Mr. Gray goes to the classroom with the students and writes several numbers on the blackboard. They are 1, 1, 2, 3, 5, 8, 13, 21...

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2 次の対話の文章を読んで, あとの各問に答えなさい ( * 印の付いている単語 語句には, 本文のあとに 注 がある ) Ann, Tom and Ken are high school students in the U.S. Mr. Gray is their *biology teacher. After lunch, they are walking outside. Ann finds a *clover with four leaves in their school garden. Mr. Gray: Oh, you found a clover with four leaves. Do you know why a four-leaf clover is a symbol of good luck? Ann: I don t know, but it s not easy to find a four-leaf clover. Mr. Gray: ⑴ Some people say you ll find one in 0,000 clovers. Ann: Wow! So this clover is very special. Wait. How about flower *petals? Mr. Gray: That s an important question. Look at the flowers in this garden. Ann: Let s see. These flowers have petals. Cherry blossoms have petals. Oh, this small flower has petals. How about the *daisies over there? Mr. Gray:. Actually, you often see these numbers in *nature. Nature has its own favorites. Tom: That s true. We can t find flowers with 4 petals easily. Mr. Gray: In fact, there is even math in nature. Let s try the *scientific method. First, have some questions, and then *logically guess answers. Then, after tests, you may find some kind of rule of nature from the information you collect. Mr. Gray goes to the classroom with the students and writes several numbers on the blackboard. They are,,,,,,,... Mr. Gray: So, as a possible solution, imagine plants use math. Look. In these numbers, the next number is always found by adding the two numbers just before it. and, the next is (+), the next is (+). Then, (+) and (+) follow. Tom: Really? But what are these numbers? Mr. Gray: They are called *Fibonacci numbers. book. Look at Picture in this You ll find another example of these numbers here. Picture So, after

3 Ann: Oh, this book shows how a tree grows and *splits into *branches. Let s see. Ken: Ann: Ken: Ann: Mr. Gray: Often one branch is stronger than the other. The other one waits and it also splits after getting enough energy. The number of the branches is,,,,,... Ann: Wait. I have heard these numbers,,,,,, before. Tom: The math of Fibonacci numbers! Mr. Gray: Yes! So, the biology of flowers only is not this math 4 makes ⑶ the 6 that 7 thing an interesting area to study. Tree branches are another example. ⑵-a ⑵-b ⑵-c ⑵-d Mr. Gray takes the students to the school vegetable garden. They see rice, strawberries, potatoes and *turnips. Mr. Gray writes *fractions,,,,, in his notebook. Mr. Gray: Here is another example. You may think small plants in this garden and big trees are *biologically far away from each other, but both use Fibonacci numbers. Ann: Fibonacci numbers here? ⑷ How did you look at this place in that way? And what are these fractions,,,,, in your notebook? Mr. Gray: I ll explain. First, look at the potatoes. How do the leaves grow out from the *stem? Ann: Let s see. Oh, the potato leaves are *spiraling up the stem. Maybe a new leaf grows a little higher up than the last leaf. Mr. Gray: Good. Actually, plant leaves use fractions of Fibonacci numbers to spiral up. A side. Ken: I see. So, in each fraction, the *numerator shows the number of *turns the spiraling leaves make, and the *denominator shows the number of leaves. Then I strawberry uses. It needs leaves to spiral up the stem time. Each new leaf grows about 0 away from the last leaf. The 4th leaf is just above the first leaf. Ann: Really? I have never thought about that. So, there really is math here. Mr. Gray: The potato in this garden is. It needs leaves to spiral up the stem times. A new leaf grows about 44 away from the last leaf. The 6th leaf grows just above the first leaf. Look at Picture and Picture. Tom: Oh, Picture is a plant from above, and Picture is the same plant from the

4 can draw a picture of a plant. Look. This is the plant ⑸ from above. Mr. Gray: Right! People may think each plant is always using many Fibonacci numbers at the same time. In fact, it is possible to say that each plant is an excellent engineer ⑹ of one special skill. It often uses one fraction well. Ann: Interesting! By the way, the first fraction is, the next is, and then. Why? Tom: I know,, and are Fibonacci numbers. But what is the rule? I have no Ken: idea. ⑺ So this is another way of using Fibonacci numbers. And oh, I ve got it. Take *successive two fractions, for example, and. Add the two numerators of these fractions, and you ll get (+). you ll get (+). Add the denominators, and Ann: They are and in the next fraction! I see. The next is, because it is just after and. So, maybe each kind of plant has its own fraction. ⑻ Mr. Gray: Wonderful! Then I have one last question. Why do plants use Fibonacci Tom: numbers? Well, that s a difficult question. Ken: Oh, I ve got it, too. Look at the potato again from above. Tom: Let s see. Oh, the leaves are *wide spread out! Ann: Mr. Gray: Yes! 4 Picture Maybe leaves can collect much light when they don t cover each other so much. Actually, after testing many fractions of bigger denominators, scientists have found using fractions of Fibonacci numbers is the best for this purpose. Ken: Mr. Gray, I ve learned one thing. You were talking about the importance of using the scientific method. I agree. After having questions about flower petals, there ⑼ was another important step before we understood Fibonacci numbers in plants. Ann: Right. We now know why only a lucky person can find a four-leaf clover. 6 4 Picture 6 4

