Elementary school mathematics, train crossing the bridge problem
The train crossing the bridge problem was a classic problem in primary school mathematics. The following are the key points and typical questions of this type of problem.
** 1. Basic Concept Understanding **
1. ** Calculating the distance of the train crossing the bridge **
- When a train crossed the bridge, the distance traveled by the train was the length of the bridge and the length of the train. This was because the train had a certain length, and one could not simply consider the length of the bridge. For example, when the train's head drove onto the bridge, the train only passed the length of the bridge, but the train's tail was still on the bridge. The complete process of crossing the bridge was to leave the bridge at the tail, so the total distance was the length of the bridge plus the length of the train.
2. ** Formula **
- The total length of the bridge car = the speed of the car x the time it took to cross the bridge. This formula was the basic formula for solving the problem of a train crossing a bridge. It could calculate the unknown quantity according to the known conditions.
** 2. Classic Questions and Solution **
1. ** Find the length and speed of the train **
- For example, it took a train 12 seconds to pass through a 420-meter-long cave, and it took 22.5 seconds to pass through a 1050-meter-long bridge at the same speed. What was the speed and length of this train?
- Solution 1 (equation method):
- Let the length of the train be (x) m. Since the speed of the train did not change, according to speed = distance/time, the equation could be obtained as: <(420 + x)> 12=(1050 + x)> 22.5>
- First, he simplified the two sides of the equation:
- \((420 + x)×22.5=(1050 + x)×12\)。
- The expansion is [9450+22.5x = 12600+12x].
- Transferring the entries will yield a result of {22.5x -12x =12600 - 9450}.
- That is,<10.5x = 3150>, the solution is
Elementary school students 'mathematics problem solving skills
The following are some elementary school math problem solving techniques: 1. Drawing Strategy: Translate the words of a difficult problem into a picture. It can quickly sort out your thoughts and find a solution. In the process of solving a problem, by drawing a diagram related to the meaning of the problem, the diagram was used to help reasoning and thinking. This was especially common when solving problems such as geometry, proportions, or scores. 2. ** Transformation Strategy **: Transform a complex problem into a simple problem, and turn an unknown problem into a known problem. This is one of the common methods used to solve problems in primary school mathematics. 3. ** List Strategy (Enumeration Strategy)**: List the condition information of the problem in the form of a table. This makes it easy to find the problem and analyze the quantitative relationship, thereby eliminating the interference of non-mathematical information. At the same time, it also helps to find a solution to the problem. When using it, one must pay attention to not repeating or missing anything. 4. ** Enumeration Strategy **: When solving some special problems that cannot be calculated, it can list all possible situations of the research object, so that the problem can be solved more easily. When listing, you have to think in an orderly manner to ensure that you don't miss anything. 5. ** Substitution Strategy **: Used to solve the problem of the relationship between several quantities and the total quantity. By using this strategy, the relationship between two quantities could be simplified into one, which would help to solve the problem. 6. ** Comparing Method **: According to the meaning of the mathematics question, compare the meaning and essence of concepts, properties, laws, rules, formulas, terms, and terms. Relying on the understanding, memory, recognition, reproduction, and transfer of mathematical knowledge to solve the question. This would help train the child to have a correct understanding of mathematics knowledge, a firm memory, and accurate identification. 7. ** Comparisons **: By comparing the similarities and differences of mathematical conditions and problems, you can study the reasons for the similarities and differences and find a solution to the problem. When using it, you need to pay attention to the completeness of the comparison, find the connection and difference, compare under the same relationship, and grasp the main content to compare carefully. 8. Formula Method: Use laws, formulas, rules, and rules to solve problems, reflecting deductive thinking from the general to the special. However, it was necessary to ensure that the child had a correct and profound understanding of formulas, laws, rules, and rules, and could use them accurately. 9. ** Analysis Method **: To break down the whole into parts, to break down complex things into various parts or elements, and to study and derive these parts or elements. The idea was to start from the problem to be solved, choose the two conditions needed correctly, and deduce them one by one until the problem was solved, which was "tracing the cause from the effect." 