Students need to understand that fractions represent parts of wholes and that the numerator and denominator play different roles. These questions surface prior knowledge about fraction magnitude and equivalence.
Compare fractions
- Compare two fractions with different numerators and different denominators. (4.NF.A.2)
Before You Play
Which is bigger: 3/4 or 2/3? How do you know?
Listen for students who reference proximity to one whole ("three-fourths is only missing one piece") or use common denominators ("I can rewrite them as twelfths"). Benchmark fraction thinking shows strong number sense.
Watch for spontaneous hand gestures showing size or fingers drawing rectangles in the air. These spatial movements often appear before verbal explanations.
What makes one fraction equal to 1 whole? Can you give me three different examples?
Listen for recognition that equal numerators and denominators equal one whole (2/2, 5/5, 100/100). Strong responses identify the pattern rather than listing memorized examples.
Watch for matching finger displays on each hand (3 and 3, 4 and 4). This physical mirroring often appears before verbal articulation.
Look around the room. Point to something that's about halfway across. Now point to something that's about three-quarters of the way across. How did you decide?
Watch for students who sweep their arm across the space while dividing it into sections, or who walk a few steps to gauge distance. These spatial estimations build benchmark fraction sense.
Listen for explanations about dividing the whole into parts: "I imagined cutting the room into four sections, then counted three of them." Students who point to the same spot for both fractions need more benchmark work.
Setup Tip
Partners should sit side-by-side with the board between them so both can reach materials easily. Place the Helper Sheet where both students can point to it and trace between fractions.
During Gameplay
Top Dog creates dozens of fraction comparison opportunities in 15 minutes. Students construct fractions from dice rolls, compare them to challenge cards, and make decisions about risk and progress. Watch for mathematical reasoning and strategic thinking.
Drawing Challenge Cards
Before you look at the challenge card, what fraction would you WANT to see? What would you NOT want to see? Why?
Listen for strategic thinking that connects board position to desired outcomes. Students near the goal might prefer low fractions (easier to beat), while students far away might want high-value cards (more movement).
Watch for students who lean forward and point to their position on the board while thinking aloud. This forward body movement and gesture shows they're connecting abstract fractions to game outcomes.
Watch For Students who run their finger across the Helper Sheet before rolling dice—they're preparing to compare by familiarizing themselves with fraction positions.
Rolling & Constructing Fractions
You rolled a 4 and a 5. What are the two fractions you could make? Which one is bigger?
Listen for students who explain that 5/4 is greater than one whole because "the numerator is bigger than the denominator" or "you have five pieces when you only need four."
Watch for dice being picked up, rotated, and repositioned multiple times. This physical manipulation supports mental comparison. Students who hold dice stationary may need prompting to consider both arrangements.
Show me with your hands: which is bigger, 5/4 or 4/5?
Watch for students who hold their hands apart to show "more than a whole" for 5/4, then bring them closer for 4/5. This gesture calibrates their fraction sense spatially. Students who use identical hand positions for both fractions need more work distinguishing improper fractions from proper fractions.
How do you decide which die should be the numerator and which should be the denominator?
Listen for articulated strategies like "I put the bigger number on top when I want a fraction greater than one" or "I try to get as close to the challenge fraction as possible without going under."
Comparing Fractions
How can you tell if your fraction beats the challenge fraction? What strategies help you compare?
Listen for multiple strategies: using benchmark fractions (comparing both to 1/2 or 1 whole), finding common denominators, reasoning about "how much is missing," or recognizing equivalence.
Watch for students who trace lines between fractions on the Helper Sheet with their finger, or who tap each fraction while comparing. This tactile engagement helps them see relative magnitude. Notice whether they rely heavily on the sheet or use it only for confirmation.
Facilitation Move When students struggle, ask "Which fraction is closer to one whole?" or "What's your instinct about which is bigger?" These prompts activate benchmark thinking without eliminating productive struggle.
Moving on the Board
You beat the fraction! Count the spaces you'll move. Are there any award ribbons you'll pass?
Watch for careful counting by touching each paw print, or students who walk their fingers across the board one space at a time. This ensures accurate movement. Students who slide their piece in one motion may be estimating rather than counting.
Listen for recognition that ribbons serve as safety checkpoints. Students who say "If I mess up later, I'll only go back to this ribbon" understand the strategic value of these positions.
Your fraction was smaller than the challenge. What went wrong? What will you do differently next time?
Listen for students identifying their specific error—misreading the comparison tool, confusing which fraction was larger, or choosing dice arrangement incorrectly. Naming the mistake is the first step toward correction.
