Check students' place value understanding and multiplication fluency before gameplay. These questions surface misconceptions and build the foundation students need.
Multiply by 10 & 0.1
- Explain patterns in the number of zeros of the product when multiplying a number by powers of 10. 5.NBT.A.2
Before You Play
What happens to a number when you multiply it by 10? What about when you divide by 10?
Listen for: Whether students describe place value shifts ("each digit moves one place") versus procedural tricks ("you add a zero"). Challenge "add a zero" thinking: "What about 3.5 times 10? Can you add a zero there?"
Watch for: Students who gesture right or left while explaining—they have spatial sense of digit movement even if they can't articulate it yet. Encourage them to draw arrows showing digit shifts on paper or a whiteboard.
Which is larger: 1.8 or 1.12? How do you know without using a calculator?
Listen for: Students who reference place value ("1.8 is eight tenths, 1.12 is only twelve hundredths") versus whole number thinking ("12 is bigger than 8").
Watch for: Students who write numbers vertically or draw place value columns while reasoning. Others might use their fingers to count tenths—all physical strategies worth encouraging.
Point to something in this room that's about 10 times bigger than your hand. Now point to something that's about one-tenth the size of this desk.
Watch for: Whether students understand relative magnitude and can estimate multiplicative relationships spatially. Some will walk to objects and physically measure with their hands—this embodied comparison builds intuition for the scale differences on the game board.
Listen for: Students who justify choices with reasoning: "That bookshelf is about 10 hand-widths tall" while actually counting hand-widths against the wall.
Setup Tip:
Place the board centrally so all players can reach it without leaning awkwardly. Students need to scan the hexagonal layout efficiently during gameplay. Keep dice and coins in a shared neutral space between players to avoid turn-taking confusion.
During Gameplay
The game creates repeated practice with multiplying and dividing by 10 while adding strategic elements through bumping and freezing. Focus on place value reasoning and helping students see patterns in how the coin flip determines where results land.
Roll Dice and Compute Product
You rolled 3 and 6. What strategies do you use to find that product quickly?
Listen for: Different approaches—some students recall instantly ("I know 3 × 6 is 18"), others use derived facts ("3 × 5 is 15, plus one more 3 is 18"), some skip-count. All are valid developmental stages.
Watch for: Students who arrange dice to help visualize (in rows or groups), tap rhythmically while skip-counting, or trace arrays in the air with their fingers. These physical strategies support computation.
Watch For:
Students still building multiplication fluency benefit from having a times table reference available. The game provides enough practice that facts become automatic over multiple sessions—focus on building confidence rather than speed initially.
Apply Coin Flip (×10 or ÷10)
You got 18 and flipped heads. Explain what multiplying by 10 does to the digits in 18.
Listen for: Place value explanations ("the 1 moves to the hundreds place, the 8 moves to the tens place") versus procedural shortcuts ("just add a zero"). Push for positional understanding, not memorized rules.
Watch for: Students who physically push imaginary digits to the left with their hand while explaining, or who point to each position on the board as they describe the shift—this spatial tracking solidifies understanding.
You flipped tails and got 1.2 after dividing by 10. Where did the decimal point come from?
Listen for: Understanding that dividing by 10 shifts digits right, creating a decimal. "The 1 becomes the ones place, and the 2 becomes the tenths place" shows stronger place value sense than "you just put a decimal point there."
Watch for: Students who trace the decimal point position with their finger or use a finger to mark where digits "slide" right—this physical marking helps track positional value.
Facilitation Move:
After several turns, pause and ask: "What do you notice about your results when you flip heads versus tails?" Help students see that heads always produces larger numbers (middle and bottom of board) while tails always produces smaller decimals (top of board).
Locate Matching Inequality on Board
You got 60. Point to all the hexes where 60 could legally go. Why does it fit in more than one place?
Watch for: Students who scan the board systematically and recognize that 60 satisfies both "40 ≤ x ≤ 60" and "60 ≤ x ≤ 80" because the inequality uses ≤ (not <). Some will touch each hex boundary while checking—this haptic searching aids accuracy.
Listen for: Whether students articulate inclusive inequality thinking: "60 equals 60, so it counts as being in that range."
Watch For:
How students navigate the board spatially. After a few turns, competent players develop a sense of where numbers "live"—they know decimals are at the top, hundreds at the bottom. Watch for the moment when students' eyes go directly to the right region rather than searching randomly.
What strategy helps you find the right hex quickly?
Listen for: Magnitude-based searching: "I got 180, so I know it's somewhere in the big numbers at the bottom" or "I look at whether my number is bigger or smaller than 10 first."
