Teaching objectives
1, so that students can master the operation sequence of addition and subtraction mixed operations and calculate correctly.
2, in the process of solving specific problems, know the meaning of each step in the formula, and explain the operation order according to the meaning of the formula.
Teaching emphasis: in the process of solving problems, master the order of addition and subtraction mixed operations.
Teaching difficulty: Explain the operation sequence according to the meaning of the formula.
teaching process
(A) the introduction of dialogue to stimulate interest
Students, what kind of scenery do you think is the most beautiful? Today, the teacher took everyone to Harbin, the ice city. (Courseware demonstration)
Is it beautiful? Appreciate pictures
(B) situational extension review of old knowledge
Let's go to the world of ice and snow!
1. What are the people doing in the picture? How many activity areas is the world of ice and snow divided into? How many people are there in each district? how do you know
The students observed it carefully. We can know from the picture that there are 72 people in the skating area, 36 people in the water skiing area and 180 people in the ice sculpture area. Think carefully, students. Can you put forward some math problems and solve them according to this information?
2. Communication and feedback
Students are great! According to three pieces of information, you can ask so many questions and solve them.
(3) Research on learning new knowledge algorithm
Students, let's go to the skating rink and have a look! Now, please listen to the person in charge of the skating rink: welcome to the skating rink, children. There were 72 people this morning, 44 people left at noon, and 85 people arrived. You also go in and have a look!
Students, do you know how many people are skating in the skating rink now?
1, and tell your deskmate what you think?
2. Feedback communication.
( 1)、72-44=28 (2)72-44+85= 1 13
28+85= 1 13
What does 72-44 mean? What does 28+85 mean?
Tell me which method is good. Why? (Method (2) can write a middle number less, so it is simpler. )
4. Use the formula of method (2).
If the teacher changed the subject, there were 78 people in the skating area this morning, 50 people came in and 37 people left in the afternoon. How many people are there now?
Let the students calculate freely, and then communicate with the whole class.
78+50-37
Say the meaning of each step.
5. Summarize the operation sequence of addition and subtraction mixed operation.
After studying these two problems, let's observe the calculation order of these two problems again. Can you sum them up in one sentence? (Add and subtract, counting from left to right. )
(D) consolidate the summary and evaluation of new knowledge.
We almost visited the world of ice and snow. We should go back to school. It's a long way. Let's take a bus!
1, (courseware presented) Let's get on the bus at "Chengnan Station". There are 36 passengers on board, 12 people get off and 15 people get on. How many people are there on the bus now?
(1) Please list the formulas quickly.
(2) After completion, talk to your deskmate about the meaning of each step and what is the operation sequence?
When we got to school, we went to the library to read for a while. Please listen to aunt librarian's introduction: Students, today is really a good day. Many people borrow story books. There are 98 story books in the library. Today, 46 books were lent out and 25 books were returned. Do you know how many story books are there in the library now?
3. Summary: What have you gained from learning this lesson? What do you think you haven't mastered?
The second lesson: mixed operation of multiplication and division
Teaching objectives:
1, by solving specific problems, listing formulas and analyzing the meaning of formulas, let students clearly understand the order of mixed operations of multiplication and division.
2. When students encounter mixed multiplication and division expressions, they can calculate from left to right.
Teaching emphasis: master the operation order of multiplication and division mixed operation.
Teaching difficulties: Let students understand the quantitative relationship of the topic and see the meaning of each step in the formula.
teaching process
(A) review the old knowledge
Yesterday we learned the mixed operation of addition and subtraction. Who can tell us the operation order of the mixed operation of addition and subtraction?
1, recall the operation order of addition and subtraction mixed operation. (In the formula with only addition and subtraction, the calculation goes from left to right. )
Look at the two problems first, and then analyze the operation sequence in combination with specific problems.
2. Talk about the operation sequence and calculation.
25+78-9 1 105-58+46
(B) to open new courses
The students seem to have mastered it well. Everyone applauded to show encouragement. Today, we will go to the "Ice and Snow World" to see if there will be any new situation there.
1, example 2.
"Ice and Snow World" received 987 people in 3 days. According to this calculation, how many people are expected to receive in 6 days?
2. Ask the students to read the questions.
3. What does this calculation mean? (refers to the number of people received every day, calculated by receiving 987 people in three days.
