How to do the two square questions in the elementary school Olympiad math
There were many ways to solve the question of two squares in the elementary school Mathematical Olympiad. The following were some common situations: ** 1. Area related ** 1. ** Area difference problem ** - If you know the difference in the perimeter of two squares, you can first find the difference in the length of the sides. For example, the difference between the circumference of two squares is 32cm. Since the circumference of a square = 4 x the length of a side, the difference in the length of a side is 32 × 4 = 8cm. If the area difference was known, it could be solved by making an auxiliary line. For example, the shadow part (the area difference part) was cut into several parts, and the area of the special figure (such as a small square) constructed from it was used to calculate the area of the rectangular shape, and then other unknown quantities such as the length of the side were calculated. 2. ** Overlapping Area Problem ** - When two squares overlapped, the area of the shadow (usually the non-overlapping part) needed to be calculated according to the known conditions (such as the length of the side, the length of the line segment of the overlapping part, etc.) through the combination and decomposition of the figures. He might use the area formula of a triangle, a echelon, and other shapes, as well as the idea of equal-area transformation to convert the area of an irregular shape into the area of a regular shape for calculation. ** 2. Edge length related ** 1. ** Proportional relationship of side length ** - If the proportional relationship between the sides of the two squares and other related conditions (such as the sum of the area, the sum of the perimeter, etc.) were given, one could set the side of one of the squares as an unknown number and solve the equation according to the conditions. For example, let the side length of a small square be x, and the side length of a large square be kx (k is a known proportional coefficient). Then, according to the perimeter sum or area sum conditions, the equation is listed to solve the side length. 2. ** The relationship between length of side and line segment ** - When two squares have a specific position relationship and the length of some line segments is given (such as the line segment connecting the two square vertexes, the distance between the two squares, etc.), the Pythagorean theorem or the similarity of geometric figures can be used to establish the relationship between the length of the line and these line segments, thereby solving the length of the line or other related quantities. ** 3. Combination Diagram ** 1. ** Construct a special pattern ** - For example, when calculating the area of the shadow part in the combination of two squares, one could construct a echelon by connecting the diagonal lines, and use the properties of the echelon (such as the equal area of the wings, that is, the area of the two non-adjacent triangle that is divided into four by the diagonal of the echelon is equal) to convert and calculate the area. 2. ** Relationship between the whole and the parts ** - Take the graph composed of two squares as a whole, analyze the relationship between the various parts (such as squares, triangle, echelon, etc.), and calculate the unknown variables such as the area and side length of the whole or part according to the known conditions. Read more exciting novels for free
Primary school Olympiad math questions vertical style complete book
The following are some examples of the types and solutions of the primary school Mathematical Olympiad vertical questions: ** 1. The vertical addition puzzle ** 1. ** When the same number is added up, the same number will still be obtained ** - For example, if a three-digit number plus a three-digit number is equal to a three-digit number, if a triangle plus a triangle is equal to a triangle, it is only satisfied when the triangle is 0, because 0 + 0=0. Then, according to the numerical relationship between the 10th and 100th digits, the circle plus the square on the 10th digit was equal to 0 (in fact, 10 to 100th digit was 1), and the square plus the square plus the carry on the 100th digit was equal to the circle. By transforming the vertical form into the horizontal form, the values of the square and the circle were solved by equivalent substitution. 