mr barton maths

Fizz Buzz
The classic counting game with a mathematical twist
1 Players
2 Rules
Fizz
Buzz
Squit
Plop
3 Options
🖥️

Whole-Class With Projector

Paste your class names in, go fullscreen, and project onto the board. The tool randomly picks who answers next — keeping everyone on their toes. Use Reveal Answer to show the correct response, then discuss. Toggle 💬 Discuss on for automatic pause-and-think prompts at key moments (combos, every 20 turns). Great for 5-minute starters or plenaries.

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Solo Practice on Phones / Tablets

Students open the page on their own device, pick a difficulty preset (or choose their own categories), and play without names. They select their answer using the buttons and submit — building a streak. The 💡 Why? explanations give instant feedback on both correct and incorrect answers, so students learn from every turn rather than just being told right or wrong.

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Pairs Challenge — Longest Streak

Pairs share a device, taking turns. One student selects the answer, the other watches. Track who gets the longest streak. You can set the same categories across the class and compare — or let pairs choose their own difficulty. The streak counter and best-streak display make this naturally competitive without any extra setup.

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Investigation — Predict the Patterns

Before even starting the game, set up the categories on the board and ask: “If Fizz is multiples of 3 and Buzz is multiples of 5, which numbers between 1 and 30 will be Fizz Buzz?” Students predict in pairs, then you play the game to check. Use the History strip to look back at patterns. Click any item in the history to see the full reasoning. Try starting from a higher number (use the Start From option) to explore whether patterns repeat.

