(3 -> 1 point for each figure)
Cut each of these figures into two parts, making only one straight cut, and fold the resulting parts into squares from the resulting parts in each case.
Fill in the empty cells of each square with letters from those already in it so that the letters are not repeated in any of the horizontal, vertical or diagonal lines of the square.
12.(5 -> 3 points for each point)
A) The first number is a three-digit number, the second number is the sum of its digits, the third number is the sum of the digits of the second number. These three numbers can be written like this: Restore the record if the same figures correspond to the same numbers.
B) The first number is some three-digit number, the second number is the product of its digits, the third number is the product of the digits of the second number. These three numbers can be written like this: . Restore the entry if the same figures correspond to the same numbers.
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Place four action signs and parentheses between the numbers in different ways to obtain correct equalities.
5 5 5 5 = 6
5 5 5 5 = 7
5 5 5 5 = 30
Place arithmetic signs and parentheses between the numbers so that the result is 1. Two adjacent numbers can be considered a two-digit number.
1 2 3 =1
1 2 3 4 = 1
1 2 3 4 5 =1
1 2 3 4 5 6 =1
1 2 3 4 5 6 7 =1
1 2 3 4 5 6 7 8 =1
1 2 3 4 5 6 7 8 9 =1
Place four action signs and brackets between the numbers in different ways so that the result of the calculation is 100.
1 2 3 4 5 6 7 8 9 = 100
1 2 3 4 5 6 7 8 9 = 100
1 2 3 4 5 6 7 8 9 = 100
1 2 3 4 5 6 7 8 9 = 100
Slides 5-6
Decipher the recordings
Restore the recording. Identical figures represent identical numbers.
How to move one digit in this equality to get the correct equality?
Divide the clock dial into 2 parts with a straight line so that the sum of the numbers on both parts is the same.
(Hint: Add all numbers, divide the sum by 2)
Connect the vertices of the square with three lines without lifting your pencil.
(Hint: these lines should be outside the square)
The kid drew 3 straight lines. Marked 3 dots on each of them. In total, the Kid marked 6 points. Draw how he did it.
(Hint: the lines intersect. Some points are at the intersection of the lines)
How many squares are there in front of you? (14)
Remove 3 sticks so that there are 4 squares.
There's a scoop in front of you. Move 2 sticks so that the fly is in the scoop.
Slides 14-15
Help Dunno draw 4 lines so that they intersect: a) at three points; b) at five points. (Different ways)
Bibliography:
- School Olympiads. Elementary School. 2-4 grades/N.G. Belitskaya, Org A.O. - 5th ed. – M.: Iris-press, 2009.
- I'm going to a lesson in elementary school: Extracurricular activities: Olympiads and intellectual games: A book for teachers. – M.: Publishing house “First of September”, 2000.
- Mathematics. Development of logical thinking. Grades 1-4: a set of exercises and tasks / comp. T.A. Melnikova and others - Volgograd: Teacher, 2009.
- Extracurricular work in mathematics in elementary school. Manual for teachers. M., “Enlightenment”, 1975.
- Assignment for the final round of the First Republican Intellectual Marathon for 5th grade students, held in Kazan (Slide 12).
Goals and objectives 1To consolidate the features of Roman numbering. Test your mental arithmetic skills. Isolation of the main feature. 1Reinforce the features of Roman numbering. Test your mental arithmetic skills. Isolation of the main feature. 2Develop thinking, memory, logical thinking, mathematical speech. 2Develop thinking, memory, logical thinking, mathematical speech. Cultivate interest in the subject. Cultivate interest in the subject.
Content. 1.Goals and objectives.Goals and objectives. 2.Our mottos.Our mottos. 3.Warm up.Warm up. 4.Who is the odd one out?Who is the odd one out? 5. Cross out the extra word. Cross out the extra word. 6. Recess. Recess. 7.Guess the word.Guess the word. 8. Competition “Rearrangements.” Competition “Rearrangements.” 9.Read.Read. 10.Geometric figure.Geometric figure. 11.Restore the recording.Restore the recording. 12. Draw straight lines. Draw straight lines. 13.Who is more?Who is more? 14.We are joking.We are joking.
Restore the entry Identical figures represent identical numbers
We're kidding. 1. The hare pulled out eight carrots and ate all but five. How many carrots are left? 2. Three horses ran 30 km. How many kilometers did each horse run? 3. Two fathers and two sons ate three oranges. How many oranges did each of them eat?
“Land of Mathematics” - Find the missing boats. Map of the country "MATHEMATICS". Create a task. 3 + 2 = 5. Travel to the country “Mathematics”. Find the neighbors of the number. That more? Find the correct answer.