2. ** Normal addition, find the relationship between numbers vertically ** - For example, when calculating the addition of two numbers, one had to consider the rules of digit alignment and addition, starting from the single digit. If the addition of the single digit had a carry, it had to be carried to the tenth digit, and when the tenth digit was added, the number of the single digit carry had to be added. For example, if two two-digit numbers were added together, the addition of the one-digit numbers was equal to 11, and the addition of the ten-digit numbers plus the one-digit carry was equal to 13. According to this relationship, the one-digit and ten-digit numbers of the two numbers could be obtained respectively. ** 2. Multiplication vertical riddle (Take a five-digit number multiplied by a one-digit number as an example)** 1. ** Confirm the range of key numbers ** - First, determine the possible value of one of the multiplying factors (one digit). For example, in a five-digit number multiplied by a one-digit number equals a five-digit number, the value of the one-digit multiplication factor is determined according to the highest digit without carry, the single-digit calculation condition, the highest digit calculation condition, and so on. For example, this one-digit number could not be 0 or 1. If this one-digit number was 9, there might be conflicts when deducing other digits according to the calculation rules (such as obtaining the same number does not meet the requirements of each Chinese character representing different numbers, etc.). The value of this one-digit number was determined by gradual elimination. 2. ** Derives other numbers based on the determined number ** - After determining this one-digit number, the numbers on the other digits were derived according to the multiplication calculation rules. For example, according to the one digit of the product of the one digit numbers and the carry situation to determine the number on the other five-digit number, then according to the calculation on the ten digit (including the one digit carry) to determine the number on the ten digit, and so on to calculate the number of other digits. These vertical questions were mainly solved by analyzing the operational relationship of the numbers, the carry situation, and the range of the numbers. They were solved by mathematical methods such as elimination and equivalent substitution. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>
Elementary school sixth grade Olympiad math thinking training textbook recommendation
The following are some recommended textbooks suitable for the sixth grade of primary school: 1. ** Gaosi Mathematics textbook + Gaosi Mathematics Competition Guide **: This is a very famous Mathematical Olympiad teaching aid. Many areas (such as Beijing) use it as an entry-level teaching aid for Mathematical Olympiad competitions. It is recommended that children read it at least two to three times. 2. [Learning and Thinking (Big White Version): The difficulty of the questions is high. Many teachers who are not very experienced may not be able to solve them.] If one could complete the questions in the Gaosi Mathematics textbook and the introductory textbook well, they could try to do this book. However, if they did not even win the third prize in the previous Mathematical Olympiad competition, it might be more difficult to do it. 3. ** Mathematical Olympiad 6th grade standard course + exercise selection + ability test three-in-one (by Chen Tuo)**: This is a course specially written for the 6th grade Mathematical Olympiad. 4. **<<Synchronization of Mathematical Olympiad Excellence>> Grade 6 (suitable for Beijing Normal University textbooks)**: It is suitable for students who use Beijing Normal University textbooks to carry out Mathematical Olympiad Excellence. 5. ** Xiong Bin's "Mathematical Olympiad Guide": It has a different style from the Gaosi Mathematics textbook + Guide, but the overall difficulty is the same. You can choose one to learn. 6. ** True questions of previous Mathematical Olympiad competitions (such as Liu Jia's imo Mathematical Olympiad yearbook)**: This is the material closest to the competition itself, but due to the difficulty, it is recommended to use it after a certain foundation. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>
Elementary school first grade Olympiad math arrangement graph problem topic
The following are some of the questions for the first grade of elementary school: 1. In a set of diagrams, observe the pattern of changes in the diagrams and find "?" What kind of figure should be filled in? 2. For example, if the figure rotated clockwise or counterclockwise, or if there was a pattern in the number and color of the figure, it was required to draw the following figure according to the pattern of the previous figure. 3. Observing the pattern of arrangement and combination of the figures, such as looking horizontally, vertically, diagonally, etc., to find out the pattern of arrangement of the figures and make inferences or choose the correct figure. 4. Give a set of diagrams that are arranged and combined according to the rules. You are required to fill in the missing diagrams correctly. For example, the pattern of the pattern could be the shape of the pattern, the number of alternating changes, and so on. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>