10. ** Holistic approach **: For some calculations, when a certain part cannot be calculated directly, this part can be regarded as a whole and solved step by step. For example, when solving an equation, if there were multiple calculation steps on one side of the equal sign and a certain part could not be calculated, one could first treat this part as a whole to solve it. 11. ** Using Aptitudes **: When you encounter complex calculation problems, you can use approximate numbers to help with quick calculations. 12. ** logical reasoning method **: When solving some reasoning or logic questions, use logical reasoning to get the correct answer. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>
Elementary school fourth grade mathematics reading problem solving
The fourth grade mathematics reading questions could be solved from the following aspects: First, he had to understand the problem. Before reading the question, read it carefully to ensure that you fully understand the meaning of the question. You can break the question into small parts and clearly understand the answers and related conditions. Secondly, if the question involved a chart, a chart analysis was required. Carefully observe the data in the chart, such as reading the values, comparing the data, or finding the patterns in it to help solve the problem. Furthermore, he had to use logical reasoning. Mathematics reading questions often needed to analyze the logical relationships, find patterns and laws, and infer the answers through the observation of the development trend and laws of things. Then, he could use the method of illustration. When answering questions, use specific examples to help you understand. These examples can be familiar to you or constructed according to the conditions given by the question. In addition, he had to think from many angles. When reading a mathematical problem, you can't be limited to one way of thinking. Try to think from different angles and use different methods to solve the problem. Use the mathematical knowledge you have learned to find a better solution. Finally, he summarized the problem. When reading, try to summarize the problems and find out the common points and rules by summarizing the problems that have been solved, so as to better solve similar problems. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>
Elementary School Mathematics Test
The primary school mathematics test had many meanings and summary points. * * 1. The purpose and significance of the test ** 1. * * Learning Mastery ** - The test after returning to school helped to comprehensively and accurately understand the degree of mastery of mathematics knowledge during the online study period. For example, they could find out the student's mastery of different unit knowledge points. For example, some re-entry tests covered multiple units of knowledge in the textbook. For example, the fifth grade re-entry test involved the knowledge of units one to four in the first volume of the fifth grade. - To understand whether students can flexibly use what they have learned to solve mathematical problems. Many times, students have a certain grasp of basic knowledge, but they are not good at solving complicated, flexible, or practical problems. 2. * * Teaching Assessment ** - To evaluate the effectiveness of teachers 'online teaching. Through the students 'test results and answers, teachers could recognize the advantages and disadvantages of online teaching. For example, if many students had a high error rate on a certain knowledge point, it might reflect that the teacher did not explain the knowledge point clearly enough or did not practice enough when teaching online. - It could provide a basis for the subsequent adjustment of teaching strategies. The teacher could adjust the key points of teaching, the way of explaining the difficult points, as well as the content of review and reinforcement according to the test results. * * 2. Analysis of student performance ** 1. * * Results ** - There were differences in grades and classes. For example, some classes had a higher excellence rate and passing rate, while some classes had a phenomenon of disparity. For example, in the third-year re-entry test, only 19 students passed, and 30 students failed. The highest score was 96 points, and there were 5 students who scored above 90 points, 4 students who scored 80 - 90 points, 3 students who scored 70 - 80 points, and the lowest score was 16 points. As for the other classes, the average score of Class 5 was 80.73 with an excellent rate of 34.55% and a passing rate of 87.27%, while Class 6 had an average score of 84.54 with an excellent rate of 46.30% and a passing rate of 96.30%. 