Reaching Best in Show
You're at Best in Show! What fractions equal 1 whole that you could roll? How many possible winning combinations are there?
Listen for students who enumerate all six possibilities (1/1, 2/2, 3/3, 4/4, 5/5, 6/6) and recognize the pattern that matching numbers always equal one whole. Students who say "I need doubles" understand the concept but may lack precise vocabulary.
Watch for matching finger pairs held up simultaneously (2 and 2, 5 and 5), or students who clap their hands together when they roll matching dice. These physical demonstrations often make the pattern clearer than verbal explanation.
After You Play
After playing Top Dog, students have made dozens of fraction comparisons. Consolidation questions help them articulate strategies, reflect on what worked, and generalize understanding beyond the game.
What strategy did you use to decide which die should be the numerator? Did your strategy change as you played more rounds?
Listen for strategic evolution. Students might say "At first I always tried to make the biggest fraction, but then I realized I needed to match the challenge card more carefully." Recognizing multiple valid strategies shows flexible thinking.
What fraction comparisons were easy for you? Which ones were hard? Why do you think that is?
Listen for students identifying patterns in their confidence. Many find benchmark fractions easier (close to 0, 1/2, or 1) and struggle with fractions between benchmarks.
If you were teaching someone who had never played this game, what advice would you give them about comparing fractions?
Listen for comparison strategies discovered through play: "Check if both fractions are more or less than one-half," "Look at how close each one is to a whole," or "If the denominators are the same, just compare the numerators."
Think about a moment when you made a really good comparison. Point to where on the board that happened. What made that decision successful?
Watch for students who locate specific positions on the board and physically point to them while reconstructing their thinking. This spatial memory helps them see the board as a record of their fraction reasoning.
Listen for explanations connecting mathematical accuracy to strategic success. "I carefully checked the Helper Sheet before I decided" shows students valuing verification. "I knew five-fourths was more than one whole" shows conceptual understanding translating to gameplay.
Extensions & Variations
Target Fraction Challenge
Players try to match the challenge card exactly using their two dice. If they succeed, they move double the spaces on the card. This requires more precise fraction construction and rewards students who can work backward from a target fraction.
Fraction Line Walk
Create a number line on the classroom floor (0 to 2) using tape. Students roll dice, construct a fraction, then walk to that position on the line. Partners challenge each other: "Who's closer to one whole?" Physical positioning builds spatial understanding of fraction magnitude.
No Helper Sheet Mode
Advanced players put away the Helper Sheet and rely entirely on mental comparison strategies. This pushes students to internalize fraction relationships and develop automatic comparison skills. Start with a few rounds, then return to the sheet for difficult comparisons.
Three-Die Advanced Play
Roll three dice and choose any two to create your fraction. The third die becomes a multiplier—if you beat the challenge, move that many spaces. Students must evaluate multiple fraction possibilities while considering the movement reward.
Equivalent Fraction Bonus
If a student's fraction is equivalent to the challenge card (like rolling 2/4 when the challenge is 1/2), they move forward 10 spaces as a bonus. This rewards students who recognize equivalence relationships. Keep a class list of equivalent pairs discovered during gameplay.
Team Strategy Mode
Partners share one game piece and must agree on dice arrangement before comparing. If they disagree, they each explain their reasoning, then jointly decide. Teams that develop clear explanation strategies typically outperform those who defer to one player.
Practical Notes
Timing
Games run 15-20 minutes with 2-4 players. The first game takes longer as students learn mechanics and practice using the Helper Sheet. By the second game, most students move through turns more quickly as fraction comparison becomes more automatic. Budget 5 minutes for setup and rule explanation.
Grouping
Pairs work best because both players stay actively engaged. With three or four players, students wait longer between turns, which can lead to distraction. If you have three players, consider having two play collaboratively as a team against the third.
Materials
Each group needs one game board, challenge cards, two dice, game pieces, and a Helper Sheet. Having two different-colored dice helps students track which die represents the numerator versus denominator. Laminate the Helper Sheet—students will point to and trace fractions repeatedly, causing wear.
Assessment
Watch for comparison fluency: students who confidently arrange dice and move forward without checking the Helper Sheet have internalized fraction relationships. Note which comparisons require Helper Sheet consultation—these reveal gaps in understanding. Listen for strategy articulation: students who explain WHY they chose a particular dice arrangement show deeper understanding than those who guess. Common errors include confusing "greater than" with "less than" and incorrectly comparing fractions with different denominators.