4. Let the students discuss the problem-solving methods in groups. You can understand them with the help of line segment diagrams, list formulas and think about what each step of the formula means.
5. Organize communication:
1. Step by step formula: 987÷3=329
329×6= 1974
Comprehensive formula: 987÷3×6
=329×6
= 1974
Draw a line: receive 987 people in 3 days.
How many people does a * * * receive?
Guide the students to draw their own line segments on the blackboard, especially to evaluate the length of the line segment representing the number of people receiving six days.
987÷3 indicates how many people are received in a day.
329×6 means that the number of people received in a day can be calculated by multiplying the number of days by 6.
Which is easier to compare, step-by-step or comprehensive? (The comprehensive type is simpler, and he can write a middle number less. )
b、6÷3×987
6÷3 means that there are two 3s in six days, that is, two 987 people.
6. Summarize the operation sequence of mixed operation of multiplication and division. (Only the formula problem of multiplication and division, the calculation is from left to right. )
7. Summarize the operation order of only addition and subtraction or only multiplication and division in formulas without brackets. (In the formula without brackets, only addition and subtraction or only multiplication and division are calculated from left to right. )
(3) Consolidate and deepen
1, oral calculation.
27÷3×7 3×6÷9 25÷5×8
45+8-23 63÷7×8 24-8+ 10
28÷4×7 35+24- 12 48÷8÷9
Driving a small train, every time you say one, other students will judge whether it is right or wrong. The students in front made a mistake, and the students behind corrected it. The sooner the better. If the students in front are slow, the students behind can answer quickly first.
2, a box of orange juice 48 yuan, Fangfang wants to buy three bottles, * * * How much?
Ask the students to answer the second question. Maybe some students will ask questions that they can't do, and they lack conditions. Guide the students to look at the pictures and find the conditions.
(d) Summarize the improvement.
What do you think you have improved through this course?
The third category: the mixed operation of product quotient sum (difference).
Teaching objectives
1. Let students master the operation order of two-level operation (without brackets) and calculate correctly.
2. Let students feel the truth of "multiply and divide first and then add and subtract" in the process of solving practical problems.
Teaching emphasis and difficulty: let students understand the operation sequence.
Teaching process:
(a) review of imports
In the first two classes, the teacher introduced some information about the "world of ice and snow" playground. Today, the teacher brought the statistics of the number of visitors to the "Snow World" playground. Let's take a look at this statistical table. What math questions would you ask?
Show the following table:
This is the statistics of the number of tourists in the "Ice and Snow World" amusement park.
Date Monday, Tuesday, Wednesday
No.3 12 306 369
Question: According to the data provided in the table, what mathematical questions can you ask? Students may ask some questions about one-step calculation, and teachers may prompt them to ask some questions about two-step calculation.
According to the students' answers, it shows:
3 days * * * received 987 people. According to this calculation, how many people are expected to receive in a week?
Students answer in columns. And talk about the calculation order.
Introduce a new lesson: On Sunday, mom and dad took Lingling to the "world of ice and snow". Let's talk about what to do at the gate of the "Ice and Snow World" amusement park. Look, everyone, the playground is here, and the sign is clearly written. Can you understand its meaning and buy a ticket?
Show the scene pictures in the courseware and guide the students to look at the pictures. Question: What do you see from the picture?
(2) Explore new knowledge
1, teaching example 3
(1) Students discuss, exchange information and report in groups.
Who can describe the problem completely in words?
Teacher's guidance, students' answers, teacher's courseware: On Sunday, mom and dad took Lingling to the "world of ice and snow". 24 yuan for each adult, half price for children. How much is the ticket?
Question: How much is an adult ticket? What do you mean by half price? How much is each child ticket? How many adult tickets should I buy? How many tickets for children? What is the problem to be solved?
Question: How much does it cost to buy a ticket? What must I ask first, then what, and finally what?
(2) Column solution.
Health 1: 24+24 = 48 (yuan) 24÷2= 12 (yuan) 48+ 12=60 (yuan)
Health 2: 24+24+24 ÷ 2
Health 3: 24× 2+24 ÷ 2
Teacher, Q: What is the connection between these three formulas? (The first formula is a step-by-step formula, and the second and third formulas are step-by-step formulas. The meaning of the last two formulas is actually the same. 24+24 and 24×2 are both counting how much are two adult tickets? )
What does 24×2 mean? What does 24÷2 mean?