“Mathematics Questions” - How many grandchildren does grandma have? The apples in the garden are ripe. Do the math for yourself. A peacock was walking in the garden, and another one came up. The boy and girl had the same number of nuts. How many more nuts does the girl have than the boy? Sveta left for camp on Saturday. Two peacocks behind the bushes. How many days later did Vova return?
“London, Paris, New York” - Selecting a mode of transport. Destination: New York. It is not recommended to take large items on board. London is the capital of England. London Attractions. Paris was founded in the 3rd century BC. There are more than 12 million people in Paris. Calculation of distance between cities. Transfer point: Paris. On the map 1cm On the ground x cm Scale 1:90,000,000.
“Journey to the country of “Mathematics”” - Questions for the “Square” team. Square. This results in a lower grade. Mathematics. Drawings for the Triangle team. Questions for the Triangle team. Nikolai Ivanovich Lobachevsky. Sniper. Solution of the equation. Cryptographer. Poem. Mathematics is the queen of all sciences. Captains competition. At the shooting bow. Warm up. Drawings for the “Square” team.
"Mathematical Journey" - Orange. Read the numbers. Physical education minute. The school year began, the desire to teach and learn coincided. Ingenuity will help in any matter. Add action signs if parentheses are needed. The first domestic textbook on mathematics. Mathematical journey. Historical bay. Checking equipment. Mathematics is the most ancient of sciences.
“Alice in the Land of Mathematics” - Only the new house caused a quarrel between the friends. Alice's workshop. Book publication. The book consists of three chapters. For students. Chapter 3. Alice's "Math Ball". Methodological training of teachers. Creation of a theoretical model. Preparation of illustrative material. Approbation of the methodology. "Math Ball" by Alice.
There are a total of 17 presentations in the topic
Here we will meet problems involving arithmetic operations on natural numbers, where some of the digits of the numbers are known, but most are not. We will denote unknown numbers with asterisks. You need to find all the numbers indicated by asterisks; if there are several answers, then you need to find them all.
It is interesting to see how in a problem where sometimes two or three, or even one, digits are known, but there are many unknown digits, it is possible to find these digits - to get everything out of almost nothing.
The problems in this topic assume that the first digit of each number is non-zero.
Restore record:
First, let's find the second digit of the divisor. Since it, when multiplied by 7, gives a number ending in 8, then this figure is equal to 4.
What is the first digit of the divisor? Obviously, 1 or 2. If the first digit of the divisor is 1, then 14 when multiplied by 7 gives a two-digit number 98, but should give a three-digit number. This means that this case is impossible.
Let the first digit of the divisor be 2. Find the first digit of the quotient. It is equal to 1 because 24 when multiplied by this figure gives the number 2*. Finally, the dividend can be easily found by multiplying the divisor of 24 by the quotient of 17.
Example 2.
Find the unknown numbers in the entry:
The first digit of the sum can only be equal to 1. Then the first digit of the second addend is 9. Hence, the first digit of the second factor is 5, and therefore the second addend is 95. Then the first digit of the first addend is 5. Therefore, the second digit of the second factor is 3 .
Answer: 19 53 =1007.
1. Recover records:
a) 97 11=1067 b) 23 34=782 c) 58 91=5278 d) 19 59=1121
2. Restore the recording:
120 98=11760 or 115 98=11270
3. Restore the recording:
a) 124 97=12028 b) 19 53=1007 c) 505 101=51005
4. Recreate the example for multiplying natural numbers if it is known that the sum of the digits of both factors is the same.
5. Is it possible to place any ten numbers in the circles of a given figure so that the sum of the numbers at the vertices of any black triangle is equal to 1996, and the sum of the numbers at the vertices of any white triangle is equal to 1997?
6. Recover records:
3*2 **3
*2*5 **3
a) 415 382=158530 b) 113 133=15029
7. Restore record: *3 3*=3**
8. Recover recording**
91 11=1001 or 13 77=1001
9. Restore record 91 **=***
10. Restore records: a) ** =1 b) *** 9=***
a) 10 1-9=1 b) 101 9=909, 111 9=999
11. How many solutions does the problem *** 9=*** have?
12. An error was made in the multiplication example. Where can you see this?
The second digit of the second multiplier is exactly 9, but its first digit must be greater than 9, and this is impossible
13. Recover recording
14. What is the smallest natural number that the number 7 must be multiplied by in order to obtain a number written as nines only?
15. What is the smallest natural number that must be multiplied by 12345679 in order to obtain a number consisting of only fives.