All-Russian Olympiad schoolchildren in mathematics. School stage.
Grade 5
1 (7 points) We added the sum of its digits to the number and got 2017 Give an example of such a number.
Examples: 2012, 1994 Other numbers do not fit.
Criteria. Any of these numbers are given: 7 points.
Any other number is given: 0 points.
2 (7 points ) The girl replaced each letter in her name with her number in the Russian alphabet. It turned out the number 2011533 What is her name?
Answer: Tanya.
There may be other sequences of letters, but only one of them is a name.
Criteria. Received the name Tanya: 7 points.
Any other sequence of letters received: 0 points.
3 (7 points) The seller bought a batch of pens and sold them. At the same time, some buyers bought one pen for 10 rubles, and some bought 3 pens for 20 rubles. It turned out that the seller received the same profit from each purchase. Find the price the seller bought the pens for.
Answer: 5 rubles.
Decision. Let the purchase price of the handle x. Then the profit for one handle is 10 - x, for 3 handles 20 - 3x. Solving the equation 10 - x \u003d 20 - 3x, we get x \u003d 5
It is not substantiated that the purchase price of the pen should be 5 rubles, but it is verified that in this case the condition is met: 4 points. Only the correct answer without any explanation: 2 points.
4 (7 points) The student spider pulled a web between 11 points so that its webs would not intersect anywhere, and at the end returned to the starting point. The spider-teacher praised him, and only noticed that the real masters observe the same conditions, but they stretch the “correct” web, in which no segments lie on one straight line. Help the spider connect all 11 points in the picture with the "correct" cobweb.
Criteria. Any true example: 7 points.
An example in which some segments lie on one straight line, but no adjacent segments lie on one straight line: 4 points. Example with adjacent line segments: 0 points.
5 (7 points) The square window opening is formed by two rectangular frames. Inside each of them was written a number equal to the perimeter of the frame. Write down the side of the square of the entire window opening and explain how you got it.
Answer: 5
Decision. Let the side of the square be a and the width of the left rectangle be b. Then the width of the right rectangle is a - b. The left rectangle gives the ratio 2a + 2b \u003d 14, and the right rectangle gives the ratio 2a + 2a − 2b \u003d 16 Adding these two ratios with each other, we get 6a \u003d 30, whence a \u003d 5
Criteria. Correct solution in any way: 7 points.
Logically correct solution, but due to an arithmetic error, the answer is incorrect: 3 points. An example is selected where the rectangles really have the required perimeter, but it is not explained how the lengths of their sides are obtained: 2 points. Only the correct answer without explanation: 1 point.
SCHOOL STAGE. 4TH GRADE
№1. (7 points)Arrange the brackets so that you get the correct equality:
90 − 72: 6 + 3 = 82 .
№2. (7 points)There are equal parts of apples in five boxes. When 60 apples were taken out of each box, after that there were only as many apples left as there were previously in two boxes. How many apples were in each box?
№3. (7 points)The rectangle is divided into squares, inside each square its number is written. It is known that the side of square # 1 is 18 cm, and the side of square # 2 is 3 cm. Find the sides of all the other squares.
№4. (7 points)A gnome with shoes weighs 2 kg more than a gnome without shoes. If you put on a scale five identical gnomes with shoes and five of the same gnomes without shoes, the scales will show 330 kg. How much does a dwarf weigh in shoes?
№5. (7 points)The apprentice spider stretched a web between 11 points so that its webs did not intersect anywhere, and at the end returned to the starting point. The spider-teacher praised him, and only noticed that the real masters observe the same conditions, but they stretch the “correct” web, in which no segments lie on one straight line. Help the spider connect all 11 points in the picture with the "correct" cobweb.
Municipal budgetary educational institution
average comprehensive school No. 1 p. Anuchino
"Spider Web"
Samusenko Z.E. -
teacher primary grades
the highest qualification
Ecological circle lesson
Theme : "Spider Web"
goal :
To form an idea that there are no uninteresting, unnecessary animals in nature. To tell about spiders, to captivate children with a small but interesting "world" in which these tiny creatures live. To consolidate the rules of behavior in nature: "Do not cut off the cobweb in the forest, do not kill spiders."
