Fraction addition and subtraction, mixed operation, lecture notes 1, 1, teaching materials
I said that the content of the class is the content of the first volume of the sixth grade mathematics of the People's Education Edition: the score of elementary arithmetic. Students are already familiar with the operation order of integer and decimal elementary arithmetic. When teaching the addition, subtraction, multiplication and division of fractions in this book, there have been some problems of two-step mixed operation. Based on this, this course teaches the elementary arithmetic problem of calculating fractions in three or four steps. Therefore, when the textbook talks about fractional elementary arithmetic, it does not explain the operation order in detail, but directly explains the same order as integer elementary arithmetic. Then use cases 4 and 5, let the students talk about the operation order and let the students calculate the results themselves. Mastering this part will lay a good foundation for studying elementary arithmetic of fractions and decimals and its application in the future.
Second, talk about teaching objectives
According to the actual situation of students and the requirements of the new curriculum, I have set the following teaching objectives for the teaching content of this class:
1, knowledge and skills: students master the operation order of fractional elementary arithmetic and can calculate it correctly.
2. Process and method: Through the four steps of "seeing, thinking, calculating and checking", students can correctly calculate fractional elementary arithmetic, and cultivate good study habits such as careful examination of questions and careful inspection.
3. Emotion, attitude and values: Infiltrate the logic of calculation into students through calculation connection, stimulate students' desire for knowledge interactively, and let students learn creatively in a democratic, harmonious and active classroom atmosphere.
Third, pressure and difficulty.
This lesson focuses on the operation order and correct calculation of fractional elementary arithmetic, in which multiplication and division with fractions is the difficulty in teaching.
Fourth, talk about teaching methods and learning methods.
Focusing on the above teaching objectives and the actual situation of students, the teaching method I adopted is based on the "inquiry-discussion" method to form a multi-directional communication classroom atmosphere. Teaching in the form of "stressing support" organically combines the explanation of arithmetic with students' independent practice. Using this teaching method, teachers' leading role is brought into play, and students' main position is reflected, that is, imparting knowledge and cultivating ability.
Students can improve their unique teaching methods through calculation exercises [], independent thinking and group cooperation and mutual evaluation activities. Through flexible and interesting exercises, students' problem-solving ability is improved, and various effective problem-solving methods are sought.
Fifth, talk about the teaching process.
First, review lesson preparation and introduce new lessons.
1, show the elementary arithmetic problems of integers and decimals, and let the students recall the operation order. It is emphasized that product sum quotient can be calculated at the same time.
2. calculation. After calculation, guide students to observe and write comprehensive formulas. What's the difference between it and the exam preparation questions, so as to reveal the questions and write "fractional elementary arithmetic" on the blackboard. The operation order of definite fraction elementary arithmetic is the same as that of learned integer elementary arithmetic. Call new knowledge with old knowledge to promote knowledge transfer. It helps students to build their own knowledge structure, deepen their understanding and form certain skills.
Second, independent exploration, cooperation and exchange.
For the teaching of examples, I boldly adopt the method of letting students explore and try to solve problems independently. Most of the teaching content in grade six is not interesting, so students need to be interested in themselves if they want to be "passionate" about learning. "Attention is the gateway to knowledge" and "Interest is the best teacher" is enough to see the importance of interest. Grade six students like challenges and the joy of success after trying to solve problems by themselves, which can greatly increase students' interest in learning. This effect can be achieved by independent exploration and solving examples. After the students finish speaking, give feedback and talk about the operation process of a student's oral answer (written by the teacher on the blackboard). Guide students to practice through four steps: "look, think, calculate and check". Look, see clearly the numbers and operation symbols in the topic; Second, think about what to calculate first and then what to calculate, and how to calculate it reasonably and concisely; Third, the writing format is correct and the calculation is meticulous; Four checks, step by step, step by step. It is worth mentioning that when doing exercises, students are not only required to solve problems according to the above four steps, but also encouraged to check each other. The whole process pays attention to students' independent inquiry and cooperative communication, and guides students to observe and communicate in time during the calculation process, which makes students highly motivated. We know that mathematical knowledge is colorful and sometimes complicated. It is important for primary school students to check carefully in their calculations. According to these four steps, the error rate of students can be greatly reduced. Students' mutual checking activities aim to improve the space for mathematical communication among students, so that each student has the opportunity to fully express his ideas and experience the happiness of successfully solving mathematical problems. At the same time, it cultivates students' thinking quality and improves their cooperation and communication ability.
Third, practice feedback and consolidate sublimation.
