Teaching plan of addition algorithm in the fourth grade of primary school

Teaching plan 1 of addition algorithm in the fourth grade of primary school

People's Education Press Primary School Mathematics Grade Four Volume II P27——32.

Textbook analysis

The textbook leads to questions through the distance that Uncle Li rode, teaching the exchange law first, and then the association law; Teach the meaning of the algorithm first, and then teach the application of the algorithm. This arrangement has three advantages: first, from easy to difficult, it is convenient for teaching. The content of commutative law is simpler than associative law, and students have richer perceptual knowledge of commutative law than associative law. Teaching the easy switching law first is helpful to stimulate students' interest in exploration. Secondly, it can improve teaching efficiency. The teaching methods and learning activities of the switch method can be transferred to the associative law to promote students' active learning. Thirdly, it conforms to the cognitive law. Understand the meaning of the algorithm first, and then apply the algorithm to do some simple calculations. It can be seen that the purpose of discovering the algorithm is to master and apply it.

Teaching objectives

Knowledge and ability

Enable students to understand and master additive commutative law and the associative law of addition, and express additive commutative law and associative law in letters.

Process and method

Make students experience the process of exploring additive commutative law and the law of addition, make comparative analysis, and discover and summarize the operation rules.

Emotion and attitude

Make students gain successful experience in teaching activities, further enhance their interest and confidence in mathematics, and initially form the consciousness and habit of thinking and exploring problems independently.

Emphasis and difficulty in teaching

Key points: Make students understand and master the associative law of additive commutative law and addition, and be able to express additive commutative law and associative law in letters.

Difficulty: Make students go through the process of exploring additive commutative law's law of addition, make comparative analysis, and discover and summarize the operation rules.

Teaching preparation

multimedia courseware

teaching process

Pre-class game: comparing eyesight

First, create situations and ask questions.

1. Introduce the dialogue and reveal the topic.

Teacher: Children, who can tell us what to learn today? (law of addition)

how do you know (Look at what's written on the big screen)

Very good. You are an observant child.

Teacher: The four operations have certain rules. We call these laws operational laws. What is the arithmetic of addition? In this lesson, we will learn the law of addition together. (Title on the blackboard-Addition Algorithm)

2. Create situations and ask questions.

(1) Teacher: During the long summer vacation, many people go out for fun, and Uncle Li is no exception. How did he leave? (slide show)

Health: Riding a bike.

Teacher: You have a good eye. Take a closer look. What else do you know from the picture?

(2) Students report what they know.

(3) According to the information, what questions can be asked? (Students ask questions)

(4) Learning question: How many kilometers did Uncle Li ride today?

Second, cooperate to explore and solve problems.

(1) Exploring additive commutative law

1. formula calculation

Teacher: How should we solve this problem? Please calculate and report by yourself. (40+56 and 56+40, if no students say the algorithm of 56+40, the teacher should guide them to list it like this)

2. The two algorithms are different, why the result is the same? Because they all represent the sum of the distance between morning and afternoon, the result is the same. )

Since the results of these two formulas are the same, what symbols can we fill in the box? ("=")

Can you give an example of this formula?

(Student example)

5. Look carefully, what are the characteristics of these formulas?

(The two addends have not changed, but the positions have been exchanged, and the sum remains the same. )

6. Can we complete this formula? Do you think the left and right sides of your example must be equal? Why? (Because no matter where they are, they are all summed up, so the left and right are equal. )

7. Reveal the law

(1) Students, the law contained in the example we just cited is the commutative law of addition. Can you tell me in your own words what the exchange law of addition is?

(student summary)

(2) Summary: Two addends exchange positions and the sum remains unchanged, which is called the commutative law of addition. (blackboard writing)

8. Since this formula can't be finished, can you find a way to summarize the commutative law of addition with a formula? Have a try.

(Students try)

9. Show students' methods.

10. additive commutative law must be represented by letters and written on the blackboard.

Teacher: Because letters are relatively simple, we usually use A and B to represent any two addends, so additive commutative law is represented by letters: A+B = B+A. (blackboard writing)

1 1. Password matching

Teacher: 83+ 17= student: equal to 17+83.

57+44 a+b 100+60 18+75 35+65 85+768

12. Introduce the application of additive commutative law in addition calculation.

(B) explore the law of additive association

1. Just mentioned that Uncle Li will travel for seven days. This is the journey that Uncle Li walked three days ago. Let's have a look. (Show Scenario 2)

2. Students observe and talk about the information they have learned.

Show me the question: Do you know how many kilometers Uncle Li rode in three days? Please calculate it yourself first.

