Jiangsu Education Press, Unit 7, Fifth Grade Mathematics, Next Term, Summary of Knowledge

Unit 7 Statistics

Statistical table of the first kind of composite broken line

Teaching objectives:

1, let students experience the process of describing data with composite polyline statistical chart, and understand the characteristics and functions of composite polyline statistical chart; Can understand the information represented by the composite polyline statistical chart and complete the composite polyline statistical chart as required.

2. Enable students to make simple analysis, comparison, judgment and reasoning according to the information in the composite broken-line statistical chart, further enhance the statistical concept and improve the statistical ability.

3. Make students know more about the connection between statistics and real life, and enhance their interest in participating in statistical activities and their awareness of cooperation and communication with others.

Teaching emphasis and difficulty: let students form a preliminary statistical consciousness, and be able to solve problems and analyze the information in the statistical chart by using the composite broken-line statistical chart.

Teaching process:

First of all, memory is the foundation.

1. Displays a bar chart showing the monthly precipitation in Qingdao and Kunming in 2003 respectively.

What do you know from the picture? What if these two statistical charts are combined into one?

2. Composite bar chart showing monthly rainfall in Qingdao and Kunming in 2003.

Tell me what you can learn from the picture. Focus on guiding students to compare the precipitation in two cities. On the characteristics of composite bar graph.

3. What other charts have we learned?

Disclaimer: We have studied the broken line statistical chart. Today, in this class, we will continue to learn the broken line statistical chart. (blackboard writing: statistical chart of broken lines)

Second, learning examples

1, which are single broken line statistical charts of monthly precipitation in Qingdao and Kunming in 2003 respectively.

Question: According to the first statistical chart, what information can be known? Can you talk about the changes of monthly precipitation in Qingdao in 2003 according to the overall shape of the dotted line in the picture? What can you know from the second chart? Answer by roll call.

If you want to compare the precipitation of two cities in 2003, which month is the closest and which month is the most different, what are you going to do?

Guidance: We have studied the composite bar chart before, so can these two charts be combined into a composite line chart?

Summary: As the students said, these two statistical charts can indeed be combined into a composite broken-line statistical chart. (Add "double" before "statistical graph of broken lines" on the blackboard to complete the blackboard writing)

3. Composite broken-line statistical chart showing monthly precipitation in Qingdao and Kunming in 2003.

Question: Can you read this statistical chart? Which broken line represents the monthly precipitation in Qingdao and Kunming? How do you know that? Find out what the legend means.

Enlightenment: From this statistical chart, can we quickly see which month's precipitation in these two cities is the closest and which month's precipitation is the biggest difference?

Follow-up: What do you think? The distance between two points indicating the precipitation in July is the smallest. What does this mean? What does it mean that the distance between two points indicating April precipitation is the largest?

It is pointed out that not only the increase and decrease of quantity can be seen from the composite broken line statistical chart, but also it is convenient to compare two groups of related data.

Further discussion: What information can you get from the pictures?

Guide students to observe and communicate from the changes of monthly precipitation in each city and the similarities and differences of annual precipitation in two cities.

Third, consolidate the practice.

(1) Complete the "practice".

1. Look at the picture and group the dialogues according to the following questions.

2. Organize class exchanges.

(1) Which dotted line in the picture represents the change of the average height of boys? Which dotted line represents the change of the average height of girls?

(2) Does the change in the average height of boys or girls here refer to a boy or a girl?

(3) From the picture, from how old to how old are boys taller than girls on average? At what age are girls taller than boys on average?

(4) How tall are you now? How does it compare with the average height of boys (or girls) of the same age?

(5) What other information did you get from the picture?

(2) Complete the 1 question in exercise 13.

1, students independently review the questions. Question: What does this question let us do? Are you confident to complete the following statistical chart as required?

2. Discussion: Which set of data are you going to draw first? Should this dotted line representing the "highest temperature" be drawn as a solid line or a dotted line?

3. Students draw a dotted line representing two sets of data in the textbook.

Remind students to carefully determine the position of the points representing the daily maximum temperature data and connect the points with solid lines; Then carefully determine the position of the points representing the daily minimum temperature data, connect the points with dotted lines, and don't forget to fill in the drawing date after drawing the dotted lines.