This lesson is mainly to let students master the operation order of fractional elementary arithmetic and calculate it skillfully and correctly, so I designed the following exercises at different levels according to the principle of "from shallow to deep, step by step".
1, basic exercises Let students sort out their own thinking process by doing some questions similar to the examples in the book, so as to rise to a rational height and learn to solve problems correctly. Develop your thinking ability and language expression ability through mutual evaluation and speaking.
2, improve exercises, such as three-step calculation of scores, elementary arithmetic problems, application problems, etc. Increase the difficulty and improve it from different levels of practice.
Fourth, summarize the problems and extend after class.
Guide students to self-evaluate the learning situation of this class, sum up problems, experience the sense of success in learning, enhance self-confidence and motivate students to learn mathematics well. (Assigning homework after class)
In my whole teaching process, I tried to run through two concepts of education, namely subjectivity and activity. Teachers provide students with sufficient time, space and conditions to think, solve problems, communicate and evaluate each other. Students have both explicit communication activities and implicit thinking activities. In teaching, I not only attach importance to knowledge and skills, but also attach importance to students' emotions and make an encouraging evaluation of students' performance. Students' thinking is alive, their emotions are rich, and their sense of cooperation is enhanced!
The influence of the mixed operation of fraction addition and subtraction on the teaching goal of the second lesson
1, so that students can get in touch with specific problem situations, understand and master the operation sequence of fractional addition and subtraction mixed operations, and can correctly perform fractional addition and subtraction mixed operations.
2. Enable students to solve some simple practical problems by adding and subtracting fractions, further improve students' ability to solve practical problems and cultivate students' awareness of mathematical application.
3. Enable students to gain a successful experience in learning activities and enhance their self-confidence in learning mathematics.
Teaching focus
Combining with specific problem situations, we can understand and master the order of fractional addition and subtraction mixed operations, and can correctly perform fractional addition and subtraction mixed operations.
Teaching difficulties
Students learn to analyze the quantitative relationship of practical problems, such as "1" as the unit of the total, and how much the rest accounts for the total, and learn to solve such practical problems by fractional subtraction or mixed operation of addition and subtraction.
Teaching process:
First, show the following picture:
1, estimate the score of each part in the total.
2. Think about it: What questions can you ask?
Second, implement the new curriculum.
(a) Show examples:
There is a garden in the campus of Hongshan Primary School, in which the rose area is 1/4, the azalea area is 1/3, and the rest are lawns. What is the area of the lawn?
(B) Let students answer independently
(c) Choose a typical solution for students to act out.
1- 1/4- 1/3 1-( 1/4+ 1/3)
Let the students talk about their ideas.
(5) Let students calculate independently.
Q: What was your experience in answering this question?
(7) Summary: The order of elementary arithmetic of integers and decimals is also applicable to the calculation of fractions.
Third, deepen understanding with knowledge.
(1) Calculate the following problem
5/9+2/3-2/5 1-( 1/2+ 1/6)
1, students calculate independently.
2, roll call board, collective evaluation (pay attention to let students feel different algorithms)
(2) Answer the following questions.
1. There is a piece of cloth 2 meters long. It took 2/5 meters for the first time and 1/3 meters for the second time. How many meters are left?
2. There is a piece of cloth with a length of 2 meters, which was used for 2/5 for the first time and 1/3 for the second time. How much is left useless?
Fourth, the summary of this lesson
What did you get from this lesson?
Mixed operation of fraction addition and subtraction and the teaching goal of the third lecture
Knowledge and ability: understand the meaning of mixed operation and cultivate students' ability of transfer, analogy, induction and generalization.
Process and method: Understand and master the order and method of adding and subtracting scores.
Emotional attitude and values: experience the wide application of fractional addition and subtraction in life and production.
Emphasis and difficulty in teaching
Teaching emphasis: master the order and calculation method of fractional addition and subtraction mixed operation.
Teaching difficulty: fractional addition and subtraction in mixed operation.
teaching tool
courseware
teaching process
First, check the import:
Tell the results of the following questions directly.
2. Say the operation order first, and then calculate.
1 12+8- 13 16-4+2 1 16-4+2 1
Operation sequence of integer addition and subtraction mixed operation:
If there are no brackets, it is calculated from left to right; If there are brackets, count the inside of the brackets first, and then the outside of the brackets.
Second, explore new knowledge.
Introduction to the new lesson: In this lesson, we will learn a new content-the mixed operation of fraction addition and subtraction.
