Activate understanding of factors and primes through conceptual questions and spatial tools. Use the hundreds chart or number line when it helps students see relationships, but rely on strong questions to surface what they know.
Find factor pairs & recognize prime numbers
- Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite. (4.OA.B.4)
Before You Play
What does it mean to say that 3 is a factor of 12? Can you give me another number that has 3 as a factor?
Listen for: "3 goes into 12 evenly" or "12 divided by 3 equals 4" or "3 times 4 equals 12" all show factor understanding. Best answers connect division and multiplication: "3 is a factor because you can multiply 3 by something to get 12." If students struggle, have them point to multiples of 3 on a hundreds chart—this spatial pattern clarifies the relationship.
Show me with your fingers: if a number has exactly two factors, what are you showing me?
Watch for: Students who hold up one finger and point to themselves (1 and the number) demonstrate prime understanding. This physical gesture makes the "exactly two" criterion concrete. Follow up: "Now show me a composite number"—students should hold up more fingers or gesture to multiple divisors.
Point to examples of primes and composites on this hundreds chart. What patterns do you notice?
Watch for: Students who scan systematically versus point randomly. First group has better number sense. Some use divisibility tricks: "ends in 5 means divisible by 5." Notice: Where students' eyes move on the chart reveals their strategy—straight across suggests counting, diagonal suggests pattern recognition.
If I give you 24, how would you find all its factors systematically? Show me with your hands how you'd organize this work.
Listen for: Testing divisors in order (1, 2, 3, 4...) shows systematic thinking. Stronger students mention factor pairs—"when I find 4 works, I know 6 works too." Some note "only check up to the square root" which is sophisticated. Watch for: Hand gestures that pair up factors (bringing hands together) versus listing them linearly (counting on fingers)—the pairing gesture shows multiplicative thinking.
Setup Tip: Place the board centrally where all players can reach it to shade hexagons. Position the digital generator where everyone can see clearly. Groups of 3-4 work best—enough for collaborative verification without long wait times. Use markers that make clear marks; faint shading makes progress hard to track.
During Gameplay
The game creates natural opportunities for systematic factorization practice. Notice student strategies, push for completeness, and help them develop efficient approaches. Use the physical board to track progress spatially and leverage collaborative work to build verification habits.
Phase 1: Generate Number
Before you start factoring, estimate: will this number have many factors or just a few? Show me with your hands how many you're predicting.
Listen for: Recognition that larger numbers often have more factors, or that numbers with small prime factors (2 and 3) tend to have many. This prediction habit builds number sense. Watch for: Hand gestures indicating quantity—spreading fingers wide for "many" or pinching for "few" makes estimates concrete. After they find all factors, compare their hand gesture to the actual count.
Phase 2: Find All Factors
How will you organize your work so you don't miss any factors? Point to where you'll start testing.
Listen for: Systematic approaches—starting with 2, then 3, then 4, testing each divisor in sequence. Best students mention checking division or thinking about multiplication facts. Watch for: Students who write factors as they find them (organized) versus announce randomly (disorganized). Groups maintaining a written list catch more factors.
⚡ Common Struggle: Stopping Too Early
Many students find obvious factors (1, 2, the number itself) then stop. Push them: "How do you know you've found all the factors? What numbers haven't you checked yet?" The "Find Factor Pairs" button serves as verification—students should find all factors independently first, then check completeness.
You found that 4 is a factor. Show me with your hands: what's the other number in this factor pair?
Watch for: Students who physically gesture multiplication—holding up 4 fingers on one hand while calculating the pair on the other. This embodied pairing speeds factorization. Students might calculate: "24 divided by 4 equals 6" and hold up 6 fingers. Physical representation makes the pair relationship concrete.
Phase 3: Shade Hexagons
Point to each factor on the board as you shade it. How are you tracking what you've already marked?
Watch for: Different tracking strategies—some shade left to right systematically, others jump around. Both work if careful. Listen for: Partners coordinating about shaded hexagons: "I already did all the 2s" or "Let me do the 3s." This division of labor is efficient. The key is developing some system rather than shading randomly.
As you shade, trace the path from the center outward. Can you feel yourself getting closer to the edge?
Watch for: Students running their finger along the bee path, physically measuring progress. This tactile feedback creates urgency and investment. Notice: Students who periodically trace the path stay more engaged than those who just mark hexagons without spatial awareness of the overall goal.
⚡ Strategic Observation: Path Building
After a few rounds, have students trace their finger along the bee path from center toward edge. Ask: "How much farther do you need?" This spatial check helps assess progress and creates urgency. Students become more invested when they can see they're "almost there."
Phase 4: Check for Prime Factors
Look at your factor list. Which are prime? Circle them with your finger.
Watch for: Speed of recognition. Common primes (2, 3, 5, 7) get recognized quickly; larger ones (11, 13, 17) require more thought. Notice: Students who instinctively know versus those who verify each time. By the third game, recognition speeds up dramatically. Physical circling gesture reinforces prime identification.
Phase 5: Continue Until Win or Loss
Late in the game, when the wasp path is nearly full, what's your decision? Compare the two paths with your fingers.