5 注 biology 生物 clover クローバー petal 花びら daisy デイジー ( 花の名 )nature 自然 scientific method 科学的手法 logically 論理的に Fibonacci numbers フィボナッチ数 ( の並び ) split 分かれる branch 枝 turnip カブ fraction 分数 biologically 生物学的に stem 茎 spiral らせん状に回る numerator 分数の分子 turn 回転 denominator 分数の分母 successive 連続した wide 大きく開いて 問 本文の流れに合うように, ⑴ に英語を入れるとき, 適 切なものは次の中ではどれか ア Yes, it is. イ No, it s not. ウ I must say it is. エ I didn t know it, either. 問 ⑵-a ~ ⑵-d の中に, それぞれ次の A ~ D のどれを入れるのがよいか その組み合わせとして最も適切なものは下のア~カの中ではどれか A B C D That s news to me, and how does that happen? Then, they are like brothers born at the same time. It says a young tree or a branch usually splits into two branches. Not really, because one grows and splits fast, but the other doesn t. ⑵-a ⑵-b ⑵-c ⑵-d ア A B D C イ A C B D ウ C B D A エ C D A B オ D A C B カ D B A C

6 問 ⑶ So, the biology of flowers only is not this math 4 makes the 6 that 7 thing an interesting area to study. とあるが, 本文の流れに合うように, 内の単語 語句を正しく並べかえたとき, 番目と 番目と 7 番 目にくるものの組み合せとして最も適切なものは次のア~カの中ではどれか 番目 番目 7 番目 ア 7 イ 7 ウ 4 6 エ 4 6 オ 6 カ 6 問 4 ⑷ How did you look at this place in that way? とあるが, このとき Ann が考えた 内容として最も適切なものは次の中ではどれか ア I thought I could find the math of Fibonacci numbers in such small plants, too. イ Can you explain how to find a garden with plants which use Fibonacci numbers? ウ It s surprising to know Fibonacci numbers in small plants follow rules of nature. エ I didn t imagine small vegetable plants were connected with Fibonacci numbers. 問 ⑸ This is the plant from above. とあるが, ここで Ken が書いた葉と茎の様子を 正しく表している絵は次の中ではどれか ただし, 下の図において, 中心を茎として, 葉については時計回りに生え, 生えた順番に葉に番号をつけたものとする ア leaf イ ウ エ

7 問 6 ⑹ In fact, it is possible to say that each plant is an excellent engineer of one special skill. とあるが, このとき Mr. Gray が言いたかったこととして最も適切なもの は次の中ではどれか ア It is interesting to know some plants use Fibonacci numbers better than other plants. イ A plant can use Fibonacci numbers in a different way from the way people often believe. ウ A plant uses several Fibonacci numbers so well that we call one an excellent engineer. エ Here are some facts to support the idea people have about Fibonacci numbers in plants. 問 7 ⑺ So this is another way of using Fibonacci numbers. とあるが, このとき Ken が考えた内容を次のように書き表すとすれば, の中にどのような英語を入れるのがよいか 本文中の連続する 語で答えなさい In a tree, the number of its branches shows Fibonacci numbers. However, in a small plant, only one fraction of Fibonacci numbers may explain how one leaf and the next leaf grow from each other on the stem. 問 ⑻ So, maybe each kind of plant has its own fraction. とあるが, その内容を次のように書き表すとすれば, 二つのの中にどのような共通する英語 語を入れたらよいか So, maybe kinds of plants use fractions of Fibonacci numbers. 7

8 問 9 ⑼ After having questions about flower petals, there was another important step before we understood Fibonacci numbers in plants. とあるが, その内容を次のように書き表すとすれば, の中にどのような英語を入れるのがよいか 本文中の連続する 4 語で答えなさい After having questions about flower petals, it was important to as the answer for the second step of the scientific method. That step helped us, and we studied some examples. Then we learned about Fibonacci numbers in plants. 問 0 本文の内容と合っているものを, 次のア ~ カの中から一つ選びなさい ア Some flowers using Fibonacci numbers for their petals are special plants which are chosen by nature. イ In fractions of Fibonacci numbers, the next fraction is always found by adding the two fractions just before it. ウ It is possible to say using Fibonacci numbers is one way to explain things happening in nature logically. エ Leaves of plants trying to receive much sunlight are spread out because they try to use Fibonacci numbers well. オ The students learned how the number of tree branches increased from the example of leaves spiraling up their stems. カ The number of the leaves of a four-leaf clover shows the amazing work of Fibonacci numbers in nature.

