Themes use pairs of numbers to determine location.

Self-study content textbook P2 case 1

Guidelines 1. Look at the pictures and questions of the example 1 and think about how the teacher determined Sean's position. What is a "column" in your own words? What is "ok"? And how to determine which column and which row? 2. According to the specific situation, if (2,3) is used to represent the position of Sean, how much data is used? What do the numbers in (2, 3) mean? 3. Use (2,3) to indicate Sean's position. Can you point out the location of Rebecca and Zhao Qiang? (Pay attention to your writing format) 4. Combined with the self-study situation, can you try to summarize the method of expressing position with number pairs and its writing format in your own words? 5. Practice and complete the "doing" of P2.

Several pairs on the grid paper were tried to determine the position of the object.

Self-study content textbook P3 case 2

Guide outline 1. What's the difference between the schematic diagram of the zoo shown in the observation book and what I have seen before? 2. Think about it carefully. In this example of 1, what are the vertical lines and horizontal lines on the square paper? Observe the position of the grid on the grid paper. Can you point out the location of the gate? Say the meaning of each number. 3. Mark the positions of Panda Pavilion, Monkey Mountain, Elephant Pavilion and Aquarium with several pairs and record them. 4. Observe and compare the pairs indicating the location of the elephant house and the aquarium, and see what you find. What are the characteristics of the site selection of these two venues? 5. Use (x, 4) to indicate the location of the elephant house. Can you determine where it is? Why? Think about it. How many numbers do you need to determine the position on the grid paper? 6. Exercise the third question of P5 in the book.

Unit 2 Fractional Multiplication

Subject score multiplied by integer

Self-study content textbook P8~9 case 1, case 2

Guidelines 1. Read the example 1 on page 8 carefully, and then express the meaning of the question in your own words. What does it mean that a person runs as far as a kangaroo jumps? Do it yourself, draw a line segment diagram and mark the known situation and problems on the line segment diagram? 3. Combine your own line drawing, use various methods to calculate the formula, and think about how to calculate the score multiplied by the integer. 4. Try to sum up Example 2 by yourself to see if the product you multiplied is the simplest score. Think about how many ways to integer fractions. Which method is simple? 5. Practice and complete P9 "Doing" 1-3.

Subject score multiplied by score

Self-study content textbook P 10~ 1 1 Case 3 and Case 4.

Guide outline 1. Observe the P 10 theme map and solve the question "How many hours do you paint this wall?" Take out a piece of paper and use it to represent this wall. Apply this paper first, then apply it. According to the coloring results. Think about how to multiply the score by the score. 3 Use your own summary method to calculate, and then origami to verify whether you have calculated correctly. 4 self-study book example 4, formulation, calculation, think about how to multiply the score by the score, how to reduce the score. 5 Calculate and observe the restoration process of textbooks in the preview book, and think about how it is different from the restoration form of P9 case 2. Think about how to divide a fraction by an integer. 6. Exercise: Complete P 1 1 "Do"

The law of integer multiplication is extended to fractions.

Self-study content textbook P 14 Cases 5 and 6

Guidelines 1. Observe three groups of formulas in case 5 of P 14. What are the differences and connections between the two formulas in each group? What's their score? What should I fill in? 2. Contact the knowledge of integer multiplication formula we have learned before. What pattern did you find? 3. Observe P 14 Case 6, and see what algorithm is used in the first step given in the textbook? And complete the calculation process. And think: why can you make the calculation simple? 4. Exercise: Complete P 14 "Doing"

This problem is to find a fractional multiplication application problem, which is a fraction of a number.

Self-study content textbook P 17 examples 1

Guidelines 1. Read carefully the example of P 17, and in my own words, "China's per capita arable land only accounts for the world's per capita arable land". Draw a schematic diagram of a line segment by yourself, mark the known conditions and problems on the line segment diagram, and think about who is the representative unit "1" in the topic? 2. Counting, what is the per capita arable land area in China? Think about the basis of the formula. 3. Exercise: P 17 "Do it", draw a line chart first, and then solve it with a column chart.

This problem solves the slightly complicated application problem of fractional multiplication (1) to find the fraction of a number.

Self-study content textbook P 20 cases 2

Guidelines 1. Look at the picture and topic of P20 Example 2, and think about what is the unit for measuring sound intensity? Then express the meaning of the question in your own words. 2. Draw a schematic diagram of the line segment by yourself, mark the known conditions and problems on the line segment diagram, and think about who is the representative unit "1" in the topic? 3. How many different ways can you think of by combining your own line drawing? 4. What is the difference between the two reading methods and problem-solving ideas? Which one do you like? 5. Exercise: On the basis of understanding the meaning of the question, draw a line drawing first and complete the book P20 "Do it".

