📜Fibionacci and his Rabbits 🐇 🧮

People didn’t always use the numbers we know today—like 1, 2, 3. Long ago, they used many different number systems, and one of the most recent before ours was Roman numerals, with letters like I, V, and X instead of digits! Have you ever tried adding with Roman numerals? 😅 Imagine trying to solve a problem like: How much is XLVII plus XXIII? (That’s 47 + 23… we think… 🤔). What about doing division or multiplication? It was slow… complicated… and even messy! 😅

Then came a boy with a great passion for numbers: Leonardo of Pisa, who would later become famous as Fibonacci. He was born in the Italian city of Pisa—a busy place of trade and learning, where ships brought goods from every corner of the Mediterranean. His father was a merchant, and young Leonardo often traveled with him. 🌍He saw new lands, people who dressed differently, ate different foods, heard different stories, and most importantly… discover new ideas—ideas that sparkled in his mind like tiny stars.🌟

In the markets of North Africa, Leonardo noticed something different. Traders there weren’t using Roman numerals. Instead, they were writing numbers like this: 1, 2, 3, 4, 5... They even used something strange and wonderful: zero—a number that meant nothing, but made everything easier.

Leonardo was amazed. These Arabic numerals helped merchants add, subtract, divide, and multiply much more quickly and clearly. He thought, Why don’t we all use these?

So, when he returned home, he sat down to write a book. Not a storybook, not a book of poems—but a book of math. He called it Liber Abaci, which means The Book of Calculation. 📖 But don’t be fooled! This book wasn’t dry or boring. It was full of clever problems that helped people figure out real things:

💰 How to exchange currency when traveling to other lands.
🥄 How to divide a sack of rice among friends.
📏 How to measure and sell cloth fairly.

Then, tucked deep inside Chapter 12, he wrote a puzzle that would make him so famous, people would still talk about him hundreds and hundreds of years later! A problem about rabbits that would hop through time and land right into our story today. 🐰✨

The original problem sounded like this : A certain man put a pair of rabbits in a place surrounded on all sides by a wall. How many pairs of rabbits can be produced from that pair in a year if every month each pair produces a new pair which from the second month on becomes productive?

🐇✨ But don’t worry—I’ve made the problem a little easier to understand so we can explore it together more clearly! 😊 Let's investigate The Curious Rabbit Puzzle 🐇

Imagine a quiet, grassy field. 🌾 In it, there’s one pair of rabbits—one male and one female.Now, here’s what happens: starting from the second month, each pair of rabbits has one new pair of baby rabbits every month. And those babies grow up and start having babies too!

So... how many rabbit pairs will there be after 12 months? 🐰📆
Let’s count month by month! 📆🐰

• Month 1️⃣: We start with 1 pair of rabbits.

• Month 2️⃣: Still just 1 pair—they're not old enough yet.

• Month 3️⃣: The original pair has babies, so now 2 pairs! 👶🐇

• Month 4️⃣: The first pair has more babies, but the second pair is still too young—3 pairs total.

• Month 5️⃣: Now both pairs are have babies—5 pairs.

• Month 6️⃣: This month, the original pair and the second and third pairs all have babies. That’s 3 new pairs added to the 5 we had—now we have 8 pairs! 🐇🐇🐇 The rabbits from earlier months are growing up and joining the baby-making fun!

• Month 7️⃣: Now those new rabbits have also grown up and joined the baby boom—13 pairs of rabbits are hopping around the field! 🐇🐇🐇🐇 The number is growing faster and faster!

• Month 8️⃣: Some of the new pairs are old enough to have babies too—21 pairs!

• Month 9️⃣: The field is getting busy—34 pairs of rabbits now! 🐇🌾

• Month 🔟: Even more babies—55 pairs hopping about! 🐇🐇

• Month 1️⃣1️⃣: Wow! 89 pairs! They’re everywhere! 😲🐇

• Month 1️⃣2️⃣: A full year has passed. Can you believe it? There are now 144 pairs of rabbits! 🐇🎉

...and the number keeps growing! So the pattern goes: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 ✨

That’s 144 pairs of rabbits after one year! 😮 Each number comes from adding the two numbers before it. This is now called the Fibonacci Sequence. 🔁

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144… 🔁

You may have already seen this sequence without even knowing! Nature seems to love Fibonacci numbers.