Tip for younger students (Year 3/4): Start with Fizz = even numbers, Buzz = odd numbers. Every number will be either Fizz or Buzz — there are no plain numbers — which makes the game accessible while still building familiarity with mathematical vocabulary.
Getting Started
  1. Using the Classic setup (Fizz = ×3, Buzz = ×5), write out what the first 20 terms of the sequence should be. Now play the game to check — how many did you get right?
  2. What is the first number that is just a number (not Fizz or Buzz) in the Classic setup? What is the second?
  3. How many of the numbers from 1 to 30 are just plain numbers in the Classic setup? Is this more or fewer than you expected?
  4. With Fizz = even, Buzz = odd — will there ever be a plain number? Why or why not?
  5. What happens if you set Fizz = ×2 and Buzz = ×4? Will Buzz ever appear without Fizz? Explain your reasoning.
Patterns & Predictions
  1. In the Classic setup, the sequence repeats in a cycle. How long is the cycle? (Hint: think about LCM.)
  2. If you know that number 14 is just “14” in the Classic setup, what will number 29 be? What about number 44? Can you explain why?
  3. With Fizz = ×3, Buzz = ×7, how many turns will it take before you see the first Fizz Buzz combo? What is the number?
  4. Does changing the start number change which labels appear, or just when they appear? Test this by starting from 50 with the Classic setup.
  5. With Fizz = ×4, Buzz = ×6, will the number 12 be Fizz, Buzz, or Fizz Buzz? What about 24? Is there a pattern to when both appear?
Combos & Overlaps
  1. In the Classic setup, Fizz Buzz happens at 15, 30, 45, … What do all these numbers have in common? Can you explain why using factors?
  2. Set up Fizz = ×3, Buzz = ×5, Squit = ×2. Is it possible to get a triple combo (Fizz Buzz Squit)? What is the smallest number that achieves this?
  3. Can you find a setup where a four-way combo (Fizz Buzz Squit Plop) happens within the first 20 numbers? What categories would you choose?
  4. With Fizz = ×2, Buzz = ×3 — how far do you have to count before seeing two Fizz Buzz combos in a row? Is this even possible? Why or why not?
  5. Set Fizz = primes, Buzz = ×2. The number 2 is the only even prime — so will “Fizz Buzz” only ever happen once? Explain.
Special Number Categories
  1. Set Fizz = square numbers. Between 1 and 100, how many times will Fizz appear? Are the gaps between Fizz getting bigger, smaller, or staying the same?
  2. Set Fizz = primes, Buzz = square numbers. Is there any number that is both prime AND square? What does this tell you about Fizz Buzz combos in this setup?
  3. With Fizz = triangle numbers — the gaps between consecutive Fizz labels follow a pattern. What is it? (Hint: 1, 3, 6, 10, 15, …)
  4. Set Fizz = Fibonacci. After the number 21, you have to wait a long time for the next Fizz. How long? Why do Fibonacci numbers get further and further apart?
  5. Set Fizz = cube numbers, Buzz = square numbers. Some numbers are both cubes and squares (like 64 = 4³ = 8²). These rare Fizz Buzz combos are called sixth powers. Can you find the first three?
Always, Sometimes, or Never?
  1. In the Classic setup: “A multiple of 15 is always Fizz Buzz.” True or false?
  2. “If Fizz = ×3 and Buzz = ×9, then Buzz always appears with Fizz.” True or false? Explain.
  3. “A prime number can never be Fizz in the Classic setup.” True or false?
  4. “Two consecutive numbers can both be Fizz.” Is this always, sometimes, or never true when Fizz = ×3?
  5. “If Fizz = odd and Buzz = ×3, then Fizz Buzz happens on every odd multiple of 3.” Is this always true? Can you find a counterexample?
  6. “With Fizz = primes, you will always eventually see two consecutive Fizz labels (like 2, 3 or 5, 7… wait, those aren’t consecutive!).” Find a pair of consecutive numbers that are both prime. Are there more?
Counting & Frequency
  1. In the Classic setup, out of the first 30 numbers, how many are Fizz (only), Buzz (only), Fizz Buzz, and plain numbers? Do the fractions simplify nicely?
  2. If you play to 100 with Fizz = ×7, roughly what fraction of numbers will be Fizz? Make a prediction, then play to check.
  3. With Fizz = primes — are there more Fizz labels in the first 50 numbers or in numbers 50–100? What does this tell you about how primes are distributed?
  4. Set up all four labels. Count how many plain numbers appear in the first 30 turns. Now add a fifth imaginary label — what category would eliminate the most remaining plain numbers?
  5. With Fizz = ×3, how many consecutive plain numbers can you find? What is the maximum possible gap between two Fizz labels?
Starting From Different Numbers
  1. Play the Classic setup starting from 1, then again starting from 100. Does the pattern of Fizz, Buzz, plain, Fizz, plain, … feel the same? Why?
  2. If you start from 15 in the Classic setup, your very first turn is Fizz Buzz. Find another starting number where the first turn is also Fizz Buzz.
  3. Start from 97 with Fizz = primes. Your first term is Fizz (97 is prime). How many of the next 10 numbers are also Fizz? Is this more or fewer than if you started from 7?
  4. Can you find a starting number where the first 3 turns are ALL labelled (no plain numbers) in the Classic setup?
Design Challenges
  1. Design a setup where every number gets a label — no plain numbers at all. What’s the simplest way to achieve this? Is there more than one way?
  2. Design a setup where the Fizz Buzz combo appears exactly once in the first 50 numbers. What categories did you use?
  3. Design a setup where exactly half of the numbers from 1 to 20 are plain numbers.
  4. Create the hardest possible setup — one where the labels are so unpredictable that even you find it difficult. What makes it hard?
  5. Design a “Year 3 friendly” setup where labels appear frequently and the pattern is easy to spot. What makes a setup accessible?
Going Deeper
  1. In the Classic setup, the cycle length is 15 (the LCM of 3 and 5). What would the cycle length be for Fizz = ×4, Buzz = ×6? Is it 24 (4 × 6), or something smaller? Why?
  2. Mathematicians use the inclusion-exclusion principle to count overlaps. With Fizz = ×3, Buzz = ×5 from 1–60: Fizz appears 20 times, Buzz 12 times, but Fizz Buzz only 4 times. So the total labelled numbers = 20 + 12 − 4 = 28. Why do we subtract? Use this to calculate how many plain numbers there are from 1–60.
  3. With Fizz = primes, Buzz = primes — every prime number would be Fizz Buzz! But we prevent duplicate categories. Why might a mathematician still find this interesting?
  4. The prime number theorem says roughly 1 in every ln(n) numbers near n is prime. If Fizz = primes, roughly what fraction of numbers near 1000 would be Fizz? How does this compare to Fizz = ×7?
  5. With Fizz = ×3, Buzz = ×5, Squit = ×7, Plop = ×11 — the four-way combo first appears at 3 × 5 × 7 × 11 = 1155. If you started from 1, how many turns would that take? Is there a quicker setup to reach a four-way combo?
Fizz Buzz
0 number 1–4 labels Space submit / reveal → next
Sequence
Fizz Buzz
Sequence