Watch for: Students who sweep their hand across magnitude regions ("definitely not up here in the decimals") or who physically divide the board into zones. Some rotate the board toward themselves—allow this manipulation.
Strategic Decision: Bump or Freeze
You landed on a hex where your opponent has a single token. Should you bump them off or would you rather have landed somewhere else? Why?
Listen for: Strategic reasoning about valuable versus common hexes. Students may notice that some ranges (like "10 ≤ x ≤ 30") get more traffic because multiple dice products land there, while extreme ranges (like "x > 240") are rare.
Watch for: Students who gesture to show traffic flow patterns ("everyone keeps landing here") or who point between their off-board tokens and empty hexes while calculating remaining moves.
Collaboration:
Players need clear sight lines to all tokens to make strategic decisions about bumping versus freezing. Encourage students to keep their off-board tokens organized (not scattered) so they can quickly count how many moves they have left.
You landed on your own token. Explain your decision: will you stack to freeze this hex, or do you wish you'd landed somewhere else?
Listen for: Strategic thinking about freezing valuable territory early versus saving tokens for later. Some students freeze aggressively, others wait—both are legitimate strategies worth discussing postgame.
After You Play
Use postgame discussion to help students articulate patterns they discovered. The goal is consolidating intuitive understanding into explicit place value knowledge and strategic thinking.
What pattern did you notice about where your tokens ended up when you flipped heads versus tails?
Listen for: Recognition that the coin flip determines magnitude regions: "Heads gave me big numbers at the bottom, tails gave me small decimals at the top." Have students physically point to or circle these regions on the board while explaining.
Which dice combinations appeared most frequently? Why do you think that happened?
Listen for: Students who notice that middle products like 12, 15, 18, 20 appear more than extremes like 2 or 36. Advanced students might reason about combinations: "You can make 12 four different ways, but you can only make 36 one way."
Point to a moment on the board where you made an important strategic decision. What made that decision successful or unsuccessful?
Watch for: Students who can reconstruct their strategic thinking by referencing specific board positions—some will physically point to the sequence of moves they made.
Listen for: Metacognitive reflection: "Next time I'll freeze the middle hexes earlier because they fill up fast" or "I should have watched where my opponent was."
Did your multiplication fluency improve during the game? Which facts became easier for you?
Listen for: Students who recognize their own growth: "At first I had to think about 4 × 6, but by the end I just knew it was 24."
Extensions & Variations
Power of 100
Add a third coin option: multiply or divide by 100. This requires an expanded board with both very tiny decimals (like 0.06) and very large products (like 3600), increasing the magnitude range and place value complexity.
Target Number Challenge
Before rolling, each player predicts which hex they'll land on. If correct, they place two tokens instead of one. This adds estimation and strategic probability thinking to the computational practice.
Floor Number Line
Create a large number line on the classroom floor marking key values (0.1, 1, 10, 100). Students compute their result, then physically walk to stand at that approximate position. This spatial embodiment reinforces magnitude understanding through full-body movement.
Capture the Range
Players earn bonus points for being the first to freeze a hex in each magnitude region (decimals under 1, teens, double-digits, triple-digits). This rewards territorial control across different number ranges.
Single Die Modification
For students still building multiplication fluency, use one die only (values 1-6). This reduces computational demand while preserving the place value practice with multiplying and dividing by 10.
Frequency Analysis
Students track which hexes received the most tokens across multiple games, then analyze why. This data collection connects to probability concepts and helps students understand why certain ranges are strategically valuable.
Practical Notes
TIMING
Plan for 15-25 minutes per game depending on students' multiplication fluency. Faster groups can play multiple rounds while others complete one thorough game—this natural differentiation works well. Allow 5 minutes for setup and 3-5 minutes for postgame discussion.
GROUPING
Pairs work best because both players can reach the board comfortably and track each other's tokens easily. Three-player games increase strategic complexity but can make the board feel crowded. Ensure all players have clear visual access to all hexes.
MATERIALS
Use visually distinct token colors for each player so territorial control is obvious at a glance. If tokens tip over easily, consider using flatter pieces or letting students use small paper squares instead. Students may naturally rotate the board to read upside-down hexes—allow this manipulation.
COMMON ERRORS
Watch for students who multiply one die by 10 before computing the product (computing 30 × 4 instead of 3 × 4, then × 10). Also notice students who struggle with decimal division—they may produce 1.08 instead of 1.2 when dividing 12 by 10. These errors reveal place value misconceptions worth addressing directly.
ASSESSMENT
Observe whether students navigate to the correct magnitude region even if they pick the wrong specific hex. Notice students who compute accurately but search the board randomly—they may need help seeing the board's organizational structure. Track which students develop automaticity with common products (3×4, 5×6) across multiple games.