資源簡介

(共39張PPT)
滬教版八年級上
Unit 2 Amazing numbers
Section 4 focusing culture
&Cross-curricular connection&Project
1
Lead in
2
Focusing culture
3
Cross-curricular connection
4
Project
目錄
CONTENTS
Lead in
Before the invention of written numbers, people used many different tools to count things.
What other tools did people use to
count things
Brainstorm
Observe and say
fingers
toes
marks on sticks and bones
tokens（ 代幣） made from clay（黏土）
or small stones
abacus
The babylonians（巴比倫人） used clay to record transactions（交易情況）.
In ancient China, people used the number of stones to count the number of objects. One stone means one, two stones mean two and so on.
Marks &Tokens
Focusing culture
How did numbers develop
Think
Focusing on culture
Numbers are everywhere today. How did people in ancient time record numbers Let's explore the development of counting methods.
Read an article from a science magazine and find out more about numbers.
In ancient times, people developed different counting methods. One of the earliest was called “tally sticks(計數(shù)棍）” Each “stick”
(or pebble 鵝卵石，or other counting tool) stands for
a thing we want to count, such as an animal or a bag of rice.
For each animal we want to count, we draw one stick.
This is called a “one-to-one correspondence(對應）” Tally sticks are easy to understand, but it can take a long time to write down large numbers. To write 1,000, you have to draw a thousand tally sticks!
tally sticks for one - to - one counting
for large numbers (e.g., writing 1,000 needs 1,000 marks).
Later, people created faster ways of writing numbers. One such system developed in ancient India. Instead of using tally sticks, people began using different abstract(抽象的) symbols to represent different numbers. Researchers do not know exactly how this happened, but some believe that the sticks slowly turned into symbols over the centuries. These Indian numerals(數(shù)字）became popular, and people in the Arab world started using them too. Thanks to the Arabs, this way of writing numbers spread to Europe and across the world. Nowadays, they are known as Arabic numerals.
stick counting
Ancient India abstract symbols
Indian numerals popularity
Arab - world adoption
Spread to Europe & world
Modern Arabic numerals
Later, people created faster ways of writing numbers. One such system developed in ancient India. Instead of using tally sticks, people began using different abstract(抽象的) symbols to represent different numbers. Researchers do not know exactly how this happened, but some believe that the sticks slowly turned into symbols over the centuries. These Indian numerals(數(shù)字）became popular, and people in the Arab world started using them too. Thanks to the Arabs, this way of writing numbers spread to Europe and across the world. Nowadays, they are known as Arabic numerals.
Tally - stick counting
Indian abstract symbols
Arab - world adoption
Global Arabic numerals
1. How did the development of number - writing methods progress from tally sticks to Arabic numerals
First, in ancient times, people used tally sticks for counting, achieving a one - to - one correspondence (e.g., marking each animal with a stick). Later, in ancient India, a new system emerged where abstract symbols replaced tally sticks to represent numbers. Over time, these Indian numerals grew popular. Then, with the help of the Arab world, this number - writing method spread to Europe and beyond. Eventually, it evolved into the Arabic numerals we use today.
2. What role did the Arab world play in the spread of the number - writing system that originated in ancient India
The Arab world played a crucial role in spreading the ancient Indian number - writing system. They adopted these Indian numerals and helped spread them to Europe and across the world. Thanks to the Arabs, this system, which later became known as Arabic numerals, gained global recognition and use.
1.What was one of the earliest counting methods mentioned in the text
A. Using abstract symbols
B. Using Arabic numerals
C. Using tally sticks
D. Using pebbles to count animals only
答案：C 解析：文本第一段明確提到 “In ancient times, people developed different counting methods. One of the earliest was called ‘tally sticks (計數(shù)棍)’” ，A選項抽象符號是后來古印度發(fā)展的；B選項阿拉伯數(shù)字是傳播后的名稱；D選項文中說鵝卵石等是計數(shù)工具，并非只用于數(shù)動物，所以選C 。
2.Why might tally sticks be not suitable for writing down large numbers
A. Because they are hard to understand.
B. Because drawing many tally sticks takes a long time.
C. Because people didn't like using them.
D. Because they couldn't represent large numbers.
答案：B
解析：文中第一段提到 “Tally sticks are easy to understand, but it can take a long time to write down large numbers. To write 1,000, you have to draw a thousand tally sticks!” ，說明計數(shù)棍數(shù)大數(shù)時要畫很多，耗時久，A選項與原文 “easy to understand” 不符；C選項文中未提及人們不喜歡；D選項計數(shù)棍能表示大數(shù)，只是畫起來費時間，所以選B 。
3.Where did the system of using abstract symbols to represent numbers develop
A. In ancient Europe
B. In ancient India
C. In the Arab world
D. In modern times
答案：B
解析：文本第二段提到 “Later, people created faster ways of writing numbers. One such system developed in ancient India. Instead of using tally sticks, people began using different abstract (抽象的) symbols to represent different numbers.” ，所以是古印度，A選項歐洲是后來傳播到的地方；C選項阿拉伯世界是使用并傳播的地方；D選項不是現(xiàn)代，選B 。
4.What can we infer about the spread of Arabic numerals
A. They spread only in Asia.
B. The Arabs had no role in their spread.
C. They spread to Europe and around the world with the help of the Arabs.
D. Ancient India spread them directly to Europe.
答案：C