This problem solves the slightly complicated application problem of fractional multiplication (2) Find the fraction of a number.

Self-study content textbook P 2 1 Example 3

Guidelines 1. Read P2 1 Example 3 and say, "Babies beat more times per minute than teenagers". What does this mean? Who is better than who in this sentence? Who is the unit "1"? 2. Draw a schematic diagram of the line segment by yourself, mark the known conditions and problems on the line segment diagram, and think about who is the representative unit "1" in the topic? 3. See how many different methods you can come up with by combining your own line drawing. 4. Exercise: On the basis of understanding the meaning of the question, draw a line drawing first and complete the book P20 "Do it".

Understanding of the reciprocity of subjects

Self-study content textbook P 24 case 1 and case 2

Guidelines 1. Calculate the example 1, and observe and compare these formulas. Think about the characteristics of these formulas. Please give the definition of reciprocity and say how you understand reciprocity and judge reciprocity, right? Why? Read Example 2, please tell me how to find its reciprocal. How to find its reciprocal? Can you sum up a method of finding the reciprocal of a number? 5. Think of 0 and 1. Are they mutual? What's the reciprocal? 6. Exercise: Finish P24' s book "Do it"

Unit 3: Fractional Division

Significance of subject score division

Self-study content textbook P 28 case 1

Guidance outline 1 .. Read the example 1 theme map and the three integer questions on the left. Please follow the instructions in the book and change it into a score question, and write it in the blank space of the book. 2. Solve the problem independently, and compare it with the multiplication formula and division formula, integer problem group and fractional problem group appearing in books. Think about it (1). Do fractional division and integer division have the same meaning? (2) What is the significance of fractional division? 3. Exercise: P28 "Doing"

Subject score divided by integer

Self-study content textbook P 29 case 2

Guide outline 1. Look at the topic of Example 2, take out a piece of paper and try to fold it, color it, and see if you can think of several different folding methods. 2. Compare different folding methods and column calculation, and pay attention to their calculation process and logic. 3. Compare the similarities and differences between the two calculation methods in books? Which algorithm do you think is more suitable? Why? 4. Read the second question of the book example, calculate independently, and use origami to verify that your calculation is correct? According to my own origami experiment and formula, can you tell me how to calculate the fraction divided by integer? 6. Exercise: P32 Exercise 8 Question 3

Divide a number by the score in a topic.

Self-study content textbook P 30-3 1 Example 3

Guide outline 1. Read the theme map and theme of Example 3. To "walk faster than who", what can you compare with them? How to form? 2. Query algorithm (1) "Two hours have passed, so how many hours have passed 1? (2) Hand-drawn line segments represent the relationship between known conditions and problems. How many ways can you think of to draw a line segment? Combined with the line chart, think: what can Xiao Ming do in the first step of speed? What is the second step? (3) Think about how to calculate with the idea of solving problems. What did it turn the organization into? How to transform? 3. Calculation Example 3 Think about what the second formula can be converted into? 4. What did you find through the above two calculation questions? Will you express the law you found in your own way? 5. Exercise: Read P3 1 Do it, and think about the key points of converting division into multiplication.

This topic involves the mixed operation of fractional division.

Self-study content textbook P 34 case 4

Guide outline 1. Read the title of Example 5, talk about the known conditions and problems of the title, and talk about your own ideas to solve this problem. 2. List the comprehensive formula, think about its operation order, and then calculate independently. 3. Do the first line of the first question independently, think about the calculation algorithm of continuous division or continuous multiplication and division of fractions, and use the simplest method you think. 4. Exercise: P34, 1 The second line of the question, the second question.

The subject knows what the score of a number is. The practical problem of finding this number.

Self-study content textbook P 37-38 examples 1

Guide outline 1. Preparation for review: Write the quantitative relationship of the following questions and list the formulas: Dad weighs 75, Xiaoming weighs his, (1) What is Xiaoming's weight? (2) The mass of water in Xiaoming's body accounts for Xiaoming's weight. How many kilograms of water is there in Xiaoming's body? 2 Read the example 1, what quantitative relationship does the two sentences of the doctor in the theme map tell us? 3. Reading Xiao Ming's words and the first question (1) requires Xiao Ming's weight. "I have 28 waters in my body" and "My weight belongs to my father", which should I choose? Why? (2) What is the quantitative relationship between Xiao Ming's weight and the water quality in Xiao Ming's body? (3) Draw a schematic diagram of the line segment, and mark the known conditions and problems on the line segment diagram. (4) Write the equivalence relation according to the quantitative relation mentioned by the doctor, make equations and calculate independently. 4. Read the example 1 question 2 and think about which two conditions appear in the following question (1)? (2) Draw a schematic diagram of the line segment, and mark the known situation and problems on the line segment diagram. Think about the difference between the line graph of the last question and the line graph of this question. (3) Write the equivalence relation, list the equations and answer them. 5. What do you find by comparing the example 1 with the topic laid out in the review? 6. Exercise: P38 "Do it"