The shape of the floor tiles, elementary school math questions
The following are some examples of elementary math problems related to the shape of floor tiles: ** 1. Calculating the floor area ** 1. ** Square tiles ** - If the side length of a square tile is known to be a centimeter, its area can be found according to the square area formula. For example, a square floor tile with a side length of 5 centimeters would have an area of 5×5 = 25 square centimeters. 2. ** Rectangle tiles ** - If the length of the rectangular floor tile is (m) cm and the width is (n) cm, according to the rectangular area formula (S=m×n)(square centimeters). For example, a rectangular floor tile with a length of 8 centimeters and a width of 3 centimeters would have an area of 8×3 = 24 square centimeters. ** 2. Tile Splicing Problem ** 1. ** Square tiles are used to cover the rectangular floor ** - It is known that the length of a rectangular floor is [A] cm, the width is [B] cm, and the side of a square floor tile is [a] cm. - First, calculate the length of the long side of the rectangular floor: <A> a>(take the whole number), and the length of the wide side: <B> a>(take the whole number). - Then the number of tiles needed to cover this rectangular floor was " For example, a rectangular floor was 120cm long and 80cm wide, and a square floor tile was 20cm long. The long side required [120 × 20 = 6] tiles, and the wide side required [80 × 20 = 4] tiles. In total,[6×4 = 24] tiles were required. 2. ** Different shapes of floor tiles are combined into a certain pattern ** - For example, using a number of isosceles-right-angled triangular tiles to form a square. Since the two sides of an isosceles-right triangle are equal, if the sides are <b>, then its area is <b>=<b>. - Using such an isosceles-right triangle to form a square with a side length of <anno data-annotation-id ="0000000 - 4445 - 4550-a110-a1100111000">(c) cm </anno> and an area of <anno data-annotation-id ="00a77a-b660 - 4550-a100-a10000000000">(c^{2}) cm </anno>. Then the number of isosceles-right-triangle tiles required is [2c^{2} Mum b^{2}](Assuming it can be divided evenly). ** 3. Problems related to the perimeter of the tiles (rare but possible)** 1. ** Square tiles ** - It is known that the side length of the square floor tile is (d) cm, according to the square perimeter formula (C = 4×d) cm. For example, a square tile with a side length of 6 cm would have a circumference of 4×6 = 24 cm. 2. ** Rectangle tiles ** - If the length of the rectangular floor tile is (e) cm and the width is (f) cm, according to the formula of the rectangular perimeter,(C=(e + f)×2) cm. For example, a rectangular floor tile with a length of 10 cm and a width of 4 cm would have a circumference of [(10 + 4)×2 = 28] cm. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>
The difference between primary school Olympiad math innovative thinking and Olympiad math tutorial
Mathematical Olympiad courses usually focused on the systematic construction of the Mathematical Olympiad knowledge system and the teaching of solving skills. They used classic Mathematical Olympiad questions as a carrier to help students understand Mathematical Olympiad knowledge in depth and improve their ability to solve problems. The content mainly revolved around mathematical knowledge, and the difficulty exceeded the level of compulsory education. It focused more on the logical thinking exercise in mathematical solving. The primary school's Mathematical Olympiad innovative thinking emphasized the cultivation of innovative thinking. It focused on developing new ways of thinking based on the knowledge of the primary school's Mathematical Olympiad. It was not only limited to conventional solution ideas, but also might involve the innovative application of traditional Mathematical Olympiad knowledge and methods, as well as combining new teaching concepts and teaching methods to inspire students to think about Mathematical Olympiad problems from different angles. It had a higher requirement for the expansion of students 'thinking. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>
Elementary school grade five or six Olympiad math overlapping graph topic book