(blackboard title: mixed operation of fractional addition and subtraction)
(1) Teaching example 1 (formula calculation method without brackets)
Guide learning, solve doubts and explore in cooperation;
1. Example 1:
Student report:
(1) Express the contents of the example 1 in your own language.
(2) Question 1: How much is the forest part relative to the grassland part? What does the forest part of the book refer to? How to form?
(3) Which do you prefer, the step-by-step total score or the one-time total score?
(4) Question 2: Compared with precipitation, how much groundwater is stored in "bare land"? What is the unit "1" in the book? What does 7/20 mean?
(5) What's the difference between the methods of comparison of improved varieties after listing? How to calculate the fraction with brackets in mixed operation?
2. Summary: The mixed operation of fractional addition and subtraction is the same as the mixed operation of integer addition and subtraction, and it is also calculated from left to right. If there are brackets, they should be counted first.
question
Third, consolidate the practice.
1. Basic questions:
Complete "Do it" on page 1 18.
Page 120, exercise 1-4, a total of 23.
2. Expanding exercises:
homework
Finish the exercises after class.
Mixed operation of fraction addition and subtraction: the teaching goal of the fourth lecture
1. Through teaching, students can master the order and calculation method of fractional addition and subtraction mixed operation, and can correctly calculate fractional addition and subtraction mixed operation.
2. In the process of exploring knowledge, cultivate students' ability of knowledge transfer, analogy and induction.
3. Cultivate students' habit of calculating carefully and solving problems with concise and flexible methods.
Emphasis and difficulty in teaching
Emphasis: the order and calculation method of fractional addition and subtraction mixed operation.
Difficulties: Flexible selection of calculation methods and correct calculation according to the operation sequence.
teaching process
First, the introduction of scenarios, review memories
Courseware demonstration:
1, calculating
2. Solve the equation
After independence, the students answered.
3. Show the Yunmeng scenery map of Hubei Province and the landform statistics map of Yunmeng Forest Park.
Teacher: Now the teacher will take you to see a beautiful scenic spot (show pictures). This is Yunmeng Forest Park in Hubei Province. There are mountains here and the scenery is beautiful. The forest is full of tall trees, low shrubs and large grasslands.
This is the statistical table (exhibition form) of Yunmeng Forest Park. What mathematical information do you find from this statistical table? Who else would say? Please say it first, and then read it together. )
Health: arbor forest accounts for12 of the park area, shrub forest accounts for 310 of the park area, and grassland accounts for15 of the park area.
Teacher: Let's draw this information into a fan-shaped statistical chart and draw a fan on the blackboard. Based on this information, you can ask some math questions orally and choose one to answer in your notebook. (feedback, according to the students' answers to the teacher's blackboard formula. )
Step 2 ask questions:
Teacher: How much of the park area does the forest part occupy than the grassland part? Can you make a formula? Is there any other way? ( 1/2+3/ 10— 1/5 1/2- 1/5+3/ 10 3/ 10- 1/5+ 1/2)
3, lead to the topic
Contrast: What's the difference between these formulas and those just now? (leading topic: mixed operation of fractional addition and subtraction)
Second, explore independently and gain new knowledge.
1, for example 1( 1): mixed operation of fractional addition and subtraction without brackets.
Teacher: How to calculate these formulas? Can you choose two of them and use what you have learned to calculate?
(1) Try to calculate
(2) Feedback
Feedback: A. What is the idea of solving the problem first? (Name said, deskmate said)
B. What do you find by observing the operation sequence of these three calculation methods? According to the students' answers, it is concluded that the order of the mixed operation of addition and subtraction of fractions without brackets is calculated from left to right. )
C, what should be paid attention to in the calculation?
(3) The teacher emphasizes the writing format and matters needing attention: using recursive equation to calculate, all equal signs are aligned, and the scores are on the same straight line; Note that the final result should be the simplest score.
2. Example 1(2): mixed operation of fractional addition and subtraction with parentheses.
Excessive language: what benefits will forests bring to the environment? This Yunmeng Park is located in the middle and lower reaches of the Yangtze River, with abundant rain (rain dynamic map). What has such a rich deposit become? Let's look at the table and read together: "Statistical comparison of precipitation transformation between forest and surrounding bare land".
Teacher: Read this form carefully and tell me what you understand. Let the students read the table first, and then guide them to understand the meaning of the table. )
(1) After precipitation, what are the forms of rainwater stored in the forest, such as groundwater and surface water? (7/20, 1/4, 2/5) Who is the unit "1"?