Course of the lesson
Motivation
Teacher:
The bell rang funny
Is everyone ready? Everything is ready?
We, now, do not rest
We are starting to work.
Updating
Conversation
Teacher:
What is nature?
Yes, these are rivers, seas, lakes and deserts, forests
and fields, sun and sky, soil and air, and all living things. And man is also a part of nature. And the smallest insect is also a part of nature.
Teacher:
Why does man need nature?
She feeds a person, dresses, puts on shoes, and provides everything necessary for life. And, perhaps most importantly, nature gives a person joy. Admiring the beauty of nature, a person becomes better and kinder. Nature teaches man wisdom.
Teacher:
The "Book of Nature" received a complaint. I will read it, and you guess who it is from (The teacher reads the letter)
« We are often called ugly and unnecessary. Although we are of great benefit: we eat harmful insects. If our web comes across in the forest, we are to blame. And sometimes people tear our web for fun. And we have to weave again. Please do not destroy our creations. "
Have you guessed who we are talking about? (about the spider).
Student reads a poem
"A wondrous miracle - a spider -
Eight legs and eight arms.
If you need to flee -
Eight legs help out.
Weave a net around a circle -
Eight hands help out.
If you are angry with someone,
Like all enemies are around, -
Hunches back, looks fiercely,
So, I got up on the wrong foot. "
S. Ya. Marshak.
3. Work on the topic
Spider image display
Teacher:
Spiders are really useful. They catch harmful insects in a web that eat our trees, fruits and vegetables. Therefore, in the forest or in nature, never cut off the web of spiders and do not kill them.
Guys, do you want to know where the spider came from? Then listen carefully, I'll tell you about it an old legend.
A long time ago, in a foreign, far from us country called Ancient Greece there lived a girl who was very fond of weaving i.e. weave from fabric threads. This girl's name was Arachne. She knew how to create such beautiful fabrics, weaved such beautiful patterns that she decided to challenge the goddess Athena herself to a competition, to find out which of them would weave a pattern more beautifully.
The patterns that Arachne wove were more beautiful and more elegant than those of the goddess Athena. Then the goddess got angry, got angry with the girl and turned her into a spider that always sits and weaves a web.
In Greek, "Arach" means "Spider". Since then, they began to call all such animals spiders.
- Teacher:
The spider is often considered by people to be unnecessary, useless. But it turns out that this is a very interesting and useful animal.
Spiders are not scary at all and are very useful. After all, they destroy a huge number of harmful insects, especially flies that carry dirt and various diseases.
4 the structure of the spider
- Teacher:
Here, look at the spider I want to show you ...
(spider demo picture)
This spider is called a cross spider. It is named so for the cross-shaped pattern on the back.
A spider is not an insect, but a special, separate species of animals.
The spider's head is connected to the breast. This part of the body is called so cephalothorax.
(Reinforce with individual and choral responses)
Most of the spider's body is called abdomen (Fix)
There are so-called leg tentacles. (Will reinforce with individual and chorus responses) The spider needs them in order to grab food and push it into its mouth. These are not legs.
And the legs of the spider are long and they are all on the breast. Let's all together calculate how many legs the spider has. (Count and fix with choral and individual answers)
Although the spider has so many legs, it does not walk well, and its web helps to move around. The spider will hook the spider web to the twig and crawl up or down along it.
The spider has 8 eyes, so it can see everything around it without turning its head. He will immediately see who can be caught in the web.
Teacher:
Guys, where do you think the spider gets the thread to weave its web?
(Children's answers)
Teacher:
The spider has special tubercles with holes on its abdomen. A liquid is released from them, which immediately becomes solid in air and turns into a thin thread. From this thread the spider weaves its web - a trap for insects.
What does a spider need a thread for?
Some species of spiders weave "nappies" from it for the eggs they lay. And when the spiders hatch, the web becomes a nest.