Watch for: Students using fingers to measure remaining spaces on both bee and wasp paths—this physical comparison makes the risk concrete. Listen for: Risk-reward weighing: "If we get a prime, we lose immediately" versus "If we get a good composite, we might win." This probabilistic reasoning is mathematically valuable even without formal probability.
After You Play
Consolidate learning by having students articulate strategies and insights. The game board provides a visual record of their work—leverage it to discuss patterns and frequency. Push students to generalize beyond this game to broader understanding of factors, primes, and multiplicative structure.
Point to the numbers on the board that got shaded most. Why do these appear so frequently?
Watch for: Students physically touching or circling clusters of 2s and 3s on the board. This tactile interaction reinforces the pattern. Listen for: "Lots of numbers are divisible by 2" or "many numbers have 3 as a factor." The spatial evidence—visible clusters—makes common factors concrete. Also valuable: "Why did 23 only get shaded once?" helps students see large primes are factors less often.
Show me with your hands how your factorization strategy changed from round one to the final round.
Watch for: Students using different gestures to show evolution—random pointing (early) versus systematic sweeping (later). Listen for: Metacognitive awareness: "I started remembering which numbers are prime" or "I got faster at using multiplication facts to find factor pairs." Physical demonstration of strategy shift makes learning process visible.
Trace the bee path with your finger. Now trace the wasp path. What kinds of numbers would have helped you win faster?
Watch for: Students using fingers to visually compare paths—this makes game tension concrete. Listen for: "We needed numbers with lots of factors but not too many primes" or "numbers like 48 or 36 would have been perfect—they have many factors." Best students recognize the tradeoff: you want composite numbers with many factors, but these inevitably contain prime factors that advance the wasp.
How is finding factors related to multiplication and division? Show me with your hands how you used both operations.
Watch for: Students making different hand gestures for each operation—perhaps splitting apart (division) versus bringing together (multiplication). Listen for: "I used division to test if numbers work—does 24 divided by 4 give a whole number?" or "I used multiplication facts—I know 4 times 6 equals 24, so both are factors." Strongest understanding sees these as two sides of the same relationship.
Extensions & Variations
🎯 Prediction Challenge
Before generating each number, students predict: "More than 5 factors or fewer?" Write predictions down, then check after finding all factors. Award one bonus hexagon per correct prediction. This builds factor intuition—students start noticing that even numbers, multiples of 2 and 3, and numbers near perfect squares tend to have more factors. Track prediction accuracy across rounds to see improvement.
⚡ Timed Factorization
Set a 2-minute timer per number. Students must find all factors before time runs out or they can't shade any hexagons that round. Disable the "Find Factor Pairs" button—students verify completeness by comparing with another group. This builds speed and systematic approaches. Start with easier numbers (under 50) until students develop efficient strategies, then increase difficulty.
🤝 Head-to-Head Race
Two teams use separate boards with identical generated numbers. First team to correctly identify all factors wins the round and shades their hexagons; the other team shades nothing. Teams must present their complete factor list for verification—missing factors or including non-factors means automatic loss. Five rounds determines the winner. This creates urgency while maintaining accuracy pressure.
📊 Factor Frequency Study
Play 3-5 complete games, then analyze the shaded boards. Which numbers appear most often as factors? Create a bar graph showing frequency. Why do 2, 3, and 5 dominate? What about larger primes like 17 or 19? Students discover that small primes are common factors while large primes rarely appear. Connects factorization to data analysis and helps students see why certain numbers are "more useful" as factors.
Practical Notes
TIMING
Plan for 15-20 minutes per game including setup and brief debrief. First games take longer (20-25 minutes) as students learn the system. By the third game, expect 12-15 minutes. Physical setup takes 2-3 minutes. You can fit two complete games in a 45-minute period, or three games in an hour block with consolidation discussion.
GROUPING
Groups of 3-4 work best. Three allows active participation for all; four lets you designate roles (generator manager, factor finder, shader, verifier). Larger groups create wait times and disengagement. Pairs work but lose collaborative verification benefits. Consider mixing ability levels so stronger students can model systematic strategies.
VERSION SELECTION
Start with Hive Factor 50 for students building factorization fluency. Smaller range means more familiar numbers and faster rounds. Switch to Hive Factor 100 when students show systematic strategies and confidence with multiplication facts up to 10×10. You can run both versions simultaneously—differentiate by readiness rather than forcing all groups to use the same version.
MATERIALS & SPACE
Ensure tables have enough space for the board to lie flat and be accessible to all players. Cramped spaces force awkward reaching, breaking collaborative flow. Position digital generators where all students can see the display clearly. Use markers that make clear, visible marks; faint shading makes progress hard to track. Consider laminating boards for repeated use with dry-erase markers.
ASSESSMENT EVIDENCE
Watch for systematic versus random factorization approaches. Students who test divisors in order (2, 3, 4, 5...) show stronger understanding than those testing haphazardly. Listen for factor pair recognition—"I found 4, so 6 is also a factor" shows multiplicative thinking. Look at completed boards: students who shade many 2s and 3s understand common factors. Check whether students identify primes quickly by the third game—speed of recognition indicates developing number sense.