(2) ask questions:
Let's take a look at the transformation of precipitation on the surrounding bare land: surface water 1 1/20, and the other 2/5. So how much of the precipitation is groundwater stored on the bare land? Think about how to answer first, and then write it down in your notebook.
(3) try to solve
(4) Feedback evaluation (two methods are shown in the courseware)
Ask the students who are performing on the board to talk about solving problems. Compare the two methods again: What did you find?
Use parentheses to emphasize the mixed operation order of fractional addition and subtraction. (Finally emphasize the answer)
(5) Infiltrate emotional education
Teacher: We know that surface water and other forms of rain generally evaporate after the rain clears, and only groundwater is stored. Compare the groundwater reserves between forest and bare ground?
What do you want to say when you find this situation? (Infiltrating environmental awareness)
Conclusion: You speak very well. Our classmates should take actions in their daily lives to green the environment and protect water resources together.
3. Summarize the order of fractional addition and subtraction mixed operations.
Teacher: What's the order of fractional addition and subtraction through the study just now?
After thinking independently, communicate in groups.
Induction: Fractional addition and subtraction mixed operations and integer addition mixed operations are in the same order, and they are calculated from left to right. If there are brackets, they should be counted first. (Write an example on the blackboard: count from left to right in brackets) Tips: What if the calculation result is not the simplest score?
Teacher: The knowledge learned today is on pages 1 17 to 1 18. Please open the book and have a look.
Third, consolidate the application.
Excessive language: the students have mastered the order of addition and subtraction of scores, and now the teacher will test you.
1, calculated by recursive equation. Let's talk about the operation order of the following questions first, and then calculate.
2. Use the knowledge learned today to solve some practical problems in life.
(1) Are there more students cleaning the blackboard and glass than sweeping the floor? How much more?
(2) Excessive language: each student's time in a day will be allocated in the following aspects: (demonstration exercise) Reading time accounts for () of the time in a day, eating time accounts for (), playing time accounts for (), and sleeping time accounts for? Will you beg? How much time does a person sleep every day?
Teacher: Actually, according to the latest report of experts, the sleep time of primary school students is 10 hour, which is more conducive to your growth and development. Remember to go to bed early at night.
Teacher: Students are really capable. These problems are easy to solve. The teacher asked a difficult question: (3) Are there more students staying at home than going out? How much is missing?
Fourth, the class summarizes.
What did you learn from today's study? What should I pay attention to?
Mixed operation of fractional addition and subtraction;
1. Through teaching, students can master the order and calculation method of adding and subtracting fractions, and the order and algorithm of adding and subtracting fractions in brackets.
2. Cultivate students' abilities of transfer, analogy, induction and generalization.
3. Make students form the habit of solving problems with simple and flexible methods.
Key points and difficulties:
Master the order and calculation method of fractional addition and subtraction mixed operation.
Teaching process:
First, check the import.
1.
1/6+5/6
4/7-2/7
2/9+4/9
9/ 10-3/ 10
1/2+ 1/3
1/8+ 1/8+3/8
2. Do the math.
100+25- 18
75-25+ 15
24-( 18+3)
Students calculate and ask questions after they finish.
3. reveal the topic.
We learned the addition and subtraction of fractions and mastered the calculation rules of fractional addition and subtraction. In this lesson, we will learn the mixed operation of fractional addition and subtraction.
Blackboard writing: mixed operation of fractional addition and subtraction
Second, the new teaching
1. Show the form of the example on page 97 of the textbook 1
(1) Let the students read the form and express it in their own language.
(2) The teacher showed me the first question: How much is the forest part more than the grassland part?
(3) Question: What does the forest part mean? How to form?
Blackboard:1/2+3/10-1/5
(4) Let students try to calculate and exchange calculation methods collectively.
The teacher made a tour and asked students with different algorithms to perform.
Ask the students to compare these two calculation methods, see which one is simpler, and decide which one they like.
(5) Summary calculation method: When calculating the mixed operation of addition and subtraction of scores, the scores can be divided step by step or once. You can choose the method flexibly according to the characteristics of the topic and your own situation.
2. Give the second question of the example 1: What percentage of the groundwater stored on the bare ground accounts for the precipitation?
(1) Let the students understand the contents of the form first, and then the teacher asks: What is the unit 1 in this question? What does 7/20 mean?
(2) Ask students to list the formulas.
1-11/20-2/5 or1-(11/20+2/5)
(3) Let students try to calculate, say and act out the calculation process of these two methods.
Q: What's the difference between these two methods? How to calculate the mixed operation of fractional addition and subtraction with brackets?