This topic is a bit complicated. The practical problem of finding this number is to know what a fraction of a number is.

Self-study content textbook P 39 case 2

Guide outline 1. Read the theme map and topic of Example 5, express the meaning of the topic in your own words, and say that "the number of art groups is more than that of model airplane groups", and who should be regarded as the unit "1". 2. Do it yourself, draw a line drawing to represent two groups of numbers, and mark the known situation and problems on the line drawing. The unknowns in the picture can be represented by x.3. Combined with the line segment diagram, the equivalence relation and the solution of the equation are listed. After the calculation, sort out your own ideas to solve the whole problem? 4. Exercise: P40 Exercise 10 Question 4

The meaning of subject ratio

Self-study content textbook P 43~44

Guidelines 1. After learning the textbook P 13 by yourself, complete the following questions, and use 10 kg salt and 600 kg water as brine. (1) What is the mass ratio of salt to water? (2) What is the mass ratio of water to salt water? 2. Teach yourself P44 and think: (1) What is the ratio of two numbers? (2) How to write and read? (3) What is the name of Bi's parts? (4) How to find the ratio? How to express the proportion? 3. What is the connection and difference between ratio and ratio? (For example, when the expressions of ratio and ratio are exactly the same, and when their expressions are different) 4. Thinking: ratio is equivalent to division formula and what are the front, back and ratio of fractions respectively? Can the last term of the ratio be 0? Why? 5. Exercise: P44 "Do it"

Basic properties of subject ratio

Self-study content textbook P 45-46 case 1

Guide outline 1. Review and recall: give examples to illustrate the basic properties of quotient invariance and scores learned before. 2. Refer to the textbook P45 for examples of the relationship between proportion and score and the relationship between proportion and division. Think about it. What are the corresponding laws in proportion? 3. What is the basic nature of the ratio? How to understand "divide by 0" in the basic property of ratio? 4. What information did you learn after reading the theme map and theme of P46 case of 1? On the meaning of "the simplest integer ratio" (1). Try to write. If you have difficulties, you can read a book and fill in the blanks according to the examples. (2) What did you find from the simplified result of the comparative example 1 question 1 (1)? (3) The difference between the first question (2) and the first question (1) and the example 1. 5. Can you record your idea of simplifying the score ratio and the score ratio? 6. Exercise: P46 "Do it"

Application of topic ratio

Self-study content textbook P 49 case 2

Guide outline 1. Look at the topic diagram of Example 2, then express the meaning of the question in your own words and talk about how the diluent is prepared. 2. Write it yourself and try to solve the problem in different ways. How many did you come up with? What is the solution to each problem? 3. Compare the connection and difference between the two solutions with textbooks, which one do you prefer? And fill in the blanks in the process of solving the problem. 4. Counting thinking: How many aspects does the complete test of this question include? 5. Exercise: P49 "Do it"

Unit 4 circle

Understanding topic circle (1)

P56~58 case 1, case 2.

Guidelines 1. What objects in life are round? Please try to draw a circle on the paper with the objects in your life. Cut it out and try to find its center. 2. The self-study textbook p56 (1) knows the center, radius and diameter of a circle. And mark the cut circle. (2) Think about it: What is the relationship between the length and radius of the inner diameter of the same circle? Not in the same circle? Please try to draw several circles of different sizes with compasses. What can you find? 4. Thinking: What's the difference between a circle and a plane figure? 5. Try to practice: p59 "Do it" 1.2.3.4

Understanding the Theme Circle (2)

Self-study content textbook p59 Case 3

Guidelines 1. Which of the plane figures we have studied are axisymmetric figures? How many axes of symmetry are there? Symmetry axis 2 of plane figure (bar). Think about it: Is a circle an axisymmetric figure? If so, how many axes of symmetry does it have? Try to fold it up and draw a picture. 3. Please creatively use circles with the same or different sizes (1~4) to design a combined figure with one, two, three and four symmetry axes. 4. Try to practice: p59 "Do it" 1, 2.