The following are some of the primary five or six grade Olympiad math overlapping graphics questions: 1. Two squares with a side length of 6, where the apex of one square is at the center point O of the other square, find the area of the overlapping part? (The solution to the problem: cross the O point to draw the vertical line of the side length of the square, and use the congruence of the triangle to prove that the area of the overlapping part after moving is equal to the area of the square. The answer is 6×6× 4 = 9). 2. As shown in the picture, between two parallel lines d and c that are 10 centimeters apart, there is a square A and a rectangular B. Square A is moving to the right along the straight line d at a speed of 2 centimeters per second. Find the time when the two figures A and B overlap? (Solution: Think of it as a combination of the area problem and the travel problem. It is analyzed in five stages. The overlapping distance is the width of A + the width of B. The answer is (20 + 8) div2 = 14 seconds.) <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>
Elementary school Olympiad math figure arrangement filling number skill teaching plan
** 1. Teaching objectives ** 1. Let the students understand the concept of the number matrix. Through the practice of arranging the numbers, the students 'observation ability and logical thinking ability will be cultivated. 2. Guide the students to master the basic skills of arranging and filling in numbers, including finding key numbers and discovering the pattern of numbers. 3. To stimulate the students 'interest in the relationship between figures and numbers in Mathematical Olympiad, and to improve the students' confidence in solving such problems. ** 2. Important and Difficult Points in Teaching ** 1. ** Teaching Focus ** - Master the method of finding rules from the sum, difference, product, quotient relationship of adjacent numbers and the relationship between interval numbers. - Learn to analyze the arrangement of numbers in the array and find the key numbers. 2. ** Teaching Difficulties ** - How to accurately discover the hidden patterns between the numbers in a more complicated array diagram? - Using various techniques to solve different types of problems. ** 3. Teaching Method ** Teaching method, discussion method, and practice method were combined. ** 4. Teaching process ** 1. ** import (5 minutes)** - It was about the story of Jingjing and Yingying in the Snow Elf Kingdom in Math Paradise. It led to the problem of filling the seven numbers 1 - 7 on the seven petals of the snowflake so that the sum of the numbers on every three petals on the same line was equal. To stimulate the students 'interest in the game, let the students have a preliminary understanding of the number array. 2. ** Knowledge explanation (15 minutes)** - ** Basic Skill 1: Analyzing the relationship between adjacent numbers ** - Take the sequence as an example, if you fill in the numbers according to the rules: 2, 1, 4, 1, 6, 1,( ),( ). He guided the students to observe and found that the odd terms were 2, 4, and 6, which was the law of increasing by 2 in turn, while the even terms were all 1. Therefore, 8 and 1 should be written in the parenthesis. - Another example is 3, 2, 9, 2, 27, 2,( ),( ). Here, the odd numbers are 3, 9, and 27, and the latter number is three times the previous number; the even numbers are all 2. Therefore, 81 and 2 should be written in the parenthesis. - ** Basic Skill 2: Analyzing the relationship between numbers ** - Give a sequence of numbers such as 18, 3, 15, 4, 12, 5,( ),( ). The students were guided to split the sequence into odd terms 18, 15, and 12, which was the rule of decreasing 3 in turn, and even terms 3, 4, and 5, which was the rule of increasing 1 in turn. Therefore, 9 and 6 should be written in the parenthesis. - For 1,15,3,13,5,11,( ),( ), the odd terms 1,3,5 are the law of adding 2 in turn; the even terms 15,13,11 are the law of decreasing 2 in turn. Therefore, 7 and 9 should be written in the parenthesis. - ** The key number in the array map ** - Using a simple triangular array as an example, the numbers on the three corners had a certain relationship with the number in the middle. For example, the number in the middle was equal to the sum of the numbers on the three corners. Starting from a number array with a complete set of known numbers, the students were guided to analyze the rules and find the key numbers (the numbers on the corners or the middle numbers) to determine the numbers in other positions. 3. ** Practice and consolidate (20 minutes)** - He gave some practice questions about the number matrix and the number sequence, such as: - Count the number of triangulations in the following picture (It involves the relationship between the number of numbers and the number of triangulations in the triangular array). - Find the pattern and fill in the numbers: 4, 7, 8, 4, 6, 13, 4, 5, 18,( ),( ),( ). - There was a numerical array diagram that showed some numbers. Students could find the pattern according to the skills they had learned and fill in other numbers. - Students were allowed to complete the exercises independently. Teachers would patrol and guide the students, and if they found any problems, they would correct them in time. 4. ** Class summary (5 minutes)** - Guide the students to review what they have learned in this lesson, including the relationship between adjacent numbers, the method of finding the relationship between numbers, and the analysis of the key numbers in the number matrix. - He emphasized that when solving the problem of arranging numbers, he had to observe carefully, think from many aspects, and try different methods to find the arrangement law of numbers. ** 5. Extension of Teaching ** He assigned homework to the students to complete some more complicated questions such as filling in numbers on a number matrix and finding the law of a number sequence to further consolidate the knowledge they had learned. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>
Elementary school fourth-grade interesting math questions and answers
The following are some of the answers to some of the interesting math questions in the fourth grade: ** 1. Number Combination ** 1. [Question: How to make the number 8 equal to 1000?] - ** Answer **: 8 + 8+8+88 + 888 = 1000. - ** Explanation **: By adding different combinations of the number 8, a number close to 1000 can be obtained. For example, 888 is close to 1000, and adding other combinations of the number 8 to get 1000. 2. [Question: Use three 3s to form the largest number?] - [Answer: 3 to the power of 33] - ** Explanation **: 3 to the power of 33 is much larger than 333, because the exponential operation will make the number grow very fast. When the base is 3 and the index is 33, this number is the largest number that can be formed by three 3s. 3. [Question: What is the largest number that can be formed by 1, 2, and 3?] - ** Answer **: 3 to the power of 21. - [Description: If it is formed according to the convention, 321 is not the largest.] Because of the nature of exponential calculation, 3 to the power of 21 was much larger than other combinations. ** 2. Points and Number of People ** 1. [Question: 100 steamed buns, 100 people eating, 1 adult eating 3, 3 children eating 1, how many adults and how many children can finish it?] - [Answer: 25 adults and 75 children.] - ** Explanation **: Suppose there are x adults and y children. You can get the equation set of <x + y=100>(the total number of people is 100) and <3x+<frac{1}{3}y = 100>(the total number of buns is 100). Transform the first equation to {y = 100 - x}, substitute it into the second equation {3x+{frac{1}{3}(100 - x)=100}, and solve {x = 25}, then {y = 75}. 2. ** Question **: There are 63 notes in total for 2 yuan and 5 yuan each, totaling 171 yuan. How many notes are there for each of the two kinds of yuan? - ** Answer **: 48 for 2 RMB and 15 for 5 RMB. - ** Explanation **: Suppose there are x pieces for 2 RMB and y pieces for 5 RMB. The equations are x + y=63 and 2x +5y =171. From the first equation, we get x = 63 - y, and substitute it into the second equation, which is x = 48. ** 3. Itinerary and Time ** 1. ** Title **: A well is seven meters deep. A snail climbs up from the bottom of the well. It climbs three meters during the day and falls two meters at night. Ask a snail how many days it takes to climb out of a well? - [Answer: 5 days.] - ** Explanation **: The snail actually climbs 3 - 2 = 1 m every day. However, on the last day, after climbing out of the well during the day, they would not fall anymore. Therefore, in the first few days, they had climbed a total of 7 - 3 = 4 meters, which required 4 days. Including the last day, it was a total of 5 days. 2. [Question: If the clock shows that it is 18 o'clock sharp, what time will it be after the minute hand has rotated 1991 times?] - ** Answer **: The minute hand rotating once is 1 hour, 1991/12 = 165…11 (12-hour cycle), 18+11 - 24 = 5 points. - ** Explanation **: First, look at how many 12-hour cycles 1991 contains. The remainder is the extra hours added, plus the initial 18 points. If it exceeds 24 points, then subtract 24 to get the final time. ** 4. Trading Profits ** 1. [Title: Someone bought a toy for 19 yuan and sold it for 20 yuan.] He felt that it was not worth it, so he bought it for 21 yuan and sold it for 22 yuan. How much did it earn? - ** Answer **: 2 yuan. - ** Explanation **: The first transaction earned "(20 - 19 = 1") yuan, the second transaction earned "(22 - 21 = 1") yuan, the total earned "(1+1 = 2") yuan. ** 5. Logic-related reasoning ** 1. [Question: Xiao Qiang's math score was only 6 points away from passing, and so was Xiao Ming's. However, Xiao Ming's and Xiao Qiang's scores were different. Why?] - [Answer: 54 points and 0 points.] - ** Explanation **: If the full score is 60 points, 54 points will be 6 points away from passing, and 0 points will also be 6 points away from passing. The requirement is that the two people are 6 points away from passing but have different scores. 