4. Show students' homework, guide mutual evaluation, affirm advantages and point out shortcomings; Then let the students further modify or improve the statistical chart according to the communication situation.

5. Guide students to look at the pictures and answer the questions raised in the textbook, so that students can further understand the characteristics and functions of the composite broken-line statistical chart.

Fourth, the class summarizes.

What knowledge and skills have you learned in this course? What did you get?

What do you think are the characteristics of the composite broken-line statistical chart? What should I pay attention to when completing the composite broken-line statistical chart as required?

The second class practice class

Teaching objectives:

1, so that students can further improve their ability to read and use maps and feel the characteristics of composite broken-line statistical maps.

2. Make students further develop statistical concepts in the process of drawing composite broken-line statistical charts.

3. Enable students to further understand the application of statistics in real life, further feel the value of statistical methods in analyzing and solving problems, and enhance their interest in participating in statistical activities.

Teaching emphasis and difficulty: The information in the statistical chart will be used for analysis, comparison and judgment.

Teaching process:

First, the dialogue reveals the theme.

Last class, we learned the statistical chart of compound broken line. Who can talk about the characteristics of the composite broken line statistical chart?

Answer by roll call. In this lesson, we will continue to learn the composite broken line statistical chart. (blackboard writing topic)

Second, comprehensive exercises.

1, showing P77 question 2.

(1) Students think independently after looking at the pictures: 1999 What kind of mobile phone users are there? What about 2003?

(2) What kind of telephone users are growing rapidly? How do you judge?

(From the trend of broken lines; Calculate the difference between each telephone user in 2004 and 1999, and further check whether the judgment made is correct)

(3) Look at this chart. What else do you think? Student exchange.

2. China's economy is developing steadily and the people's living standards are improving day by day. Show me question 3. (1) What is the statistic of this graph?

(2) In which two years, the number of households with telephones grew fastest? What about the computer? The students think independently and then answer, Q: How do you know? Let the students talk about their own judgment methods.

(3) What else can you think of from the above statistics?

Third, the application of statistical knowledge in life.

1, complete P78 question 4.

Guide students to understand the horizontal axis and vertical axis of statistical chart, and communicate with classmates after completing independently.

According to the data in the statistical chart, the root system of daffodils grows faster. The reason why the growth rate of buds is slower than that of roots is mainly because the germination time is relatively late. But from the eighth day, the growth rate of buds and roots is roughly the same)

We also have our own potted plants in the Agricultural College. Please be a little scientist, observe a plant and make records.

2. Complete question 5 of P78

Discuss and communicate topic by topic, and pay attention to guide students to judge the relationship between the corresponding points in two broken lines.

3. Complete P79 question 6 independently, (1) to guide students to use the legend correctly.

(2) Communicate and evaluate each other, and further master the drawing methods and skills.

(3) Discuss communication problems. Combined with "Why is the temperature change just the opposite?" A student read "Do you know? Let's start with the reason.

Fourth, the class summary

1, guide students to evaluate their learning situation and summarize what they have learned.

2. Complete the related exercises in the workbook.

Unit 8: Fractional addition and subtraction

Title 1: Addition and subtraction of fractions with different denominators (1)

Teaching objectives:

1, so that students can experience the process of exploring the addition and subtraction methods of different denominator fractions and can correctly calculate the addition and subtraction operations of different denominator fractions.

2. Enable students to further understand the internal relationship between mathematical knowledge in the process of exploring the addition and subtraction of fractions with different denominators by combining existing knowledge and experience.

Teaching emphasis and difficulty: can correctly calculate the addition and subtraction of different denominator scores.

Teaching process:

I. Learning examples 1

1, reading questions

2. Query calculation

(1) Question: We have learned the addition of fractions with the same suffix before, so how to calculate the addition of fractions with different denominators?

(2) Group instruction operation: color in half with 1/2 and 1/4 respectively, and then look at the sum of 1/2 and 1/4.

