资源简介

(共30张PPT)
Unit 2 Amazing numbers
主题范畴：
人与社会
主题群：
历史、社会与文化；科学与技术
子主题：
对世界、国家、人民和社会进步有突出贡献的人物；科学技术与工程，人类发明与创新
Key question
What is the role of numbers in our daily lives
know something about Fibonacci sequence；
learn to use strategies such as locating key words to understand the text;
know the impact of numbers and mathematical laws in fields like nature and culture.
Learning objectives 学习目标
At the end of the class, I’ll be able to:
0、1、1、2、3、5、8
Lead-in
Look at the numbers and find out the rule!
From the third number on, each number is equal to the sum of the previous two ones.
Fibonacci numbers
斐波那契数列
If you carefully observe the natural world around you, you may find interesting
mathematical patterns!
Cross-curricular connection| Mathematics*
Read the article on Fibonacci numbers and find out more about Maths in nature.
Fibonacci was a famous Italian mathematician born in the 12th century. He created many maths problems. The most famous one was about rabbits. Imagine that a pair of rabbits can have two babies every month. After two months, the new rabbits can have babies too. What will happen if you have a pair of new born rabbits on your farm How will the number of rabbits grow over time Let’s look at the answers this way:
The amazing Fibonacci sequence’ of numbers
This is the beginning of the Fibonacci sequence. Look at the numbers. Can you see any pattern That’s right-each number is the sum of the two previous ones. As we can see, the numbers in the Fibonacci sequence grow very quickly. What numbers come after 8 in the sequence
Fibonacci numbers are very special because they show up everywhere. They appear in artworks and famous buildings, and also in living things. In fact, nature likes to follow the Fibonacci sequence. Flower petals② often come in Fibonacci numbers. The same thing happens with the spirals③ of pine cones④ and sunflower seeds. We do not know yet why these numbers are so common, but Fibonacci’s discovery can help us understand the natural world.
Fast reading
Fibonacci was a famous Italian mathematician born in the 12th century. He created many maths problems. The most famous one was about rabbits. Imagine that a pair of rabbits can have two babies every month. After two months, the new rabbits can have babies too. What will happen if you have a pair of new born rabbits on your farm How will the number of rabbits grow over time Let’s look at the answers this way:
What is paragraph one about
It introduces __________, a famous Italian mathematician in the 12th century. He derived (引出) ____________________ from the problem of rabbit reproduction.
Fibonacci
the Fibonacci sequence
This is the beginning of the Fibonacci sequence. Look at the numbers. Can you see any pattern That’s right-each number is the sum of the two previous ones. As we can see, the numbers in the Fibonacci sequence grow very quickly. What numbers come after 8 in the sequence
What is paragraph two about
It presents the beginning of the Fibonacci sequence and explain its pattern.
Fibonacci numbers are very special because they show up everywhere. They appear in artworks and famous buildings, and also in living things. In fact, nature likes to follow the Fibonacci sequence. Flower petals② often come in Fibonacci numbers. The same thing happens with the spirals③ of pine cones④ and sunflower seeds. We do not know yet why these numbers are so common, but Fibonacci’s discovery can help us understand the natural world.
What is paragraph three about
It shows that Fibonacci numbers are very ________ and widely exist in _________, _________ and ___________.
special
artworks
buildings
living things
Read in detail
Fibonacci was a famous Italian mathematician born in the 12th century. He created many maths problems. The most famous one was about rabbits. Imagine that a pair of rabbits can have two babies every month. After two months, the new rabbits can have babies too. What will happen if you have a pair of new born rabbits on your farm How will the number of rabbits grow over time Let’s look at the answers this way:
Where does Fibonacci come from
Italy.