2. [Question: There are three empty rooms. One room has three lights, and the other room has three switches. Each switch can only turn on one light. If you can only enter each room once, how do you know which switch controls which light?] - Answer: Enter a room with a switch, turn on one switch, turn it off after 5 minutes, turn on the other switch, and then enter a room with a light. The light that was on was controlled by the switch that was turned on the second time. He touched the other two lights that were not on. The one that was hot was controlled by the switch that was turned on the first time, and the remaining one was controlled by the switch that had not been turned on. - ** Explanation **: Use the characteristics of the light bulb to judge whether the switch that is turned on will make the light on or heat up. Use different operations to distinguish the lights controlled by different switches. 3. [Title: Two chess friends played a total of nine games in a day. They won the same number of times without a draw. What's going on?] - [Answer: Not all nine games were played by the two of them.] - [Description: If the two of them played all nine games, the number of times they won would not be the same without a draw. Therefore, there must be a situation where they played against someone else.] <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>
Elementary school second grade math questions, line segments, angles
Here are some ways to count lines and angles: ** 1. Counting Line Segments ** 1. ** Basic Concepts ** - A line segment was made up of two straight lines with two ends. 2. ** Method ** - ** Shooting Method (Counting in order with the end point as the starting point)**: Count the line segments with the leftmost end point as the starting point, then count the line segments with the left end point as the starting point, and so on. Finally, add all the numbers. For example, if there were four end points on a line, there would be four line segments starting from the leftmost end point, three line segments starting from the second end point on the left, two line segments starting from the third end point on the left, and one line segment starting from the fourth end point on the left, then there would be a total of 4+3 + 2+1 = 10 line segments. - ** According to the basic line segment calculation method **: First determine the number of basic line segments (line segments between two adjacent ends), and then calculate the number of line segments composed of basic line segments. For example, there are four basic line segments in the graph, three line segments composed of two basic line segments, two line segments composed of three basic line segments, and one line segment composed of four basic line segments. Therefore, there are a total of 4+3+2 + 1=10 line segments. - ** Numbering Method **: Starting from 0 on the left, the number of the end points will be marked. When it reaches the last end point on the right, it will be the total number of end points minus 1. When a line has five ends, there are four lines from the leftmost point, which are 3, 2, 1, and 0. Then, add these numbers to get the total number of line segments. The rule is that the total number of line segments =(the number of ends of the line- 1)+ each number that successively decreases by 1 + 0. 3. ** Pattern summary ** - After 2 points, a line segment can be drawn;3 points: 2+1 = 3 lines;4 points: 3+2+1 = 6 lines;5 points: 4+3+2+1 = 10 lines;n points: (n - 1)+...+3 + 2 +1=n(n - 1)/2 lines (This rule is for reference, the second grade exam generally does not exceed 6 points). ** Two, several dimes ** 1. ** Basic Concepts ** - An angle was a geometric figure formed by two rays with a common end point. 2. ** Method ** - Angles could be counted using a method similar to counting line segments. Each side of the angle was regarded as the end point of the line segment, and then it could be added directly according to the standard number method of counting line segments. For example, if a geometric figure had three line segments forming an angle, then the number of angles would be counted down from the number one less than three, that is, 2+1 = 3 angles; if it was four line segments forming an angle, the number of angles would be counted down from the number one less than four, that is, 3+2+1 = 6 angles. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>
30 compulsory questions for the primary school Mathematical Olympiad
The following are some of the common types of questions for the primary school Mathematical Olympiad exam: return to one problem, itinerary problem, cow eating grass problem, etc. However, because the reference materials did not completely list the 30 compulsory questions, the contents of all 30 compulsory questions could not be provided. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>