2. * * Answer Status ** - * * Basic Knowledge ** - Some students performed better in some basic questions. For example, most students could correctly answer the basic calculations such as oral calculation, estimation, and pen calculation in the second grade re-entry test paper. However, there might be weak links in basic knowledge such as unit conversion. For example, the unit conversion in the fifth-grade re-entry test was very poor, involving the unit conversion between area, volume, mass, and volume, as well as the conversion from complex numbers to single numbers. - * * Knowledge Usage ** - Students had varying degrees of difficulty in solving problems that required flexible use of knowledge. For example, when solving applied problems, some students couldn't solve them well in combination with the reality of life, or they didn't understand the problems that required multi-step thinking. In some of the application questions of the re-entry test, such as the itinerary and engineering problems, some students could not accurately find the solution. * * 3. Teachers 'strategies ** 1. * * Tutor students with learning difficulties ** - For students with learning difficulties, teachers should carefully analyze the reasons and weaknesses of the students, so that the tutoring work has a definite target. For example, for students who lacked online learning resources and did not have a solid grasp of knowledge, they should focus on and provide targeted tutoring. 2. * * Teaching method adjustment ** - Teachers could use the results of the re-entry test to adjust their teaching methods. For example, he planned to make full use of micro-classes in future teaching and adopt a combination of online and offline teaching to help students learn better. - He explained and reviewed the important and difficult content of the online teaching and the missing points of the knowledge again, and consolidated them with the exercises. For example, after discovering that students did not have a good grasp of the important and difficult knowledge of a certain unit, the teacher could re-design the teaching process and add relevant exercises. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>
Elementary School Mathematics Teaching Skills Lecture
The following is a model essay on a lecture on primary school mathematics teaching skills: " Elementary School Mathematics Teaching Skills Lecture Experience " In the process of participating in primary school mathematics teaching, constantly learning and exploring effective teaching skills was the key to improving the quality of teaching and promoting the development of students. The lectures on teaching skills that I attended recently have benefited me greatly. The following are some of my experiences after the lectures. ** 1. Deepen the student-centered concept ** The lecture emphasized the main role of the students in the teaching process, which gave me a deeper understanding of the "student-centered" teaching philosophy. Traditional teaching often focuses on imparting knowledge to teachers, while modern teaching requires us to pay more attention to the needs, interests, and learning abilities of students. In mathematics teaching, this means that we have to design the teaching content and teaching methods according to the actual situation of the students. For example, to understand the students 'existing mathematical knowledge base, their understanding of mathematical concepts in life, and the differences in learning styles of different students. This would make the teaching more targeted, stimulate the students 'enthusiasm for learning, and allow each student to find their own rhythm in mathematics learning and make progress. ** 2. The importance of diverse teaching methods ** 1. ** Situation Teaching Method ** By creating mathematical situations that were relevant to real life, abstract mathematical knowledge could be made more intuitive and easier to understand. For example, when teaching addition and substitution, they could create a shopping situation and let the students simulate customers and cashiers to calculate change. This way, students could feel the application value of mathematics in their daily lives, thus increasing their interest in mathematics. 2. ** Investigative Teaching Method ** To encourage students to explore and discover mathematical laws is an important way to cultivate students 'mathematical thinking. Teachers could ask questions to guide students to explore independently. For example, when learning how to calculate the area of a graph, they would first let the students try to measure and calculate the area of the graph in different ways, and then organize the students to discuss and communicate. In this process, students not only learned knowledge, but more importantly, they developed their ability to explore, cooperate, and think logically. ** 3. The optimization of teaching feedback and evaluation ** The effective teaching feedback and evaluation can help students adjust their learning strategies and enhance their learning motivation. In