解析：文中第二段 “Thanks to the Arabs, this way of writing numbers spread to Europe and across the world. Nowadays, they are known as Arabic numerals.” ，說明是在阿拉伯人的幫助下傳播到歐洲和世界，A選項只在亞洲錯誤；B選項阿拉伯人起到了作用，錯誤；D選項不是古印度直接傳播到歐洲，是經(jīng)阿拉伯人，所以選C 。
5.What is the main idea of the text
A. How tally sticks were used in ancient times.
B. The development of number - writing methods.
C. Why Arabic numerals are popular.
D. The difference between tally sticks and abstract symbols.
答案：B
解析：文本先是講了古代計數(shù)棍的計數(shù)方式，接著講后來古印度發(fā)展抽象符號代表數(shù)字，以及經(jīng)阿拉伯人傳播成為阿拉伯數(shù)字，整體是在說數(shù)的書寫方法的發(fā)展歷程，A選項只涉及計數(shù)棍，片面；C選項未重點講阿拉伯數(shù)字流行原因；D選項只是部分內(nèi)容對比，所以選B 。
People from different cultures use different numerals. Below are three ways of writing the numbers one to five.
Chinese numerals:—、二、三、四、五
Roman numerals: I，II， III，IV，V
Arabic numerals: 1, 2, 3, 4, 5
Notes
2 Complete the summary below with the information from the article on page 30.
In ancient times, people developed a counting system called (1) _______. Later, people replaced this system with abstract (2)_________. These were more convenient because they were quicker to write. The numbers we use today are called (3)________________. They were invented in (4)_______,Thanks to the ⑸_______，this system spread to other parts of the world. Sometimes we also see numbers written with ⑹______________ on clock faces and buildings. These are called Roman numerals.
tally sticks
symbols
Arabic numerals.
Arabs
India
Roman numerals
3 Complete the sentences with the words below change the form if necessary.
exactly represent symbol system
(1) The Roman symbol IV _________ the number 4 in Arabic numerals.
(2) This palace was a(n)_________of the king's wealth and power.
(3) The Roman alphabet is not the only writing ________ in the
world — there are many others.
(4) We don't know_______ how many animal species there are on Earth.
represents
symbol
system
exactly
4 What influences did the development of counting methods have on people's daily lives
...
...
Your ideas
The development of counting methods helped people in daily life a lot. Tally sticks were slow, but new systems like Indian numerals made counting fast. This helped in trade (e.g., counting goods), record-keeping (e.g., taxes), and building. Arabic numerals spread globally, making math easier for everyone, even on clocks and in books today.
People used counting rods in ancient China. What do you know about this way of counting Do some research and share your findings with your classmates.
Explore more
Cross-curricular connection
Cross-curricular connection I Mathematics
If you carefully observe the natural world around you, you may find interesting mathematical patterns!
1 Read the article on Fibonacci numbers and 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 newborn rabbits on your farm How will the number of rabbits grow over time Let’s look at the answers this way:
This is the beginning of the Fibonacci sequence(斐波那契數(shù)列) . 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
Number of pairs
2 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
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 petals (花瓣) often come in Fibonacci numbers. The same thing happens with the spirals(螺旋形)of pine cones (松果) 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.
2 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
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 petals (花瓣) often come in Fibonacci numbers. The same thing happens with the spirals(螺旋形)of pine cones (松果) 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.
1.Who was Fibonacci and when did he live
Fibonacci was a famous Italian mathematician, and he was born in the 12th century.
2.Describe how each number in the Fibonacci sequence is generated.
Each number in the Fibonacci sequence is the sum of the two preceding numbers.
3.According to the text, in what kinds of things (art, nature, etc.) do Fibonacci numbers appear
Fibonacci numbers appear in artworks, famous buildings, and living things like the spirals of pine cones and sunflower seeds.
4.What activity involving a pine cone is suggested to understand the Fibonacci sequence And why is this activity relevant
The text suggests finding a pine cone and counting the spirals. This is relevant because the number of spirals often corresponds to Fibonacci numbers, helping illustrate the sequence in nature.
短語積累
1. instead of - 代替；而不是
2. spread to - 傳播到；蔓延至
3. over time - 隨著時間推移
4. in nature - 在自然界中
5. be born in - 出生于
6. think about - 思考；考慮
7. a pair of - 一對；一雙
8. according to - 根據(jù)；按照
9. turn into - 變成；轉(zhuǎn)變?yōu)?br/>10. thanks to - 多虧；由于
11. carefully observe - 仔細觀察
12. be famous for - 因……聞名
13. count the spirals - 數(shù)螺旋紋
14. write down - 寫下；記下
15. help sb. (to) do sth. - 幫助某人做某事
16. show up - 出現(xiàn)；顯現(xiàn)
17. a long time - 很長時間
18. the sum of - ……的和
19. living things - 生物
20. grow up - （引申“grow”相關(guān)，增長/成長 ）
Project
Project
Making a booklet about numbers
Our world is full of amazing numbers. How much do you know about them In this project, you will explore different types of number in groups and make a class booklet about your findings.
Step 1 Brainstorm some number-related topics in your group Use the following spidergram to help you, write down your own ideas .
Step 2 Decide on a topic and then research it.
Step 3 Write a short passage on your topic. Illustrate your passage
with pictures, graphs, etc.
Step 4 As a class, put all your passages together to make a booklet
about numbers.
Number rules the universe.
Pythagoras
Numbers
THANK YOU

展開更多......

收起↑