Compared with the addition and subtraction of fractions with the same denominator, the addition and subtraction of fractions with different denominators are more commonly used to solve practical problems. Therefore, it is the focus of the score addition and subtraction unit and the whole textbook. This section is taught by students after learning the total score, the reciprocity between fractions and decimals, the addition and subtraction of fractions with the same denominator, and understanding the addition and subtraction operations of numbers with only the same unit. The teaching content is relatively simple, which is suitable for students to try to experience teaching independently.

Teaching content: People's Education Publishing House, Volume II, No.5, p 1 0 ~112, p.1page.

Teaching objectives:

1. Make students master the addition and subtraction of different denominator fractions through teaching; Cultivate the habit of checking calculations;

2. Infiltrate ideas and cultivate students' ability to solve problems with old knowledge. And the ability of analysis, judgment and induction;

3. Let students feel the joy of success through learning and receive environmental education.

Teaching emphases and difficulties:

Guide students to master the addition and subtraction of different denominator fractions, and be able to calculate and apply them skillfully and correctly.

Teaching preparation: PPT courseware

Teaching process:

Dialogue between teachers and students, asking questions and revealing topics.

1. Recall old knowledge and pave the way.

Teacher: Some time ago, we were all studying grades. (blackboard writing: fractions) What have we learned about fractions?

[By recalling, arouse students' memories of old knowledge and pave the way for new lessons. ]

Step 2 introduce fun and ask questions

(1) Students report their simplest scores.

Teacher: Now, close your eyes and think of the simplest score you like. Are you ready? Who will say one? (Write it on the blackboard in time)

[Close your eyes and think of the simplest score you like, which is fresh and interesting, and arouse students' enthusiasm for learning. ]

(2) Students ask research questions.

Teacher: If you choose these two scores, what can you study? Today, we will continue to learn fractional addition and subtraction. Blackboard writing: addition and subtraction

Einstein said: It is greater to ask a question than to solve it. Guide students to ask their own questions and cultivate their ability to ask questions. ]

3. Combination formula, cultivate ability

(1) combination formula

Teacher: Please look at the blackboard. Of these three fractions, (circle two fractions with different denominators, and then circle a fraction that can be converted into finite decimals), choose two to form an addition and subtraction formula and write it in a notebook. Just write the formula, you don't have to work out the answer. )

[It is challenging to choose two of the three scores to form an unknown formula, and at the same time, it exercises the students' combination and collocation ability]

2 Report formula:

4. Guide the comparison and reveal the topic.

Teacher: Look at these formulas carefully. What's the difference from what you just learned? Next, we will learn the addition and subtraction of fractions with different denominators. Blackboard Writing: Different Denominators

By introducing this link, teachers can creatively deal with teaching materials, change the traditional way of giving examples and stimulate students' interest in learning. In the whole process, students' learning initiative is fully exerted. ]

Second, explore independently, try to experience and obtain methods.

(A) questioning the problem, infiltration methods

Teacher: According to past study experience, what should I do if I encounter new problems? .....

Infiltrate the idea of mathematical transformation and teach students the method of learning. ]

(B) the first attempt, experience method

Teacher: Then please choose the first one to do it.

1. Students try independently.

2. Report the results. Teacher: Who can tell me? )

Two situations:

A: Divide into fractions with the same denominator before adding and subtracting. If there is no process, the teacher should remind the students to write out the process. )

Total research score

Teacher: (pointing to the general process. ) What are we doing this step? Why do you want to divide it? (Emphasis: Addition and subtraction can only be performed if the counting units are the same. )

B: decimal system.

Teacher: Whose method is different? (The blackboard student answers: How does he (she) calculate? Final comparison: this decimal is a fraction. )

3. Summarize various methods

Teacher: The students in our class are really amazing! Fractions with different denominators are converted into the addition and subtraction of fractions with the same denominator or the addition and subtraction of decimals. Below, we use these two methods to calculate the second question (which can still be reduced to a finite score).

(3) Try again and get familiar with the method (calculating the second question)

1, students try independently.

2. Report the results.

(d) Three attempts to optimize the method.

1. Ask questions.

Teacher: If it is these two scores (if you connect them, there will be a score that cannot be reduced to a finite score), how can you find their sum?

2. Feedback communication.

Teacher: Who will give the feedback and write it on the blackboard? Follow-up: Is there a decimal calculation? What did you find?

[The exploration of the above teaching links adopts the method of trying to teach, which gives students the initiative to learn and allows students to try to get the addition and subtraction of scores with different denominators. First, the first attempt makes students come to the conclusion that the addition and subtraction of fractions with different denominators should be converted into the addition and subtraction of fractions with the same denominator and the addition and subtraction of decimals. The second attempt made students familiar with and strengthened the method, and the third attempt caused cognitive conflict. The method leading to the total score is more general. The algorithm is optimized. ]

(5) Optional calculation and merging methods.

Teacher: Next, choose a topic in your notebook in your favorite way, and pay attention to the format!

Report feedback (student oral answer form)

【 Practice again on the basis of students' optimization algorithm, which plays a solid and effective role. ]

(six) to guide the calculation and cultivate habits.

Teacher: I wonder if I did it right? How to check? (Check the last question) The students said that the teacher was writing on the blackboard.