addition to the traditional evaluation of students 'homework and examination results, the lecture made me realize the importance of process evaluation. In daily teaching, one should pay attention to the students 'performance in class, such as their enthusiasm in participating in discussions, the depth of their questions, and the ability to cooperate with group members. Give positive feedback and encouragement in a timely manner. Guide the students 'mistakes and help them analyze the reasons for their mistakes and find the correct solution. For example, when a student made a mistake in solving a math problem, don't point out the answer directly. Instead, ask them questions to guide them to reconsider the solution. ** 4. Cultivation of mathematical thinking ** Mathematics teaching was not only about imparting mathematical knowledge, but more importantly, it was about cultivating students 'mathematical thinking. This included logical thinking, abstract thinking, spatial imagination, and many other thinking abilities. In the teaching process, there are many ways to cultivate these thinking skills. For example, mathematical games and puzzles could be used to stimulate students 'logical thinking ability, and spatial imagination could be cultivated by letting students observe the changes of objects and graphics. At the same time, they should pay attention to the infiltration of mathematical thinking methods, such as classified discussion of ideas, transformation of ideas, etc., so that students could master the basic thinking methods of solving mathematical problems while learning mathematics knowledge. ** 5. Use modern educational technology to assist teaching ** Modern educational technology provided rich resources and diverse teaching methods for primary school mathematics teaching. For example, the multi-media teaching software could vividly display mathematical concepts in the form of animations and videos to help students better understand them. The online education platform provided more learning resources, such as mathematics learning games and online exercises, to meet the learning needs of different students. Teachers should be good at using these modern educational technology means to combine traditional teaching with modern technology to improve teaching efficiency and quality. After attending this elementary school mathematics teaching skills lecture, I deeply realized that teaching is a process of continuous learning and innovation. As a primary school mathematics teacher, he should always pay attention to the updating of teaching concepts, the improvement of teaching methods, and the comprehensive development of students. He should constantly improve his teaching level and lay a solid foundation for students 'mathematics learning. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>
Elementary School Mathematics Line Section Formula
1. ** Method 1 Induction Formula **: When there are N points, the number of line segments starts from N - 1 until it reaches 1. For example, the number of line segments with 5 points is 4+3+2+1 = 10. 2. ** Formula Method **: Number of line segments = number of end points ×(number of end points- 1) div2. For example, if there are 4 points, the number of line segments is 4×(4 - 1) div2 = 6. 3. ** Based on the number of ends and segments of the line segment **: Number of line segments = number of ends × number of segments div2. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>
Elementary School Mathematics Ancient Interesting Problems
The following are some of the interesting ancient math problems in primary school: ** I. The problem of "things do not know their numbers" in Sun Tzu's Arithmetic Classic ** 1. ** Title ** - There was a pile of items, 3 3 left 2, 5 5 left 3, 7 left 2. Find the number of items in this pile. 2. ** Solution Method ** - The total number of items was not unique. It was an arithmetic progression with a difference of 3×5×7 = 105. Each answer could be broken down into the sum of three numbers. The first number could be divided by 5 and 7, and the remainder after dividing by 3 was 2; the second number could be divided by 3 and 7, and the remainder after dividing by 5 was 3; the third number could be divided by 3 and 5, and the remainder after dividing by 7 was 2. - It was easy to deduce that the first number was 140, the second number was 63, and the third number was 30. Then, 140+63 + 30 = 233 was a solution to the original question, and 23, 138, 233, and 338 were all solutions to the original question. ** II. The problem of "pheasants and rabbits in the same cage" in Sun Tzu's Mathematical Classics ** 1. ** Title ** - Today, there are chickens and rabbits locked in a cage. There are 35 heads and 94 feet. How many chickens and rabbits? 2. ** Solution (One of the Arithmetic Methods)** - Think about it with rabbit feet as the main element: Imagine that the first 35 are all rabbits, then there should be 35×4 = 140 feet, so there are 46 more feet. You can replace the same number of chickens with rabbits to reduce the number of feet. Every time you remove a rabbit (exchange a chicken), you will lose 2 feet. - Therefore, the number of chickens was 46 div2 = 23, and the number of rabbits was 35 - 23 = 12. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>