Sometimes the thread serves as a ladder for descent and ascent. Or by airplane - the wind will pick up the spider's web and carry it to another place.
But the main thing is that the spider weaves a net from the thread - a trap for insects.
The web may seem abandoned. There is no spider in it, but it is not, in fact, it is hiding and waiting for prey to fall into the network. Spiders have a perfect camouflage color. The spider recognizes that someone has got into the net by the trembling of the signal thread, which stretches from the middle of the web to the ambush site. No one can get out of the network, as the threads are smeared with a sticky substance.
FIZMINUTKA
To the musical melody "Song of the Spider"
5. Comparison of spider and insect
(Images of spider and insects shown)
Teacher:
Look closely, think about what they have in common?
How do they differ from each other?
(Children compare and answer. The teacher summarizes their answers)
In distant, hot countries there are large spiders that can bite a person and even kill with their venom. And in our forests and parks live not dangerous, not scary spiders, but on the contrary, very useful ones. Therefore, guys, if you saw a spider in the forest, do not offend him, do not cut off his web. After all, the spider does a useful thing: it destroys insects - pests.
Drawing a spider
The net weaves around the circle
One circle, two circle.
Teacher:
In nature, there is a huge variety of spiders: a spider - a cross, a spider - a tarantula, etc. (the teacher draws the attention of children in the illustrations) They amaze us with their mystery. Notice how cleverly and quickly the spiders weave the web.
The spider in the corner has hung a net
He really likes to hang,
And the net knits tightly.
Spider has eight legs.
Or maybe paws.
Or maybe hands.
But eight is for sure.
- Teacher
Today we will draw a spider on the web
(The teacher prepares sheets of paper with a picture of a cobweb in advance. The task of the children is to draw a spider in the web.)
(Children do the work with music, the teacher provides individual assistance with advice or demonstration)
Teacher:
Guys, look at the pictures (children look at the work and share their impressions). What unusual spiders turned out to be: funny and sad, dexterous and even sleepy spiders. Well done!
Just remember, children, take care of nature. And bugs and spiders! After all, everything in the world is needed!
Reflection
Student reads a poem
"A wondrous miracle - a spider -
Eight legs and eight arms.
If you need to flee -
Eight legs help out.
Weave a net around a circle -
Eight hands help out.
If you are angry with someone,
Like all enemies are around, -
Hunches back, looks fiercely,
So, I got up on the wrong foot. "
S. Ya. Marshak.
- Teacher:
Can't be dispensed with
Without absurd monsters
And even without predators -
Angry and ferocious.
We need everything in the world!
We need everything -
Who makes honey
And who makes the poison.
If we are with someone
Not very friendly
We are still very
We need each other!
And if we have someone
It will seem superfluous
Then this, of course,
It turns out to be a mistake!
The world needs
And it's all
SPIDER
Once a spider weaved a spider web
And hung the spider web on a twig.
- Kwa! - exclaimed the Frog.
- What a network!
Just love, just expensive to watch!
I would like, spider, to make myself a net.
The Stork snapped its long beak:
- Click! yes click!
Fi, yes master!
The cobweb is pure silk!
Everyone knows that I am a fisherman.
You can't do without networks.
The Hedgehog walked quietly with leaves rustling,
And she said: - The web is good!
Spider, spider, give me a piece of nets.
I found mushrooms in the forest
How can I get them home?
The spider praised the Owl-Owl:
- There is good rumor about you everywhere.
Spider, spider, give me a piece of nets.
I need a hammock for sleeping:
My bed is a pine tree.
Spider looked around, and in the corner
only the thread remained on the knot.
He became bugs, screaming different butterflies
Jump through a string!
The cobweb came in handy for good.
Then it's time to end the fairy tale.
Many people confuse spiders with insects. A spider can be easily distinguished from an insect: for this, it is enough to count the number of legs: a spider has 4 pairs of legs, and an insect has 3 pairs. Many people confuse spiders with insects. A spider can be easily distinguished from an insect: for this, it is enough to count the number of legs: a spider has 4 pairs of legs, and an insect has 3 pairs.