[Check teaching, let students develop rigorous study habits. ]

Third, review the classroom, organize knowledge and enhance awareness.

Teacher: Think back, what did we learn today? How to calculate? What do you think should be reminded to ensure the correct calculation?

[The design of class summary includes the summary of knowledge and the reminder of study habits and skills. It is scientific, reasonable and comprehensive. Can enhance students' consciousness of careful calculation and paying attention to checking calculation]

Transition: It seems that our classmates in class X study really well! The teacher really admires you! Now, let's gather together and see what problems today's knowledge can solve. Please look at the big screen.

Fourth, combine practice, apply knowledge and improve ability (courseware)

1. Life problems:

Ask questions and list formulas according to the information in the picture.

The garbage that people produce in their daily life is called domestic garbage. What information did you find from the picture? How do you feel? According to the information in the diagram, can you ask different questions and calculate in parallel?

【 Exercise is close to life, friendly and natural. It cultivates students' ability to discover information, process information, ask questions and solve problems, and enables students to receive environmental education. ]

2. Contrast questions:

Right and wrong court. Item by item display

2/3-4/9=2/9( ) 7/ 10-3/5=4/5( )

3/5+4/7=7/ 12( ) 1/2+3/7= 13/ 14( )

Teacher: That's right. Could you please tell me how to calculate it? Explain the cause of the error.

[Right and wrong judgment, sharp contrast, deepen the understanding and mastery of new knowledge. ]

3. Expansion problem:

See who can calculate quickly.

First, find the law

(1) The teacher gives a question and the students do a question (the type of the question is 1, and the denominator is the addition and subtraction of two coprime fractions, such as1/3+1/41/6).

(2) Ask students to write questions (after 4 questions)

The teacher asked: can you say a few formulas like the teacher? Students say, others answer.

Follow-up: Why do some people calculate so fast? What's the mystery? Would you please observe these formulas carefully? What did you find?

B, application rules

The content of the instructional design article "Addition and subtraction of different denominator fractions" you are reading now is from! This website will provide you with more excellent teaching resources! Let students learn the teaching design rules of adding and subtracting different denominator scores in the trial experience: teachers ask questions and students answer them; The students asked each other questions.

[Finally, this extended question allows students to calculate the experience first and then find the rules, which is in line with students' cognitive characteristics, challenging and easy to stimulate students' interest. It can not only consolidate new knowledge, but also cultivate students' analytical and inductive application ability.

Design concept:

1. Change the presentation of examples to stimulate students' interest.

The presentation of the example is not simple and direct, but designed: I want to like the simplest score and give it to the simplest score. Then I put forward my own research problem to study the addition and subtraction of scores, and then I choose two of the three scores to form the addition and subtraction formula. Finally, I naturally lead to the research on the addition and subtraction of fractions with different denominators. Through this kind of teaching, let students participate in the presentation of examples, let them feel that they are discoverers and explorers, and experience the joy of success. It not only cultivates their questioning ability, but also exercises their comprehensive mathematics quality. Stimulated their interest in learning.

2. Try to experience and build knowledge independently.

As the saying goes, you don't know what to do until it's on paper. It can be seen how important it is to try and experience yourself. The famous educational psychologist Suhomlinski also published a theory about students' learning needs. In fact, for students, the knowledge gained through their own attempts is the real knowledge. They have mastered it more easily and deeply. In this design, considering the structural characteristics and difficulty of the textbook, when exploring the addition and subtraction methods of different denominator scores, the teaching method of trying to experience is mainly adopted. In the first attempt, according to their own learning experience, students can easily get the result that the addition and subtraction of fractions with different denominators can be converted into the addition and subtraction of fractions with the same denominator (that is, general fractions) and the addition and subtraction of decimals. Some people may also mention points; Explain the method of sharing points while affirming; Then, make a second attempt, the main purpose is to consolidate and strengthen the previous methods; At this point, students have thought that the addition and subtraction of fractions with different denominators can be calculated like this. Then, the third attempt is made to select two scores whose single scores cannot be converted into finite decimals from the simplest scores reported by students and find their sum. Because of the characteristics of the topic itself: it can't be converted into finite decimals, students naturally adopt the method of dividing points. Then, create a questioning situation at this time: Is there a decimal? What did you find? Thanks to three personal experiences, it seems natural for students to draw and optimize the addition and subtraction methods of different denominator fractions.

3. Pay attention to comparative transformation and cultivate mathematical methods.

Comparison and transformation are two very important methods to learn mathematics. It is easier for students to deepen their understanding and mastery of knowledge in comparison, to realize the integration of old and new knowledge in transformation, and then to obtain methods. For example, in this design, when students list all the formulas, they design a question: What is the difference between these formulas and the knowledge they just learned? This question can not only arouse students' understanding of what they have just learned, but also make them compare with the new knowledge now. It is easy for students to come to the conclusion that scores in today's study are characterized by different denominator scores. Then, a question is designed: according to the previous learning experience, what should I do if I encounter new problems? Mathematical thought of infiltration transformation. Under the guidance of teachers, students can quickly find the connection point between old and new knowledge through memory. Then get the method. In addition, after students explore the solutions of adding and subtracting different denominator fractions, they design the third attempt experience. After comparison, the method that students can get the total score independently is more universal. Thereby deepening the impression of the total score method.