Elementary school mathematics abstract teaching plan
The following are some elementary school mathematics abstract lesson plans: ** 1. Teaching plan for understanding the rectangular, square and circle ** 1. ** Teaching goal ** - Through practical activities, students will have perceptual knowledge of cuboids, cubes, columns, spheres, as well as cuboids, squares, circles, and triangles, and be able to recognize their names. He could feel the connection between the form and the body. - He applied his knowledge to his daily life and judged the shape of objects in his daily life. - Cultivate the students 'observation skills, spatial concepts, and hands-on operation skills. 2. ** Teaching Difficulties ** - ** Important point **: Students will be able to intuitively recognize the rectangular, square, and circle in the activity exploration, and be able to abstract the planar figure from the surface of different objects in life. - [Difficulty: Let the students abstract a planar figure from the surface of an object and feel the connection between the shape and the body.] 3. ** Teaching process ** - For example, let the students touch a bag with cuboids, cubes, columns, balls, and other objects, and then tell them the shape and characteristics of the objects they touched. - The students were guided to observe the footprints of different shapes, find footprints, draw footprints, divide footprints, recognize footprints, and so on. - Ask the students to give examples of objects in their daily lives that are rectangular, square, or round in order to enhance their understanding of the shapes. ** 2. Polygon (such as a quadrilateral, triangle, echelon, etc.) teaching plan ** 1. ** Teaching goal ** - Let the students grasp the characteristics of the shape of a hexagon (such as a quadrilateral, triangle, echelon, etc.). - To make students understand the core methods of calculating the area of a hexagon (such as conversion-known-unknown, cut and divide, combination, cut or supplement conversion, etc.). - Through practical homework, students could improve their core mathematics quality. 2. ** Teaching Difficulties ** - ** Main point **: Teach the shape characteristics of a hexagon and related calculation methods. - [Difficulty: Guide students to use transformation thinking to calculate the area of a hexagon and understand the relationship between the graphs.] 3. ** Teaching process ** - Divide the teaching modules, such as the knowledge points such as paralleled quadrilateral, triangle, echelon, and hexagon. - He explained the core calculation methods, such as using methods such as cutting, combining, and so on to transform the unknown figure into a known figure for calculation when calculating the area of a triangle. - Arrange practical assignments, such as making a graphic mold frame, building a graphic combination tool, calculating and drawing a polygraph, etc., so that students can understand the knowledge of the polygraph in practice. ** 3. Teaching plan for mathematical graphs (related to mathematical graphs)** 1. ** Teaching goal ** - Combining the problem situation, he experienced the process of abstracting real-life problems into mathematical problems of graphs and using a variety of drawing strategies to solve the problem, developing geometric intuition. - In the process of counting the figures, gradually form a good habit of orderly thinking and develop reasoning ability. - In the process of discovering the rules, they could think independently and explore independently, enhance their self-confidence in learning, and increase their interest in exploring mathematical problems. 2. ** Teaching Difficulties ** - ** Main point **: Experience the process of abstracting real-life problems into mathematical problems and using a variety of drawing strategies to solve the problem. - [Difficulties: Gradually form a good habit of thinking in an orderly manner, summarize and discover patterns, and develop reasoning skills.] 3. ** Teaching process ** - Create a situation, such as a "mole drilling hole" or a modified "riding a bullet train" situation. Take the example of "mole burrowing". First, let the students think about how many different paths the little mole can take and guide the students to solve them in different ways. For example, some students might describe it in words, while others might use symbols to express it. - In the process of counting figures (such as the number of line segments), guide the students from simple to complex. For example, start from 4 points, count the line segments without repeating or missing, and then gradually increase the number of points to 5, 6, etc., so that the students can feel the value of orderly thinking and discover the rules in this process. - The migration law could solve other similar problems. For example, in the case of "vegetable field travel"(or train ticket problem), the method learned from "mole drilling hole" could be used to solve the problem of the number of line segments (the type of ticket) corresponding to different points. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>