The Mixed Operation of Fraction Addition and Subtraction —— On the Teaching Objectives of Lecture 6
(1) To understand the mixed operation of fractions and decimals, we should choose a reasonable and correct calculation method according to the specific situation of the topic.
(2) Cultivate students' habit of analyzing specific problems.
Teaching emphases and difficulties
Choose a reasonable and correct calculation method.
training/teaching aid
Teaching AIDS: slides, cards.
Learning tool: feedback card.
Teaching process design
Review preparation
1. Extract the following score. (Dictation card)
2. Decimal following components. (Dictation card)
3. Which of the following fractions can be reduced to a finite fraction? What can't be converted into finite decimals? (Students use feedback cards. If you can tick, you can't tick. )
4. How to judge whether a fraction can be reduced to a finite decimal?
Teacher: We learned the addition and subtraction of decimals and fractions. If fractions and decimals appear in the same question at the same time, how to calculate them? This lesson will learn these contents. Teacher's blackboard topic: mixed operation of fraction and decimal addition and subtraction.
Learn a new course
1. The score in the topic can be reduced to a finite decimal.
Teacher: Think about it. How are you going to calculate this problem?
After the students answer, please answer according to your own ideas. Please write it on the slide. )
(2) Select several students' slides for evaluation. When selecting slides calculated by different methods, the calculation is wrong.
First, evaluate the wrong calculation, find out the cause of the error, and then project the correct calculation:
Teacher: Please tell the two students who did this problem about their own algorithms:
Teacher: Comparing these two algorithms, which is simpler? Why?
After the students answered, the teacher wrote under Example 4 on the blackboard:
Solution 1: Decimal score.
Option 2: Fractions and decimals are more convenient.
(3) Write the following questions by hand: (Please write some slides. )
Please observe after modification: Observe the scores in the above questions. What are the same characteristics? After the students answered, the teacher wrote on the blackboard at the bottom of Example 4: The score can be reduced to a finite decimal. Teacher: Tell me clearly, what did you learn from doing this set of questions? After the students answered, the teacher concluded that if the score can be reduced to a finite decimal, it is easier to choose to reduce it to a decimal.
2. The score in the topic cannot be reduced to a finite decimal.
Teacher: Look at the score of this question. What's the difference between the score in Example 4 and that in Example 4?
Teacher: What method should be used to calculate this problem? Please have a try. Ask some students to write slides. )
(2) Select several slides written by students to evaluate and find out the causes of calculation errors.
Teacher: Why not use fractions and decimals to calculate this problem? (teacher writes on the blackboard: decimal fraction. )
After the students answered, the teacher wrote down on the blackboard that some scores could not be reduced to finite decimals.
Teacher: Calculation questions generally require accurate results and cannot be approximated at will, but if the questions allow approximations, such questions can also be calculated by fractions and decimals. For example, this question:
Teacher: Please tell me when to use "√" and "=" during peeling.
After the students answer, the teacher will explain: in the calculation, which step is approximate, which step uses "√" and which step uses "=".
(3) Look at the score characteristics of each question before calculation. (On the notebook, modify collectively. )
Teacher: Tell me about your experience in doing this group of questions.
After the students answer, the teacher completes the blackboard: when some scores in the topic cannot be reduced to finite decimals, they should generally be calculated by fractional components.
Calculation exercise: (Let some students write slides. )
(3) Integrated feedback
1. Group the following formulas. Group A is the one that you think is easy to convert fractions into decimals. Those who convert decimals into fractions are in Group B, and put A or B in brackets after the questions. (projection)
Please choose an appropriate method to write the first step of the operation. Please write it on the slide. )
3. Calculate the following questions. Ask several students to write down each question on the projection board. )
4. Discuss with the students' slides.
(d) class summary and homework
1. How to choose a suitable calculation method?
Teacher's blackboard writing: analyze specific topics and choose appropriate methods for calculation.
2. Homework: Exercise on page 15 1 in the textbook.
Description of classroom teaching design
Decimal, decimal addition and subtraction mixed operation, is decimal, decimal mutual; Comprehensive application of decimal, fractional addition and subtraction knowledge. For different topics, it is better to choose fractional calculation or decimal calculation, so the teaching choice in this section allows students to calculate and discuss according to the topic group, with the aim of allowing students to gain some judgment on the overall situation, choose algorithm experience, improve their ability to examine questions, and at the same time let students realize that the most important thing is concrete analysis of specific problems. In the whole learning process, arrange students to analyze and discuss right and wrong issues, help students improve the accuracy of calculation and develop good habits.