Let the students answer independently.
(3) Clear the solution method of the comprehensive formula.
24+24+24÷2 24×2+24÷2
=24+24+ 12 =48+ 12
=48+ 12 =60 (yuan)
=60 (yuan)
The solutions of the above two comprehensive formulas are given, although both formulas are for buying tickets. How much will it cost? But the writing is different.
(4) Guide students to compare.
What is the difference between the formula of the review question and the formula of Example 3?
Reveal the topic: this is what we are going to learn in this class today. (blackboard title: mixed operation of sum (difference) of product quotient)
Question: In the formula without brackets, there are multiplication, division, addition and subtraction. What should be counted first?
The students answered, and the teacher concluded: in the formula without brackets, there are multiplication, division and addition and subtraction, and multiplication and division must be calculated first.
2. Q: Can you ask any other questions? Discuss and communicate in groups.
Students may ask:
(1) How much is it to buy 1 adult tickets and three children tickets?
(2) Buy three adult tickets and pay 100 yuan. How much should I get back?
Students independently list the comprehensive formula solutions and tell the calculation order.
3. Comparison: What are the similarities and differences between these formulas and examples?
Students answer, the teacher summarizes and deepens the operation order.
4. Feedback exercise: the first 1 question of "doing" on page 7.
Draw "√" in the same operation order and "×" in different order.
( 1)2×9÷3 (2)36-6×5 (3)56÷7×5
2+9-3 36÷6×5 56+7×5
(3) Consolidate and improve
1, tell the operation sequence of the following questions, and then calculate.
203- 134÷228+ 120×8
97- 12×6+4326×4- 125÷5
Let's talk about the operation order of each question first. Please ask four students to perform on the blackboard, and the other students will finish it on their own draft paper. Proofread after completion, and point out any mistakes in time.
Step 2 solve the problem.
(1) Students plant trees. There are 140 students in Grade 4, each of whom plants 2 trees; There are 120 students in grade five, each of whom planted 3 trees. How many trees have been planted in these two grades?
(2) There are 48 apple trees in the orchard, the number of peach trees is twice that of apple trees, and the number of pear trees is more than the total number of apple trees and peach trees 12. How many pear trees are there in the orchard?
3. Summary of the course: What have you learned from this course? Please ask your deskmate to comment on whether you are doing well in this class.
The fourth category: the mixed operation of the sum (difference) of two quotients (products)
Teaching objectives:
1. By solving practical problems, the operation sequence of mixed operation with brackets is summarized.
2. Let students analyze the quantitative relationship in the problem and improve their ability to analyze and solve problems.
Teaching emphasis: according to the analysis of quantitative relationship, summarize the mixed operation sequence with brackets.
Teaching difficulty: solving problems.
Teaching process:
(1) review and preparation
1. What do you know about mixed operation? (Write on the blackboard according to the students' answers)
There is only addition and subtraction from left to right.
There are only multiplication and division from left to right.
Multiplication and division, addition and subtraction are both multiplication and division and addition and subtraction.
2. Finish the operation sequence and quickly calculate the result.
5 1+ 16- 1867-29+ 15
5× 15- 12÷3 56÷8-2×3
Ask four students to talk about the operation sequence first and report the answers quickly.
(B) new knowledge learning
The "Ice and Snow World" has a lot of traffic these days, especially tourists. In order to keep the "world of ice and snow" in a good environment, the service department decided to ask some cleaning staff to help manage hygiene. Tourists in the ice sculpture area in the morning 180, 270 in the afternoon. If every 30 tourists need a cleaner.
1, do you understand the meaning of these three messages? How to understand the sentence "every 30 tourists need a cleaner"? Every 30 tourists will be assigned a cleaner. The standard of afternoon and morning is the same. Every 30 tourists will be assigned a cleaner. )
Teachers can also ask: How many cleaners do 60 tourists send? What about 90 tourists? How many tourists will send five cleaners?
2. Can you make up an application problem based on these three pieces of information? You can do it by yourself or as a group.
3, communication, blackboard writing.