Communication: Can you tell the number of 1/2 plus 1/4 according to the operation?

Follow-up: How do you know that the number of 1/2 plus 1/4 is 3/4? When the colored part is regarded as 3/4, how much is the original 1/2? Think about it. What should I do first to calculate 1/2+ 1/4?

Clear: When calculating 1/2+ 1/4, divide 1/2 and 1/4 into fractions with the same denominator.

(3) Complete the blanks in the example according to the method just discussed.

Talk about students' filling in the blanks and calculating.

Discussion: What knowledge is used in the process of converting 1/2 and 1/4 into fractions with the same denominator? (Basic Properties of Fractions) How to apply the basic properties of fractions to calculate the addition of fractions with different denominators? (Total score)

Second, learn to "give it a try"

1. Students are required to calculate independently.

2. After the students finish the calculation, organize a discussion:

(1) Example learning is the addition of fractions with different denominators, and 5/6- 1/3 is the calculation of fractions with different denominators-(subtraction) (add "sum and subtraction" after "addition of fractions with different denominators" on the blackboard to complete the blackboard writing of this question).

(2) What should I do first when calculating 5/6- 1/3? Think about it, what is the purpose of sharing points? What is 5/6- 1/3? As a result, 3/6 or 1/2 is more concise? How can I convert 3/6 into 1/2?

It is pointed out that if the calculation result can be simplified, the quotation will be the simplest score.

(3) How to calculate1-4/9? How did you come up with the idea of converting 1 into 9/9?

It is pointed out that when calculating the fraction of 1, 1 should be converted into a false fraction with the same denominator as subtraction.

3. Question: Will you check the above two questions? How are you going to check?

After the exchange, ask the students to check their calculations and determine the calculation results of the above two questions.

4. Guide students to summarize the addition and subtraction methods of different denominator fractions.

(1) Requirements: What should I pay attention to when calculating the addition and subtraction of fractions with different denominators?

(2) On the basis of students' full communication, when calculating the addition and subtraction of scores with different denominators, it is necessary to divide the scores first, and then calculate according to the addition and subtraction of scores with the same denominator; The calculation result can be simplified to the simplest score; Consciously check after calculation.

Third, do "exercises"

1, students calculate independently and check as required.

2. Explain the calculation process of 7/ 12+ 1/4, and remind students to simplify the calculation results to the simplest score.

Fourth, do exercises 14, questions 1-4

1, do 1 problem.

Students color as required and write down the numbers.

Please explain with pictures: Why is 1/5+3/5 equal to 4/5? 1/4+3/8 equals 5/8?

Clear: scores with the same score unit can be added directly; However, scores with different fractional units cannot be added directly, and they should be converted into scores with the same unit first, that is, divided first and then added.

Step 2 do the second question

Clear: to calculate the addition and subtraction of fractions with different denominators, it is necessary to divide first, and then calculate separately according to the addition and subtraction method of fractions with the same denominator; If the calculation result can be simplified, the quotation will be the simplest score.

Step 3 do questions 3 and 4

After reading the questions by name, ask the students to calculate independently. After the students answer the questions, tell the process of their thinking and calculation. The fourth question reminds students to choose the right conditions according to the required questions.

Verb (abbreviation of verb) class summary

What is the content of this lesson? Can you tell other students about your experience in calculating the addition and subtraction of fractions with different denominators?

Topic 2: Addition and Subtraction of Fractions with Different Denominators (2)

Teaching content: 82 pages of exercises in the textbook 14, questions 5-9.

Teaching objectives:

1, so that students can master the addition and subtraction of fractions with different denominators correctly and flexibly. Learn to estimate the addition and subtraction of different denominator fractions.

2. Make students further develop mathematical thinking in solving new calculation problems.

3. Make students further feel the challenge of mathematics learning, experience the fun of successful learning and enhance their confidence in learning mathematics well.

Emphasis and difficulty in teaching: the addition and subtraction of different denominator scores can be flexibly estimated according to the actual situation.

Teaching process:

First, review.

1, general practice (oral answer)

5 and 3 10 and 7 9 and 38 and 5 20 and 15 35 and 7.