4. Show students' algorithms.

(88+ 104)+96 88+( 104+96)

Which algorithm is simple and why?

5. Let's look at these two algorithms.

Teacher: Algorithm 1: Calculate the distance you rode two days ago, and then add the distance on the third day.

Algorithm 2: Calculate the distance of riding in the last two days, and then add the distance of the first day. This method is very simple.

Teacher: The algorithm is different. Why is the result the same? (Because they are all three-day trips)

Since the result is the same, what symbol can we use to connect the two formulas? (equal sign)

7. Compare the following two formulas.

68+ 152+48 68+( 152+48)

(225+ 175)+67 225+( 175+67)

8. Ask the students to write several groups of formulas according to the figures and show them.

9. Observing these formulas, what do you find?

Student: Add three numbers, first add the first two numbers, or you want to add the last two numbers, and the sum will remain the same.

10. Reveal the law of additive association.

(1) Teacher: This law of addition, which we just discovered, is called the law of additive association. Can you tell the law of addition and association in your own words?

(2) Summary: When three numbers are added, the first two numbers or the last two numbers are added first, which is called the law of addition and association. (blackboard writing)

1 1. Try to express the additive associative law with symbols.

Teacher: The law of addition and association is expressed by letters: (a+b)+c = a+(b+c), and A, B and C respectively represent any three addends.

Third, consolidate exercises and test feedback.

1. Fill in:

(1) Two addends are exchanged (), and the sum is unchanged. This is called addition ().

(2) When adding three numbers, add () or () first, and keep the same. This is called addition ().

(3) additive commutative law is represented by letters:

a+b=________ .

(4) The law of additive association is expressed by letters:

(a+b)+c= ________ .

2. Use the learned laws and fill in the appropriate numbers in the following ().

( 1)29+ 17=( )+29

(2) 120+( )=35+( )

(3) 138+(62+365)=( + )+365

(4)( +358)+ ( )= 198+( +42)

3. Again and again, what is the basis of each group of connections?

63+325 64+( 19+8 1)

87+32+68 325+63

(64+ 19)+8 1 87+(32+68)

36+78+64 78+(36+64)

Compared with each other, this group runs faster.

( 1)( 195+32)+68 (2) 195+(32+68)

(205+59)+24 1 205+(59+24 1)

486+78+ 14 78 +(486+ 14)

Teacher: By using the law of addition operation, the calculation can be simplified.

4. Cooperation summary, consolidation and internalization.

1. What did you learn in this class?

Please tell your deskmate what you learned in this class, why and why.

Teacher: The students did well today. With their keen eyes and clever minds, they discovered the rules in the addition formula, understood and understood additive commutative law's addition associative law, and could be applied preliminarily. You see, we can also sum up the operation rules that mathematicians can sum up. I believe that as long as we use our brains and make more efforts in future study, we will certainly learn mathematics better!

blackboard-writing design

Law of addition operation

Additive commutative law a+b=b+a

Additive associative law (a+b)+c=a+(b+c)

The addition algorithm can make the calculation simple.

The second teaching goal of "addition algorithm" in the fourth grade of primary school;

1. Make students understand and master the associative law of additive commutative law and addition, and be able to express additive commutative law and associative law in letters.

2. Make students experience the process of exploring additive commutative law and the law of association, and find and summarize the operation rules by comparing and analyzing the solutions to common practical problems.

3. Enable students to gain a successful experience in mathematics activities, further enhance their interest and confidence in mathematics, and initially form the consciousness and habit of thinking and exploring problems independently.

Teaching emphasis: Understand and master additive commutative law and the law of association.

Teaching difficulties: skillful application of addition exchange and associative law.

Teaching tools: course fragments

Teaching process:

First, review the old knowledge.

1, oral calculation

25+75= 48+70= 133+77= 150+390=

820+ 180= 725+36= 30 1+299= 999+ 10=

Secondary lesson preparation: in 25+75= 100, 25 is (), 75 is (), and 100 is ().

2. Introduce new courses

Teacher: We learned the knowledge of addition calculation. In fact, there are many rules in operation, which we call operation rules. Today, we will further learn some knowledge about the regularity of addition, which will be of great help to us in learning decimals and fractions in the future. Blackboard writing: addition algorithm

Second, explore new knowledge.

(A) Learning from additive commutative law (Example 1)

1, create a situation and cite an example.

Teacher: Students, do you like sports? What sports do you like to do in your spare time? Uncle Li likes riding a bike very much. He is going to travel by bike. (Showing pictures) You see, this is the data about the riding distance he introduced to us on a certain day. Let's help him figure it out together. (Show the theme diagram of the example 1 and give the content of the example 1)

2. Read the questions, show the line chart, and let the students analyze the quantitative relationship.

Lesson preparation in the second quarter: If students have no difficulty in analyzing, they don't need to draw a line diagram to help analyze. It depends.