4. Can you answer? Solve the first problem first.
The teacher asked everyone to think carefully after reading the questions, list the formulas and calculate them, and say the meaning of each step. If there is a solution, discuss it at the same table. Is there any other solution?
5. feedback.
6. Can you write the above two formulas into a comprehensive formula?
a、 180÷30+270÷30
B, (270+ 180)÷30 Why do you want brackets? (because the total number of tourists is counted first, if you don't put brackets, you can divide them first, which makes it meaningless to send cleaning staff in the morning and tourists in the afternoon. )
7. Summarize the operation sequence of mixed operation with brackets.
8. Which is simpler than the two methods?
9. Solve the second problem.
Tourists in the ice sculpture area in the morning 180, 270 in the afternoon. If every 30 tourists need a cleaner. How many more cleaners were invited in the afternoon than in the morning?
List the formulas, and tell the operation sequence and the meaning of each step.
The students really helped my uncle and aunt a lot in the ice sculpture area. They can arrange cleaning staff as soon as possible according to their own opinions. Next, let's solve some problems.
(3) Consolidate exercises
1. Mom bought Lingling a winter coat and a pair of gloves for 100 yuan. How much is left?
2. Miss Wang has to correct 48 compositions, which have been corrected 12. If you grade nine articles every hour, it will take several hours to finish.
3. The fruit shop delivered 8 boxes of apples and 8 boxes of bananas, each containing 25 kg of apples and 0/8 kg of bananas/kloc. How many kilograms of fruit did a * * * send?
(4) Summarize the whole class
(1) What did you gain from this lesson?
(2) Can you summarize what you learned today in a few short sentences? (The operation order of the expressions in brackets: calculate the ones in brackets first. )
Lesson 5: Three-step calculation problems with brackets.
Teaching objectives:
1, guide students to summarize the order of elementary arithmetic in combination with specific elementary arithmetic questions.
2. By discussing why the numbers, arrangement order and operation symbols involved in the operation are the same, but the calculation results are different, students can re-understand the function of brackets and further master the order of mixed operations.
Teaching emphasis: summarize the operation order of elementary arithmetic.
Teaching difficulty: cultivating students' computing consciousness.
Teaching process:
(A) the new knowledge of direct teaching
A few days ago, we all went to the "world of ice and snow" to find math problems. Today, we won't go. Please look at the teacher's two questions. Can you calculate them?
1, showing:
( 1)42+6×( 12-4) (2)42+6× 12-4
2. Compare the similarities and differences between these two issues. Numbers are the same as operation symbols, the first question has brackets, and the second question has no brackets. )
3. Can sum, difference, product and quotient be used to describe the operation process? (Question 1: Find the difference first, then the product, and finally the sum. The second question: first quadrature, then sum, and finally difference.
4. Can you answer? Ask two students to perform on the blackboard, and the rest of the students to perform on the draft paper.
4. Feedback and communication, pointing out the shortcomings.
42+6×( 12-4)
=42+6-8
=42+48
=90
In the form of an interview, I asked my classmates: What did you do before calculating? (Determine the operation sequence first) What is the basis for you to determine the operation sequence? (first count what is in parentheses, then multiply and divide, and finally add and subtract)
42+6× 12-4
=42+72-4
= 1 14-4
= 1 10
The teacher asked: How to determine the operation sequence?
5. What do you want to say after calculating these two questions? (Numbers are the same as operation symbols. Because one has parentheses and the other has no parentheses, the operation order is different, which leads to different operation results. )
6. Summarize the operation order of elementary arithmetic,
(1) makes it clear that addition, subtraction, multiplication and division are called four operations.
(2) Recall the learning of mixed operation and summarize the operation order of elementary arithmetic in groups.
(3) communicate and form a blackboard writing.
(2) Practice in time to deepen understanding.
1, tell the operation order of each problem first, and then calculate.
(1) Let the students talk about the operation order of sum, difference, product and quotient.
(2) calculation, write out the calculation process.
(3) communicate and correct mistakes.
2. The school canteen bought 850 kilograms of rice, shipped three cars, and there was 100 kilograms left, with an average of how many kilograms per car.
(1) Let two students read the questions, and the other student will tell us what you read.
(2) Analyze the quantitative relationship, give the column solution, first talk about the meaning of each step of the formula, and then talk about the operation order to see if the meaning of the formula is consistent with the operation order.