2, calculation exercise (named board performance)

1/5+3/ 10 3/5-3/8

Second, explore the law.

1. Presentation exercise 14, question 5. Read the questions and observe.

1/2+ 1/3 1/9+ 1/ 10 1/4+ 1/7 1/5+ 1/8

1/2- 1/3 1/9- 1/ 10 1/4- 1/7 1/5- 1/8

2. Through communication and observation, it is found that.

3. Each person chooses two groups of questions to calculate the results and proofread the results.

4. It was discovered after AC calculation.

5. Teacher's summary: The greatest common factor of two scores is 1, and the denominator and numerator are both fractions of 1. The denominator of a number is the product of the original two denominators, and the numerator of a number is the sum or difference of the original two numerators.

6. According to the law, let the students write several groups of such formulas for adding and subtracting fractions, work out the results, and then communicate.

Third, estimate the addition and subtraction of different denominator scores.

1, exercise 14 question 6

(1) Presentation topic: Which of the following scores is close to 0? Which ones are close to 1/2 or 1?

4/7 1/ 10 8/9 2/25 9/20 1 1/ 13 7/ 15

(2) Students communicate after independent thinking and talk about their own thinking methods.

(3) Teacher's summary: The greater the difference between denominator and numerator, the closer the score is to 0; When the numerator is close to half of the denominator, the score is close to1/2; The closer the numerator denominator is, the closer the score is to 1.

2. Exercise 14, question 7

(1) Display questions: first estimate which questions are closer to 1/2, and then calculate.

4/5+2/3 1/ 10+3/7 2/9+ 1/3

5/8- 1/5 3/5- 1/2 1- 1/9

(2) Students communicate after independent thinking and talk about their own thinking process.

(3) Then each person chooses three topics for calculation and verification.

(4) The teacher pointed out that estimating before calculating can improve the accuracy of our calculation and cultivate flexible thinking ability.

Fourth, solve practical problems.

1, exercise 14, question 8

Say the meaning of the picture first, then fill in the blanks, and then calculate.

2. Exercise 14, question 9

Say the meaning first, then estimate and then calculate.

Verb (abbreviation of verb) summary and expansion

Question: Please fill in the corresponding scores in the brackets below.

1/( )+ 1/( )+ 1/( )= 1

Addition and subtraction of the third kind of fractions (1)

Teaching objectives:

(1) Guide students to understand the order of adding and subtracting scores by using existing knowledge, so that they can calculate correctly.

⑵ Cultivate students' analogical reasoning ability.

Teaching emphasis: make students master the operation order of fractional addition and subtraction mixed operation.

Teaching difficulties: understand the calculation method of fractional addition and subtraction, and cultivate students' analogy ability.

Teaching process:

First of all, understand the order of fractional addition and subtraction mixed operations.

(1) Example 2 Understand the meaning of the question.

(2) List the formulas and exchange the reasons for the formulas.

Name the students and say the formula. Health1:1-1/4-1/3 healthy 2:1-(1/4+1/3).

Communication summary: the thinking method of column is the same as that of integer and fraction application problems.

Note: A garden is represented by the unit "1", which is equivalent to the total.

(3) Understand the operation sequence.

Talk about the operation sequence of formulas "1- 1/4- 1/3" and "1-(1/4+1/3)".

Classroom communication, the teacher wrote on the blackboard: add and subtract points, if there are no brackets, count from left to right; If there are brackets, count them first, and then count the outside.

(4) Complete the above calculations independently and exchange answers at the same table.

5] Verify the answer.

Inspection method: check the formula again.

Verification algorithm: the answers of the two methods are the same, indicating that the answers are correct, and one method (formula) is the verification calculation of the other method (formula).

Second, consolidate the practice and initially form the calculation ability.

1, finished practicing.

Complete independently, proofread and communicate, and clarify the meaning of the formula.

2. Exercise 15 Question 1

(1) Students calculate independently, and three people perform.

(2) proofreading and communication, paying special attention to comparing the advantages and disadvantages of various methods.