3. Independent column solution. Name the students and answer them.

Method 1: 40+56=96 km.

Method 2: 56+40=96 km

4. Question: Why do you use addition calculation? what do you think? What kind of operation is addition? Addition is the operation of combining several arrays into one number. )

5. Guide students to observe and compare the results of the two algorithms.

The above two algorithms are to find out how many kilometers Uncle Li rode in a day, and the results of the two formulas are equal. What symbols can we use to connect these two formulas? (Equal number) Blackboard: 40+56 (=) What does the equation 56+40 mean? (Swap the positions of 40 and 56 addends, and the sum remains the same)

6. Guide students to sum up the rules.

Display: 36+84 84+36158+68 68+158

What are the similarities between each of the above formulas? What is the difference? What pattern did you find? (Students discuss at the same table, and the teacher takes part in the patrol) Group communication, and the teacher writes it on the blackboard according to the students' summary. (Blackboard: Add two addends, exchange the positions of addends, and keep the sum unchanged. This is called additive commutative law. Additive commutative law: a+b=b+a)

7. Practice (fill in the appropriate numbers with additive commutative law)

65+ 145 = _+_ 09+3 1 = _+_ b+ _ = _+_ a+_ = 10+_

(2) Learning the law of additive association (Example 2)

1. Show examples, ask questions and understand the meaning of the questions.

2. Students try to answer.

3. Questions and answers:

(1) You can see what you want before you see what you want. How did you make it?

Blackboard: (88+104)+96.88+(104+96)

4. Observation: Think about the similarities and differences between these two formulas. Similarity: the calculation results are the same. Difference: The operation sequence is different.

5. By comparison, we find that:

(69+ 172)+28□69+( 172+28)

155+( 145+207)□( 155+ 145)+207

6, observation:

(1) How many formulas are there in each group? (2)

(2) How many numbers are added to each formula? (3)

(3) What is the difference between the two formulas in each group? (Calculation order is different)

(4) What are the similarities between these two formulas? (In each equation, each group of formulas has three addends, and the addends in each equation are the same. )

(5) Two formulas in each group have changed, but what hasn't? (and there is no change)

7. What laws have you found through these two equations? Show the content and let the students fill in the blanks after thinking. () Add, add () first, or add () first, while () remains unchanged. This is the so-called law of addition and association. (Students read together and remember after understanding)

8. If three addends are represented by letters A, B and C respectively, how do you represent the laws of addition and association by letters? Teacher's blackboard writing: (a+b)+c=a+(b+c)

9. Practice (fill in the appropriate numbers with the rules of addition and association)

(43+ 145)+55=_+(_+_) 2 15+(85+30)=(_+_)+_

( 134+ 1 12)+88=_+(_+_)

Third, consolidate the exercise (what is the law used in the following equation? )

82+0=0+82 ( ) 47+(30+8)=(47+30)+8 ( )

(84+68)+32=84+(68+32)( ) 75+(48+25)=(75+25)+48 ( )

Summary: The biggest difference between additive commutative law and associative law is that commutative law changes the position of numbers; What the association law changes is that

Operation sequence. The important sign of the law of association is the application of parentheses.

Fourth, summary.

What did you learn from this course?

Blackboard design:

Law of addition operation

Additive commutative law: A+B = B+A Additive Law: (a+b)+c=a+(b+c).

Second lesson preparation: In teaching, put 40+96 = 96+40 (88+104)+96 = 88+(104+96) on the blackboard, and it will be easier for students to express it in different forms according to the formula.

Teaching reflection:

The new knowledge in this lesson has a corresponding cognitive basis in previous mathematics learning. Learning the new knowledge in this class can promote students to have a deeper understanding of the knowledge and methods they have learned before. In the teaching process of addition algorithm, I have always been student-oriented, grasped the law of students' understanding according to their age characteristics, and achieved good teaching results.

1, which is closely related to students' real life.

When teaching, I make full use of the specific situations presented in the textbook, introduce the answers to practical questions that students are familiar with, and stimulate students' demand for active learning. By solving the problems in the situation, let the students observe and compare the two formulas, awaken the students' existing knowledge and experience, and make them feel the law of addition operation initially. In the process of exploring the law of addition operation, students are provided with time and space to explore independently, so that they can experience the process of exploration, gain successful experience and enhance their confidence in learning mathematics.