3. How to calculate the points on the following four playing cards to get 24? How many ways can you think of?
(1) Work in groups to see which group lists the most formulas.
(2) communication, listing various methods.
(6+4-2)×3 6×4÷(3-2) 6
4. The travel agency has put forward two kinds of tourism price schemes, namely "one-day tour in the scenic spot".
(1) Analyze the significance of the two schemes. (The first option is to buy according to the number of people, and the fare for adults and children is different; Option 2 is priced according to the group, and the price of more than 5 people is per person 100 yuan. )
(2)*** Solve the problem (1) Let students buy tickets separately according to the two schemes to see which scheme is cheaper?
(3) Answer the second question independently. (For the same reason as the (1) subproblem)
(C) the end of the new lesson summary
Do you have anything to say after this class?
Lesson 6: Operation on 0
Teaching objectives:
1. Systematize scattered operational knowledge about 0, and improve students' calculation accuracy and ability to sort out and summarize knowledge.
2. With the help of stories, let students recall the relevant knowledge of 0, so that learning becomes active.
The difficulty of this lesson is to explain why 0 can't be divided and why 0 can't be divided.
Teaching preparation:
Courseware (the story of Zero King bravely fighting and eating several wild animals)
Teaching process:
(A) the story import
Today, the teacher tells you a story. The title of the story is-Zero King fought bravely and ate several beasts. Please listen carefully, think carefully and think it over. Why did King Zero defeat the Food Beast? What do you think of 0?
The story begins: One day, a three-legged monster suddenly broke into the digital kingdom, scaring digital citizens to flee everywhere. The monster opened his mouth and swallowed 24, and then swallowed 44. Counting to five scared his feet weak. Strangely, the monster didn't look at it.
(1) Listen to the story.
(2) Why did King Zero defeat the food beast? What do you think of 0? King Zero seized the weakness of the man-eating beast. It seems that we should not underestimate this 0, although it is meaningless, but its role should not be underestimated. )
(B) knowledge carding
Students are really good at listening to stories, and they can also listen to stories for analysis. Today we will also learn 0.
1, think about it, what operations do you know about 0? What should I pay attention to when calculating?
(1) Discuss in groups. You can speak freely in the group and send one person to take notes.
(2) The whole class communicates and the teacher writes on the blackboard.
Addition: Adding 0 to a number will return the original number.
For example: 6+0 = 6 23+0 = 23 0+91= 91.
Subtraction: the minuend is equal to subtraction, and the difference is 0; A number minus 0 or this number.
For example: 5-5=0 60-60=0 8-0=8.
Operation of 0
Multiplication: Multiply a number by 0 to get 0.
For example: 3×0=0 0×9=0.
Division: divide 0 by a non-zero number to get 0; 0 cannot be partitioned.
For example: 0÷5=0 5÷0 is meaningless.
(3) Ask several students to summarize the operation about 0.
2. What happens if you divide by 0?
Guide the students to analyze: A, 5÷0 means a non-zero number divided by 0, what does it mean in the sense of division, and what is the quotient? Guide the students to say that the product is 5, one factor is 0, and find another factor. How to multiply 0 and several to get 5? Because a number multiplied by 0 still gets 0, it is impossible to get a quotient from 5÷0. B, 0÷0, what does it mean in the sense of division? What is the quotient? Guide the students to say that the product is 0, one factor is 0, and find another factor. If you want to multiply 0 by a few, you will get 0. Then ask: can you find such a number? Yes, because 0 can be multiplied by any number, it is pointed out that 0÷0 can't get a definite quotient, so we don't study it, and finally we come to the conclusion that 0 can't be divisible.
(3) Math games
After summarizing the knowledge of 0, let's relax and play a math game. Show:
(1) See the game requirements clearly.
(2) Play games in groups to see which group can find faster and record it.
(4) Consolidate and improve
1, oral calculation.
79+0 6×0 9-0 0- 1 1
0+35 0÷7 1 6-6 4×0
0×53 54+0 54-0 0×900
In the form of a small train, the students in front can't go on, and the students behind can answer first.
3. crack the password.
First, calculate the numbers in the circle and box to form a password. Pay attention to the derivation of the calculation process.
(5) class summary.
What is your biggest gain today?