can change quickly—no one is ever truly out

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These variations transform a simple counting frame into a versatile mathematical tool that grows with students from basic addition through sophisticated place value understanding. The game-based approach ensures high engagement while building critical numeracy skills.