The story of me and mathematics, elementary school student
The following are some examples of elementary school students and mathematics stories: ** 1. The story of actively exploring mathematical knowledge ** 1. ** Love to read mathematical works ** - Some primary school students had a strong interest in mathematics works since the third grade. Every time they went to the bookstore, they would go straight to the mathematics section. For example, Zhang Cang's "Nine Chapters on Arithmetic" and Eugene's "Elements of Geometries". Although they were only in the third grade and did not understand much knowledge, they still loved them. Even if they swallowed the books they had not finished, they would still buy the books they had not finished and continue reading. 2. ** Exploration in the classroom ** - In the Mathematical Olympiad class, some primary school students were unable to solve difficult Mathematical Olympiad questions at the beginning, but when they encountered an extremely difficult Mathematical Olympiad question, they could solve it in less than five minutes, and the answer was completely correct. This showed the exploration spirit and potential of primary school students in mathematics learning. 3. ** The effort to improve my math results ** - Some primary school students had poor math results at first. For example, in kindergarten, their grades were the last in class because of their weak foundation. However, under the guidance of his parents, he studied hard and his grades improved by leaps and bounds, becoming the first in the class. After entering elementary school, because of his pride, his grades fell to the top 30 of the class in the second grade. Later, under his mother's guidance, he paid attention to mathematics and studied hard through his spare time. When he was not careless, his grades could reach the top 10 of the whole grade. They would even wake up in the middle of the night to solve math problems. ** 2. Interesting Math Stories in Life ** 1. ** A small mistake in shopping ** - A primary school student went to a convenience store to buy snacks. He bought a bag of potato chips, two bags of biscuits, and a bottle of green tea. He silently calculated that the total price was 18.6 yuan. In the end, he paid one yuan less and made a fool of himself. This reflected the application of mathematics in daily life and the possible mistakes. 2. ** Mathematical calculations in grocery shopping ** - When I went to the market with my mother to buy vegetables, I was faced with two different ways of promoting cabbage. When a mother wanted to buy 7 catties of cabbage, the primary school student could calculate the price of different purchase combinations and find a cheaper purchase method. For example, the actual unit price of 4 catties of cabbage at stall A was 1.5 yuan, and the actual unit price of 5 catties at stall B was 1.52 yuan. Then, the purchase method of 1.9×6 = 11.4 yuan was cheaper. 3. ** Interesting Mathematics Quiz ** - For example, in the story of Tang Sanzang and his disciples picking peaches, Bajie, Monk Sand, and Wukong tested Tang Sanzang in different ways of counting peaches (3 3 ground numbers, 4 ground numbers, 5 ground numbers, and 1 ground number). This was also an interesting mathematical situation that primary school students could come into contact with. There was also the question of how many buckets of water there were in the pond when the king asked the minister to answer, the little boy's answer that was out of the ordinary (it depended on the size of the bucket. If the bucket was as big as the pond, it would be a bucket of water, etc.), and the story of the little bear being taught a lesson by the little monkey and the little rabbit when he sold peaches due to mathematical calculations. These all showed the embodiment of mathematics in interesting stories. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>
Elementary School Mathematics Outstanding Case List
The following are some excellent elementary school math case studies: 1. Mary had five apples. She ate three. How many were left? 2. Xiao Ming has 8 candies and he wants to divide them into 2 equal portions. How many candies are there in each portion? 3. Enen scored 36 points on the test, out of 100 points. What was her score percentage? 4. The speed of the car was 60 kilometers per hour. How long would it take to travel 360 kilometers? 5. Xiao Lin had 20 fruits. Seven of them were apples and the rest were oranges. What was the ratio of apples to oranges? 6. Little Light had 40 yuan. He spent 15 yuan on books and 5 yuan on pens. How much money was left? 7. The children were divided into watermelons. Each of them had 10 watermelons, nine less, eight more, seven more. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>