(3) Teacher's summary:

The operation order of fractional addition and subtraction mixed operation is the same as that of integer, and several fractions involved in the operation can be calculated by division step by step; You can also calculate it once. The score of the intermediate process will be segmented in time if it is easier to segment first and then participate in the operation. How to calculate it is simple.

3. Exercise 15, question 3

Answer the first two questions after you understand the meaning.

Encourage students to ask different problems of fractional addition and subtraction according to the known conditions in the questions, which can be calculated in one step or two steps, and let students try to solve some of the problems raised.

4. Exercise 15 Questions 4, 5 and 2

Students exchange proofreading after completing independently.

Fourth, summary.

What is the content of this lesson? Can you tell other students about your experience in calculating the mixed operation of addition and subtraction fractions?

The fourth quarter fractional addition and subtraction mixed operation (2)

Teaching content: Exercise 5- 10 on page 85 of the textbook.

Teaching objectives

1, so that students can further master the mixed operation of fraction addition and subtraction.

2. Make students understand the operation law of integer addition and the operation nature of subtraction, which is also applicable to fractional addition and subtraction, and can apply the operation law or operation nature to some simple operations of fractional addition and subtraction.

3. Make students further feel the challenge of mathematics learning, experience the fun of successful learning and enhance their confidence in learning mathematics well.

Teaching emphasis: we can correctly apply the algorithm or the nature of operation to perform some simple fractional addition and subtraction operations.

Teaching difficulty: reasonable choice of simple algorithm.

First, oral calculation.

Exercise 15 question 5

Proofread after collective oral calculation, and ask the students who made mistakes to explain the reasons for the mistakes.

Second, use a simple method to calculate the following problems

(3/8+ 1/ 12) 2/3- 1/4- 1/4 5/6+2/5+ 1/6+3/5 5/9+(4/5+4/9)

1. It is pointed out that the law of integer addition operation is also applicable to fractions, and the nature of integer subtraction operation is also applicable to fractions.

2. Students are independent and perform on six boards.

3. Exchange calculation methods, applied knowledge and calculation results.

(1) additive associative law; (2) additive commutative law; (3)(4) The nature of subtraction operation; (5)(6) additive commutative law and the law of association.

Third, solve the equation

1. points out that x in the equation can be not only an integer or a decimal, but also a fraction.

2. Students finish independently, and three people perform.

3. Exchange calculation methods, applied knowledge and calculation results, and ask the wrong students to talk about the reasons for their mistakes.

Fourth, solve practical problems.

1, exercise 15, question 10.

After students finish independently, exchange the meaning and results of the formula and emphasize the unit "1".

2. Revision exercise: Revise "Xiaohua investigated the gifts given to * * * by the whole class on Mother's Day" to "Xiaohua investigated the gifts given to * * * by 30 students on Mother's Day".

(1) How to solve the problem?

(2) Why is the method unchanged?

Emphasis: In the two questions, as long as the class size is regarded as the unit "1", and 1/3 for flowers and 1/4 for greeting cards are removed from the unit "1", the rest is that the number of people who send pictures accounts for a few percent of the class size, and the questions asked have nothing to do with the actual total class size.

Verb (abbreviation of verb) summary and expansion

Complete the thinking questions in the book.

1, find the law after calculation.

2. Write numbers directly by applying laws.

3. Self-made addition formula by law.

Practice ke Jing Cai graphic mipu

Teaching content: 86-87 pages of the textbook.

Teaching goal: to observe, operate, think and design simply according to the characteristics of plane graphics. Through activities, students can further understand the characteristics of plane graphics, feel the challenge of mathematical activities, cultivate innovative consciousness and aesthetic taste, and experience the wide application of mathematical knowledge and methods in life.

The focus of teaching is to initially understand what is graphic dense shop and know which floor plans can be dense shop.

Teaching difficulties: designing simple and dense patterns.

Teaching process:

I. Observation and understanding

1, show pictures,

Observe carefully.

2. Communication:

What graphics are laid on each floor or wall?

How are these numbers arranged together?

3, clear:

4. Example: Can you give some similar examples?

Second, thinking and operation