9 次の文章を読んで, あとの各問に答えなさい ( * 印の付いている単語 語句には, 本文のあとに 注 がある ) Emi, are you ready for your flight? asked my mother. I m leaving for India. I finished university five years ago, and I am working at a *company. I remember my high school days. At that time, I started to think about my future. I was in the volunteer club when I was a high school student. members, Nobuo, Taku, Aditi and me. 9 Our club had only four We sometimes cleaned the streets or played with little children as our volunteer activities, but we wanted to do something *unique and new. day, our activities were reported in a local newspaper. our club activities. One One of its readers became interested in He was Mr. Kitano, and he was working for a company called Tachibana. Everyone in my town knew the company because it was quite big in this small town. Tachibana was making machines for *agriculture. It was thinking of doing something to *contribute to *society, and decided to do something for our *community with local people. Then, Tachibana made a small team for this, and Mr. Kitano became a leader. they could do something with us, and came to school. He thought Mr. Kitano told us about *Corporate Social Responsibility called CSR in a very simple way, and said, Today, many people are looking for more than just good *products when they buy something. Imagine a company makes very good products. ⑴ We will find some good ways, said Nobuo. and I knew almost everyone living there. Aditi said, I lived in a small town in India, When something happened, we helped each other. However, here in this small town, though we live or work in the same community, we don t really know each other. This is sad. If we have a chance to do something together, our community will become a better place for everyone. All of us agreed with her. ⑵ After that, we studied about some examples of CSR activities and tried to find what we could do for our community. We went to the library and read a lot of books. We also looked for some examples on the Internet. One week later, we had a meeting. *apple-orchards, and it was famous for its apples. now there are fewer apple-orchards. I said to the members, Our town used to have a lot of However, some people left this town, and I continued, I like to do something to *revive our town with apples. Then Nobuo said, I agree with Emi. I also remember Aditi s words. If we share or do something together, we will have stronger *connections between us. Taku smiled and said, Both ideas are great. How about putting these two ideas

10 together? I know a family who used to grow apples in their large apple-orchard. They stopped growing their apple trees and already removed the trees. apple-orchard, we can plant and take care of new apple trees. even know how trees grow, so we can learn it from growing apple trees. 0 If Tachibana buys their Then I said, Most of us don t People in this town will experience a lot of things, said Taku. We all agreed with him. After this meeting, we talked about our idea with Mr. Kitano and his project members. Two months later, Tachibana decided to buy some of the apple-orchard, and plant 0 young apple trees there. We wanted a lot of people to join our project, so we asked people in our town to be a part of it. We gathered in the apple-orchard one day in October. There were three friends of ours, Mr. Kitano and his two project team members. There were no other people. This made us ⑶ very sad. The land was very bad because it was not used for several years. We needed to remove *weeds and small trees before planting apple trees. The work made us very tired, but we had a good time. We talked and laughed a lot. We named ourselves Apple Tree Project Team. We gathered again the next weekend. We were surprised to find there were ten local people. They thought we were enjoying our work. So they decided to join us. We did this work during that winter, and more and more people came. planted 0 young apple trees. That spring, we Time passed. taking part in the the project 4 people increased 6 number ⑷ 7 of. Not only the project members but also people living and working in our town went there to take care of the trees with the help of farmers. our community. each other. We were sure we were contributing to Before the Apple Tree Project, people in our town didn t know much about After starting the project, many people had lunch parties outside or played sports. If little children were alone at home, other families invited them and had dinner together. When we saw each other on the street, we said hello. That fall, the apples were not ready for harvest, but we had a one-year *anniversary lunch party in the apple-orchard. A magazine company came, and reported this kind of activity would be more popular in the near future. Our project became famous, and we were proud of that. ourselves. We had to wait for more than three years to have a good harvest. to give up everything, because we had so many things to do. More than that, we were proud of ⑸ We sometimes wanted For example, the trees needed water and *fertilizer. ⑹-a Also, we needed to protect the trees from weeds, insects and diseases. ⑹-b When we needed to do some dangerous work such as *pruning or spraying chemicals, the farmers and people who knew plants well did it. I got interested in agriculture while we were growing the apple trees.