The spider's body has two parts. The first part is the cephalothorax, it is made of a durable material, chitin. The second part is the soft abdomen. A tiny tube connects the cephalothorax and abdomen. Eight legs, two jaws, and a pair of pedipalps (sensitive tentacles) are associated with the cephalothorax. Eight eyes are usually located on the cephalothorax. The brain is located in the cephalothorax, and the heart in the anterior upper side of the abdomen.
Spiders have many enemies. Birds catch large numbers of spiders on the ground or directly from their nets. Wasps are also enemies of spiders. Wasps specialize in hunting a specific species of spider and use a captured spider to lay their eggs inside these spiders. The larvae then eat the paralyzed spider. Ants also catch spiders. Praying mantises are great killers, they eat any insects and spiders. Wasp and Spider Mantis
The modern spider uses its jaws (chelicerae) to grab and bite through prey. Most spiders use venom to kill their prey. There are two hollow and very sharp syringe-like structures at the end of the jaws. They are used to puncture the victim's body and inject poison. The poison is produced by special glands.
The lethality of spider venom for humans is very exaggerated. However, there are spiders that are really dangerous to humans. The Black Widow species, the Australian Sydney Tunnel Spider and some of the wandering spiders from the American South are indeed dangerous. There is a substance in the venom of these spiders that violates nervous system and can interfere with heart rate, seizures, tremors, pain, and dizziness. The bite of such a spider can be fatal for children and people with a weak physique.
Task 1. (7 points)
We added the sum of its digits to the number and got 2017. Give an example of such a number.
Examples:2012, 1994. Other numbers don't fit.
Criteria.Any of these numbers are given: 7 points.
Any other number is given: 0 points.
Task 2. (7 points)
The girl replaced each letter in her name with its number in the Russian alphabet. It turned out the number 2011533. What is her name?
Answer:Tanya.
There may be other sequences of letters, but only one of them is a name.
Criteria.Received the name Tanya: 7 points.
Any other sequence of letters received: 0 points.
Task 3. (7 points)
The seller bought a batch of pens and sold them. At the same time, some buyers bought one pen for 10 rubles, and some bought 3 pens for 20 rubles. It turned out that the seller received the same profit from each purchase. Find the price the seller bought the pens for.
Answer:5 rubles.
Decision.Let the purchase price of the handle x... Then the profit per handle is 10 - x, for 3 handles 20 - 3x... Solving equation 10 - x= 20 - 3x, we get x= 5.
Criteria.
It is not substantiated that the purchase price of the pen should be 5 rubles, but it is verified that in this case the condition is met: 4 points.
Only the correct answer without any explanation: 2 points.
Task 4 (7 points)
The apprentice spider stretched a web between 11 points so that its webs did not intersect anywhere, and at the end returned to the starting point. The spider-teacher praised him, and only noticed that the real masters observe the same conditions, but they stretch the “correct” web, in which no segments lie on one straight line. Help the spider connect all 11 points in the picture with the "correct" cobweb.
Decision.One of the possible ways is shown below.
Criteria.Any true example: 7 points.
An example in which some line segments lie on one straight line, but none neighboringthe segments do not lie on one straight line: 4 points.
Example with adjacent line segments: 0 points.
Task 5. (7 points)
The square window opening is formed by two rectangular frames. Inside each of them was written a number equal to the perimeter of the frame. Write down the side of the square of the entire window opening and explain how you got it.
Answer:5.
Decision.Let the side of the square be aand the width of the left rectangle is b... Then the width of the right rectangle is a- b.
The left rectangle gives the ratio 2 a+ 2b\u003d 14, and the right rectangle gives 2 a+2a- 2b\u003d 16. Adding these two ratios with each other, we get 6 a\u003d 30, whence a= 5.
Criteria.Correct solution in any way: 7 points.
Logically correct solution, but due to an arithmetic error, the answer is incorrect: 3 points.
An example is selected where the rectangles really have the required perimeter, but it is not explained how the lengths of their sides are obtained: 2 points.
Only the correct answer without explanation: 1 point.