And it all began with one boy, curious enough to follow a better way of counting, and brave enough to write a book that would change the world.

🤔 But do you know why do we call him Fibonacci? Leonardo was called Leonardo of Pisa during his life, but many years later, people began calling him Fibonacci. That name comes from the Italian words filius Bonacci, which means "son of Bonacci." Bonacci was his father's name. So Fibonacci simply means “Bonacci’s son.”📚✨

🌟 Now that you know about this magical number pattern that started with rabbits...
🎯 Let’s become Fibonacci detectives and try to continue the pattern 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144..... ? ✨Or investigate for other examples of fibionacci sequence. 🌻 Sunflowers – Count the spirals in the center going left and right. Are they Fibonacci numbers?🌲 Pinecones – Look at the scales. How many spiral rows do you see?🍍 Pineapples – Check the diamond patterns. Can you find Fibonacci numbers here too?🌼 Flowers – How many petals? 3, 5, 8, 13? Many flowers grow in Fibonacci numbers! 🎵 Even some composers use Fibonacci rhythms and lengths in their compositions! Can you find some melodies to listen?

Or solve problems from his book The Book of Calculation. 📖📊

🪙 Merchant Problems (Money & Trade)
A merchant has 12 bezants and wants to exchange them for Roman denarii. If 1 bezant is worth 24 denarii, how many denarii will he receive? 💡 Can you find out how many bezants he would get if he had 2400 denarii instead?

🧵 Cloth and Fair Trade
A roll of silk costs 20 bezants. A merchant buys 3 rolls and sells them for 75 bezants. Did he make a profit or a loss? How much?💡What if he bought 5 rolls and sold them for 115 bezants?

🍯 Mixture Problem
You want to mix two kinds of honey: one costs 5 bezants per jug, the other 8 bezants. If you mix 3 jugs of the cheap honey and 2 of the expensive, what’s the total cost? What is the average cost per jug?💡 Try changing the quantities and finding a new average.

🧮 Sharing and Proportion
A father wants to divide 60 gold coins between his 3 sons in the ratio 1:2:3. How many coins does each son get?💡 Try dividing 120 coins between 4 children in the ratio 2:3:4:5.

📏 Measurement and Proportion Problems
If one roll of silk costs 7 bezants, how much will 3 and a half rolls cost?💡 Try finding the cost of other fractional amounts too!

🍞 Problems with Sharing and Division
If a man has 30 loaves and wants to divide them among 5 friends, how many does each get?
💡 What if he shared 45 loaves between 9 people?

⏳ Time and Work Problems
If one man can dig a ditch in 5 days, and another in 3 days, how long will it take them working together? 💡 Can you figure it out using the idea of “work per day”?

🐎 Problems with Animals and Travel
Many word problems used horses, camels, and wagons to make the problems fun and relatable.
A horse eats 2 bushels of grain every 3 days. How much will it eat in 20 days?”

🐪 Camel Caravan Problem
A camel carries 500 pounds of grain. It eats 50 pounds every 100 miles. How far can it travel before all the grain is used up—if it must carry enough for its journey and to feed itself? 💡 Try estimating and drawing it out!

🏰 Problem with Bricks
If it takes 12 workers 6 days to build a wall, how many days would it take 4 workers?💡 Introduce the idea of work as “worker-days” and let children experiment.

🎒Riddle Problem (Like the Rabbit One!)
A man puts 1 grain of wheat on the first square of a chessboard, 2 on the second, 4 on the third, doubling each time… How many grains would be on the 64th square?
💡 Let them explore how fast the number grows—it’s exponential! You can even make a mini chessboard to visualize it.

With Montessori joy,
Vanina 😊