Do you know what other math problems he created
Leonardo Fibonacci
(about 1175-1250)
背景链接
中世纪意大利数学家，是西方第一个研究斐波那契数列的人，并将现代书写数和乘数的位值表示法系统引入欧洲。其写于1202年的著作《计算之书》中包含了许多希腊、埃及、阿拉伯、印度以及中国的数学相关内容。
这类问题看似基础，却在当时帮助欧洲人理解变量、方程和比例关系，取代了繁琐的罗马数字计算方式。
Do you know what other math problems he created
鹰与鸽子的相遇问题 (Hawk and Dove Problem)
这是一个涉及速度和相遇的行程问题，可简化为：一只鹰从点A出发，速度为每天50里；一只鸽子从点B出发，速度为每天30里。A、B两点相距1000里，两者同时出发相向而行，问多久后相遇？
水池注水问题(Water Filling Problem)
一个经典的工程问题，涉及多速率协作：一个水池有3个进水口，单独开第一个口，1天可注满；单独开第二个口，2天可注满；单独开第三个口，3天可注满。若同时打开三个口，多久能注满水池？
通过计算各口的注水速率（如第一个口速率为1池/天，第二个为1/2池/天等），求和后取倒数即可得总时间，这类问题至今仍是中小学数学中的常见题型。
遗产分配问题（Inheritance Division）
一个复杂的比例分配问题，涉及遗嘱中的财产分割：
某人去世后留下若干金币，遗嘱规定：长子分得1枚金币加剩余的1/7；次子分得2枚金币加剩余的 1/7；三子分得3枚金币加剩余的1/7……以此类推，最后所有儿子分得的金币数相等。问此人有几个儿子？共留下多少金币？
这类问题需要通过逆向推理或方程求解，体现了斐波那契对递归和比例关系的深刻理解。
This is the beginning of the Fibonacci sequence. Look at the numbers. Can you see any pattern That’s right-each number is the sum of the two previous ones. As we can see, the numbers in the Fibonacci sequence grow very quickly. What numbers come after 8 in the sequence
What numbers come after 8 in the sequence
Thirteen.
5+8=
Fibonacci numbers are very special because they show up everywhere. They appear in artworks and famous buildings, and also in living things. In fact, nature likes to follow the Fibonacci sequence. Flower petals② often come in Fibonacci numbers. The same thing happens with the spirals③ of pine cones④ and sunflower seeds. We do not know yet why these numbers are so common, but Fibonacci’s discovery can help us understand the natural world.
What natural things are mentioned as following the Fibonacci sequence
Flower petals, pine cones and sunflower seeds.
Find a pine cone and count the spirals. How does the number of spirals illustrate the Fibonacci sequence Think about things around you in nature. Have you ever noticed
any interesting patterns
Words:
mathematician n. 数学家
imagine v. 想象
newborn adj. 新生的
pattern n.规律；图案
sum n. 总和
previous adj. 以前的；先前的
special adj. 特殊的
artwork n. 艺术作品
seed n. 种子
Our world is full of amazing numbers. How much do you know about them In this
project, you will explore different types of numbers in groups and make a class booklet about your findings.
Making a booklet about numbers
Project
Step 1
Brainstorm some number-related topics in your group. Use the following spidergram to help you. Write down your own ideas in the spidergram.
Step 2
Decide on a topic and then research it.
Numbers connected to festivals
Numbers in science
Step 3
Write a short passage on your topic. Illustrate your passage with pictures, graphs, etc.
Number 1
Chinese New Year (Spring Festival): The festival marks the start of a new lunar year, emphasizing “new beginnings” (the first year in the 12-year zodiac cycle). On the first day of the lunar year, families visit relatives to exchange greetings, symbolizing unity and fresh starts.
In daily calculations or popular science, the speed of light is often simplified to 3×10 metres per second.
3108
Step 4
As a class, put all your passages together to make a booklet about numbers.
智慧角
数字主宰宇宙。
——毕达哥拉斯（古希腊数学家）
Wits corner
Numbers rules the universe.
— Pythagoras
Language points
1. Fibonacci was a famous Italian mathematician born in the 12th century.
mathematician n. 数学家
拓展：①mathematical adj. 数学的 ②Maths n. 数学
用以上词汇填空：
The _____________ solved a difficult problem.
We use ____________ methods to analyze data.
I like _____________ because it’s interesting.
mathematician
mathematical
Maths
2. Imagine that a pair of rabbits can have two babies every month.
imagine v. 想象
拓展：①imagination n. 想象力 ②imaginary adj. 想象的
③imaginative adj. 富于想像的；有创造力的
④ imagine doing sth. 想象做某事
Translate.
我无法想象没有手机的生活。
孩子们通常有丰富的想象力。
这个故事围绕一个虚构世界展开。
她是个有创造力的作家。
I can’t imagine living without my phone.
Children often have vivid imagination.
The story is about an imaginary world.
She’s an imaginative writer.
1. 我无法想象没有手机的生活。
2. 孩子们通常有丰富的想象力。
3. 这个故事围绕一个虚构世界展开。
4. 她是个有创造力的作家。
基础作业：
完成相关练习；
小组合作完成项目式学习，制作小册子；
小组合作准备班级分享活动。
拓展作业：
欣赏其他小组的作品，修改和丰富本小组的作品。

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