11 I also hoped to make society better through growing apples. I studied agriculture at university for those reasons. ⑹-c After several years, Tachibana bought the whole apple-orchard for the project. The project won the hearts of people in our town. ⑹-d When we have big problems with the environment or we want to change society, we often think we can t do anything. In this world which we don t understand easily, we often say to ourselves, What can I do? I m just one person. However, our club members learned big changes often begin with one person or a small group. We also learned another important lesson, and it was, If we have an idea which we really want to realize, we should keep trying. This is the only way to *accomplish anything. Sometimes we may feel it is difficult to *reach our goal, but it may be too soon to ⑺. Now I am working for Tachibana. This year, Tachibana gave me a chance to work in a small town in India. Aditi and I are going to work for Tachibana s CSR project, Apple Tree Project in India. Aditi studied agriculture with me at the same university. Aditi will be a leader of the project. We will make people happy by growing apples. 注 company 会社 unique 独自の agriculture 農業 contribute to ~ ~に貢献する society 社会 community 地域社会 Corporate Social Responsibility 企業の社会的責任 product 製品 apple-orchard りんご園 revive 元気にする connection 関係 weed 雑草 anniversary 周年記念の fertilizer 肥料 pruning or spraying chemicals 実がよくつくようにしたり木の形を整えるため に, 枝の一部を切ったり, 薬剤を散布すること accomplish 成し遂げる reach 到達する

12 問 ⑴ の中には次の~4の文が入る 本文の流れに合うように正しく並べかえたとき, その組み合わせとして最も適切なものは下の中ではどれか However, what will happen if it does something bad for the environment? Companies need to think about a lot of things these days. Many people who know this will not buy their products. 4 Some of the examples are protecting the environment or contributing to the society. ア 4 イ 4 ウ 4 エ 4 問 ⑵ All of us agreed with her. とあるが, このときボランティア部の全員が考え ている内容として最も適切なものは次の中ではどれか ア We will be able to work together for a project because people in our town help each other. イ People in our town will be able to start to work together after they know each other well. ウ We need something people in our town can do together to make our community better. エ People always have to live or work in the same town when they want to know each other. 問 ⑶ This とあるが, その内容を次のように書き表すとすれば, の 中にどのような英語を入れたらよいか 本文中の連続する 9 語で書きなさい There were actually not many people, though our volunteer club members.

13 問 4 ⑷ taking part in the the project 4 people increased 6 number 7 of. と あるが, 本文の流れに合うように, 内の単語 語句 を正しく並べかえたとき, 番目と 番目と 7 番目にくるものの組み合わせと して最も適切なものは次のア ~ カの中ではどれか なお, 文頭にくる語も小文 字になっています 番目 番目 7 番目 ア 6 4 イ 7 ウ 7 エ 7 6 オ 7 6 カ 6 問 ⑸ More than that, we were proud of ourselves. とあるが, ボランティア部の部員 がそう感じた理由として最も適切なものは次の中ではどれか ア We had a one-year anniversary lunch party in the apple-orchard after the harvest. イ We started our apple tree project, and we were able to improve our community. ウ A magazine wrote something about our project and named it Apple Tree Project Team. エ A magazine said that an apple tree project would be more popular in the near future. 問 6 本文の流れに合うように, 次の 文を入れるとき, 最も適切な場所は下の中 ではどれか The apple-orchard became a symbol of our town. アイウエ ⑹-a ⑹-b ⑹-c ⑹-d

14 問 7 本文中の ⑺ にどのような英語を入れるのがよいか 本文中の連続 する 語で書きなさい 問 本文の内容と合っているものを, 次のア ~ カの中から一つ選びなさい ア Mr. Kitano was already interested in the activities of the volunteer club before a local newspaper wrote about them. イ At first, the volunteer club members had some different ideas, and then Mr. Kitano gave them the idea of planting apple trees. ウ Many farmers used to move to Emi s town and grow a lot of apple trees, so they were able to revive the town with apples. エ Emi thought it was necessary for the local people to study how to grow apple trees before planting them in the apple-orchard. オ Emi became interested in agriculture after graduating from university, and started working at a company she already knew. カ When we want to bring some change to a society, even one person or a few people can start a project or an activity. 問 9 この文章を読んで, 下の英文の指示にこたえる英文を 0 語以上 40 語程度の英語で書きなさい 英文は二つ以上になってもかまいません ただし, 本文中の活動例を用いてはいけません., などは, 語数に含めません これらの符号は, 解答用紙の下線部と下線部の間に入れなさい Imagine you are a leader of a CSR project team at a company. You need to do something to contribute to a community or a society with people living there. What would you like to do? Write one of your ideas. Explain what you want to do, and why you want to do it. 4