Elementary School Puzzle Mathematics Questions and the Answer
The following are some elementary school math questions and answers: * * One, three squares and circles combined to find the shadow area ** 1. [Question: Given that the sides of the three squares are 10 cm, 8 cm, and 6 cm respectively, with point C as the center and 10 cm as the radius, draw a quarter circle in the big square, then connect dm and em to find the area of the shadow in the picture.] 2. * * Solution **: The area of the shadow = the sum of the areas of the three squares-the area of the white part in the upper left corner of the big square, ADC-the area of the triangle, AHM + the area of the triangle, ENM. The area of the white part in the upper left corner of the big square Jiuge = the area of the square Jiuge-the area of a quarter circle; the area of the triangle DIM = HH × HH div2 (the length of HH is equal to the sum of the sides of the three squares); the area of the triangle EMN = Mn × EN div2 (mn is 6 cm, en = 8 - 6 = 2 cm). 3. Answer: - The area of the white part in the upper left corner of the big square, ADC, is: 10 × 10 - 3.14 × 10 2 div4 = 100 - 78.5 = 21.5 (square centimeters) - The area of the triangle is: (10 + 8 + 6) × 6 div2 = 24 × 6 div2 = 72 (square centimeters) - The area of the triangular EMN is: 6 × (8 - 6) div2 = 6 (square centimeters) - The sum of the three squares is: 10 × 10 + 8 × 8 + 6 × 6 = 100 + 64 + 36 = 200 (square centimeters) - The area of the shadow is: 200 - 21.5 - 72 + 6 = 112.5 square centimeters * * 2. Rectangle is divided into squares to calculate the area of the rectangular shape ** 1. [Question **: Given that the rectangular ADC is divided into 6 squares, the area of the shadow square is 4, so the side length of the shadow square is 2. Find the area of the rectangular ADC.] 2. * * Solution idea **: Let the sides of the squares numbered 1 and 2 be x, and the sides of the other squares numbered 3, 4, and 5 be x +2, x +4, and x +6 respectively. Thus, it can be seen that the ADC = 3x +2 and ADC = 2x +10. Then, using the property of the length equality of the rectangular pair, that is, 3x +2 = 2x +10, x = 8. Then, the length and width of the rectangular shape were calculated, and the area was calculated. 3. * * Answer **: The area of the rectangular shape is 572. * * 3. Find the area of the original square after cutting off the rectangular shape of the square plank ** 1. [Title: There is a square wooden board. First, cut off a 4-decimeter wide rectangular board, and then cut off a 6-decimeter wide rectangular board. The remaining area is 216 square decimeters less than the original square.] Find the area of the original square board. 2. * * Solution **: The total area of the shadow is 216 decimeters square. If you add the area of the 6 decimeters long and 4 decimeters wide rectangular shape in the upper right corner, it is equivalent to the area of the rectangular shape with the length of the original square as the length and the width of 4 + 6 = 10 decimeters. From this, the length of the side of the square was calculated, and then the area of the square was calculated. 3. Answer: - Transform the total area of the shadow into a rectangular area of 216 + 4 × 6 = 240 (square decimeters) - The length of the rectangular shape (that is, the length of the original square) 240/(4 + 6)= 24 (decimeters) - The area of the square wooden board is 24 × 24 = 576 square centimeters. * * 4. Tile and puzzle in the living room ** 1. [Title: A rich man's living room is a square with a side length of 10 meters. He ordered 25 large tiles, 20 of which are squares with a side length of 2 meters, and the other 5 are rectangular with a length of 4 meters and a width of 1 meter.] Without cutting the tiles, would it be feasible to use these 25 tiles to cover the living room? 2. * * Solution **: Using the dyeing method, divide the living room into 100 squares with a side length of 1 meter, and choose the odd-even property as the invariable property to dye. Then analyze the number of small pieces of a certain color (such as red) in the living room, as well as the number of small pieces of this color in each tile, to determine whether it can be pieced together. 3. * * Answer **: The number of red pieces in the living room after using a specific dyeing method is 51. No matter where the square tiles were placed, they would always contain one or three red tiles, and the rectangular tiles would contain two red tiles. The combination of 20 square tiles and five rectangular tiles containing red tiles could not reach 51 tiles, so the idea of the nouveau riche could not be realized. <a href="/?from=ask_words" style="color:red" target="_blank">Read more exciting novels for free</a>