Perimeter of the theme circle

Teaching materials for self-study p62~64 cases 1

Guidelines 1. Find three circular objects with different sizes, measure the circumference and diameter of their circular surfaces, and record them in the table of p63. Tell me how you measured it. The circumference of a square is always four times the length of its side. Guess: Is the circumference of a circle a constant multiple of its diameter? Tell me your reasons. 4. Access to information: understand pi and talk about your feelings. 5. Try to derive the formula of the circumference of a circle. Are there any different answers to the first question and the second question in the self-study textbook p64? 6. Try to practice: p64 "do" 1.2

Area of theme circle

Self-study content textbook p67~69 cases 1, case 2.

Guidelines 1. Recall the area formula and derivation process of plane graphics you have learned. What are the different deduction methods? 2. How to calculate the area of a circle? Can you convert a circle into a learned figure to calculate it? Spell a circle in the attached page 1 3. What approximate figure did you put this circle together? What is the connection between them? Try to deduce the area formula of a circle. 4. Self-study textbook p67~69 and complete it. 5. Thinking: What is the relationship between the perimeter of the combination figure and the perimeter of the circle? 6. Try to practice: p69 "do" 1.2

Subjects determine the starting line.

Self-study content teaching materials p75~76

Guidelines 1. Do you know the shape of track and field? 2. Do all track and field athletes start at the same starting line? If not, please give an example and try to tell the reason. 3. The self-study textbooks p75~76 calculate the length of each runway according to the data provided by the textbooks. Fill in the p76 form (you can use a calculator or calculate according to the rules you find). If you are the referee, how many meters should the starting line of the 400-meter race differ? What method was used to get the result? What about 200 meters? 5. Thinking: How to determine the starting line for long-distance running events such as 1500m and 3000m?

Unit 5 Percentage

Significance and writing method of percentage of class hours

Self-study content teaching materials p77~78

Guidelines 1. P77~78 Where have you seen percentages in your life? 2. Choose a picture of p77 and tell me the specific meaning of the percentage in the picture. What should I pay attention to in reading and writing percentage? 3. What kind of figures are percentages similar to those we have learned? Why do these examples choose percentages instead of fractions? 4. Have you found the percentage of fractional units? Why? 5. Thinking: What is the difference and connection between percentage and score? 6. Try to practice: p79 "Do" 1.2.3.

Interchange of topic percentage and decimal

Self-study content textbook p80 case 1, case 2

Guidelines 1. Self-taught textbook p80 case 1, case 2, and completed it. 2. What is the method of converting fractions into decimals and decimals? 3. Observation example 1, example 2, is there any other method? 4. Try to practice: p80 "Do it"

The relationship between topic percentage and score

Self-study content textbook p8 1~82 Case 3

Course outline 1. Self-study textbook p8 1 Example 3 If the numerator of percentage is decimal, how to divide it by the number of components? (such as 3.5%) 2. Try to practice: p8 1 "do" 1.2 3. Self-taught textbook p82 Case 4 (1) How many ways can you turn a score into a percentage? (2) How many decimal places are reserved by dividing the fraction by the percentage by the numerator? Where is Shang? (For example,) 4. Try to practice: p82 "Do" 1.2

Percentage of problems solved (1)

Self-study content textbook p85~86 cases 1

Guidelines 1. Self-taught textbook p85 Case 1( 1) Solution Ideas: (1) What percentage of the total number of students meet the standards? (2) What is the proportion of students who meet the standards in the total number of students? What is the connection between them? 2. What is the compliance rate? Why is it necessary to multiply the compliance rate by 100%? Is there any change in the calculation results? 3. What is the germination rate? Example 1(2) 4. Can you give some examples of percentages? Give some concrete examples to talk about how to ask. 5. Thinking: Is the sentence "the qualified rate of a product 10 1%" correct? Why? 6. Try to practice: p86 "Do" 1.2

Percentage of problems solved (2)

Self-taught content textbook p90 Case 2

Guidelines 1. Look at the problem and review the groundwork: (1) What is the actual percentage of hectares planted? (2) What proportion of the area was originally planned for afforestation? Solve the problem and mark the unit "1" in the problem. 2. Solve the problem "What percentage has the actual afforestation increased compared with the original plan? (1) Tell me the meaning of this sentence. Compared with (), () hectares increased by a few percent? (2) Please draw a line chart to show the quantitative relationship. (3) try to solve the problem. (4) With reference to p90, do you know these two methods of solving problems? Talk about solving problems. 3. Solve the second question "How much is the original planned afforestation less than the actual afforestation?" (in two different ways) 4. Find examples of "increasing a few percent", "decreasing a few percent" and "saving a few percent" in life and talk about how to solve such problems. 5. Try to practice p90 "Do it"