2. Cultivate students' ability to summarize.

In teaching, the two algorithms allow students to find the similarities and differences of different solutions to practical problems through observation, comparison and analysis, and feel the algorithms initially. Then let the students give more examples according to their initial perception of the operation law, further analyze and compare, find the law, and describe the found law. Then let the students express the rules in their favorite way, instead of using letters as in the past. Let students realize the simplicity of symbols, so as to develop their sense of symbols.

The teaching of this course allows students to experience the process of exploration, discovery and reflection, and have a full understanding of additive commutative law and the law of additive association. But there are still many shortcomings in the teaching process:

1, in the process of exploring the law of additive combination, we should be more open, guide students to observe, compare and analyze, find out the similarities and differences of different solutions to practical problems, and feel the operation law initially.

2. When teaching the law of additive association, let students give more examples, let students evaluate the examples themselves, and let students find out for themselves that the combination is to put together the numbers that can get all 100, rather than making them up casually.

The third teaching goal of "addition algorithm" in the fourth grade of primary school;

1. By trying to solve practical problems, observing and comparing, we found and summarized the associative law of additive commutative law and addition.

2. Learn to use the law of addition to make simple calculations and solve practical problems.

3. Cultivate students' observation ability, generalization ability and language expression ability.

Teaching process:

First, create a situation

1. Introduce the dialogue.

How many students will learn to ride bicycles in our class? Where did you ride the farthest?

Cycling is a healthy exercise. No, there is an uncle Li riding a bike here!

(See main picture: Uncle Li travels by bike. )

Get information.

Students exchange information at the same table and then report to the class. )

With the students' answers, the multimedia shows the line chart from left to right. There is a problem.

How many kilometers in the morning? How many kilometers in the afternoon? How many kilometers is a * *?

Solve the problem.

Q: Can you solve this problem by formula calculation?

(Students answer in parallel by themselves. )

Second, explore the law.

1. additive commutative law.

(1) Solve the problem of 1.

Write on the blackboard according to the students' answers: 40+56=96 (km)

56+40=96 km

Q: What do these two formulas mean? How about counting? ○ What symbol should I fill in?

40+56○56+40,

(2) Can you give a few more examples?

(3) What laws can be drawn from these examples? Please summarize it in the most concise words.

(4) Feedback communication.

The two addends exchange positions, and the sum remains the same.

(5) reveal the law.

Q: ① Do you know what this rule is called?

② When the addend is replaced by any other number, is the commutative law still valid?

(3) How to express the addition of any two numbers and the exchange of addend position and invariance? Would you please express it in your favorite way? (The deskmate speaks softly. )

Exchange feedback and then read a book: see what the children in the textbook say.

⑤ Check the password according to additive commutative law.

Teacher: 25+65 = _ _ _ (Student: 65+25)

78+64=________

⑥ Complete the "doing" on page 28 of the textbook:

300+600=_______+________ ________+65=________+35

2. Additive associative law.

Look at the main picture: Uncle Li's three-day riding distance statistics.

(1) Find information to solve problems.

Q: Can you solve the problem raised by Uncle Li?

Students communicate their daily itinerary after completing it independently.

According to the different formulas listed by the students, the line segments representing the three-day journey appear one after another.

* * * How many kilometers did you ride in three days?

Q: What did you find through the demonstration of line segment diagram? No matter which two days are added first, the total length remains the same.

Let's study the formula of adding the distances traveled in three days in turn, and how to calculate it:

Compare 88+104+9688+(104+96)

= 192+96 =88+200

=288 =288

Why count 104+96 first? (The last two addends are added first, which adds up to exactly one hundred. )

Display: (88+104)+96 ○ 88+(104+96), how to fill in?

(2) Can you give more examples of this?

Q: Observe and compare these formulas, and tell me what secrets you have discovered. Encourage students to say it in their own words.

(3) reveal the law.

When three numbers are added, the first two numbers are added first, or the last two numbers are added first, and the sum remains the same. This is the law of addition and association.

(4) Symbolic representation. (Students complete independently and check collectively. )

(▲+★)+●=________+(________+________)

(a+b)+c = _ _ _ _ _ _ _ _+(_ _ _ _ _ _ _ _+_ _ _ _ _ _ _ _)

(5) Q: ① Which is more obvious, using words or letters?

② What numbers can A, B and C represent here?

Third, practice consolidation.

1. Point out which of the following questions uses the law of addition and the law of operation respectively.

(1)4+5=5+4 (using additive commutative law)

(2) Using the method of "add up to ten" 7+9=6+( 1+9) (using the law of additive combination)

2. One company after another.

83+3 15 64+(73+37)

87+42+58 3 15+83