Solve the problem by percentage (3)

Self-taught content textbook p93 Case 3

Learning guidance outline 1. Review, pave the way for the school library 1400 original book. The number of books has increased this year. How many books are there in the library now? (Two different answers) 2. Read the question and understand the meaning of the question (with the help of a line chart) 3. Solve problems independently (try to solve them in two different ways) 4. Referring to p93, talk about the solution ideas of these two solutions. 5. Thinking: What are the similarities and differences between percentage application problems and corresponding fractional application problems? 6. Try to practice: p93 "do" 1.2

Theme discount

Self-taught content textbook p97 Case 4

Guidelines 1. Where have you seen "discounts" in your life? For example. 2. Self-study textbook p97 (1) to understand what "folding" is? (2) What do you mean by "15% discount" and "10% discount" in Example 4? (3) Write a few discounts and turn them into corresponding scores and percentages. 3. Solve the problem p97 cases 4. Try to practice: p97 "Do" 5. Read p 103 "What is Chengdu?" What's the difference between "entering the number" and "entering the number"? 6. Thinking: Give a 10% discount on a commodity first, and then increase the price by 10%. Is the current price the same as the original price?

Subject tax, interest rate

Self-study content textbook p98~ 100 Case 5, Case 6.

Guidelines 1. Self-study textbook p98 (1) Know what is tax payment? What taxes are there? How much is the tax rate? (Draw directly on the book) (2) Talk about the significance of paying taxes according to the things around you? (3) Combined with p99 Case 5, how to calculate the tax payable? 2. Self-study text p99~ 100 (1) What is the meaning of saving? What are the bank deposit methods? What is the headmaster? Interest? Interest rate? (Draw directly on the book) (2) How to earn interest? Combined with case 6 of p99, what is grandma's interest after two years? How much interest can grandma get? (3) How much can Grandma get back after the expiration? Do you know the two solutions of P 100? (4) Do you have to pay interest tax on all interest? (See Resources) 3. Try to practice: p 100 "do" to understand the function of each column of the deposit certificate, get information from it and answer it.

Unit 6: Statistics

Departmental statistical chart of the theme

Self-study content textbook p 106~ 107

Guide outline 1. Review the histogram (1), read the textbook p 106, and tell me what information you can get from the histogram. (2) Think about it: What are the characteristics of bar charts? 2. Do you know what the sector chart (1) represents with a whole circle? What do you mean by the size of each sector in a circle? (2) What information can be learned from the fan map? (3) What questions can be raised by observing the fan-shaped statistical chart? And answer seriously. 3. Thinking: What are the characteristics of fan maps? 4. Read p 109 "Do you know?" 5. Try to practice: p 107 "Do it"

Subject reasonable deposit

Self-study content textbook p1/kloc-0 ~11

Guidelines 1. What problems are the activities of defining problems centered around? 2. How many forms of savings deposits are provided in the textbook 1? (2) What forms of savings deposits do not need to pay interest tax? (3) Investigate the educational savings deposit and the interest rate of national debt. 3. The design scheme still only saves the principal of 10,000 yuan, excluding the interest already earned. (1) What are the options for choosing a time deposit? Fill in the first form of p 1 1 1. (2) What are the options for choosing education savings deposit and purchasing national debt? Fill in the second form of p 1 1. 4. Choose Scheme (1) Which deposit scheme has the greatest benefits? How much can * * * get back after the expiration?

Unit 7: Mathematical Wide Angle

The chicken and the rabbit are in the same cage.

Self-study content textbook p 112 ~114 cases1.

Guidelines 1. I read the book P 1 12, The Story of a Chicken and a Rabbit in a Cage. Can you express the meaning of the topic in your own words? 2. Read P 1 13 cases 1. According to the tips in the book, will you find a few chickens and rabbits by listing? How many different lists have you come up with Suppose the cage is full of chickens or rabbits, what will happen to the number of feet? Can it be solved continuously? 4. Write it yourself and try to solve the problem of the number of chickens and rabbits with equations? If you have any difficulties, please refer to the reference book P 1 14 5. Solve the problem of P 1 12 "chickens and rabbits in the same cage" by assuming or solving the equation. 6. Read the reading materials of P 1 14 to understand how the ancients solved the problem of chickens and rabbits in the same cage. 7. Practice: P65438.