The teaching objectives of the model essay on the second volume of mathematics teaching plan in the fifth grade of primary school (1);
1. Make students know the background of negative numbers in real situations, have a preliminary understanding of negative numbers, know the reading and writing methods of positive numbers and negative numbers, and record the opposite quantities with positive numbers and negative numbers. Know that 0 is neither positive nor negative, and all negative numbers are less than 0.
2. Make students experience the close relationship between mathematics and daily life, and further stimulate their interest in learning mathematics.
3. In association, generalization and deduction, experience the richness and connection of mathematics and its application value in life, and infiltrate the simplest philosophical and ideological education such as unity of opposites and development of connection.
Teaching emphasis: understand the meaning of negative number and initially establish the concept of negative number.
Teaching difficulties: understanding the relationship between positive numbers, negative numbers and 0.
Teaching process:
Let's start with the "life case"-understand the source of negative numbers.
1. Students, it's almost autumn (the courseware presents beautiful pictures of autumn scenery). What do you think of the weather in Suzhou these two days? After the students answer, the courseware presents Suzhou weather forecast and thermometer map. This thermometer shows the highest temperature yesterday. Can you see what the highest temperature was yesterday?
Students' reporting process is small, so that students can understand that there are generally two lines of scales on the thermometer, and there are scale names on the left and right sides. The left side stands for degrees Celsius, usually expressed by the letter℃, and the big grid stands for two degrees. )
According to scientific research, the human body feels most comfortable when the temperature is 18-24℃. We felt very hot when the temperature reached 28℃ yesterday. Guess: How will the red alcohol column on the thermometer change from now on?
(Design intention: Temperature change is a natural topic that students face and feel every day in their lives. It is natural and appropriate to take this as the beginning of classroom teaching, which can attract students' extensive participation. Considering that students are not very familiar with thermometers, let's arrange an episode to watch thermometers alone to pave the way for new knowledge teaching later. )
Second, understand the meaning of negative numbers from "opposition"
(A) teaching example L, a preliminary understanding of negative numbers.
1. The teacher is also a person who is very concerned about atmospheric changes, and watches the weather forecast of CCTV almost every day. Once I recorded the lowest temperatures in three cities. The first one is Shanghai, the oriental metropolis (show the thermometer map). Can you see the lowest temperature in Shanghai that day from the thermometer?
2. The second city is (showing the thermometer map). Can you see the lowest temperature in Nanjing from the thermometer? How does this temperature compare with that in Shanghai?
The third city is Beijing, the capital of our great motherland. According to your life experience, how does the temperature in Beijing usually compare with that in Shanghai and Nanjing? After the students guess, show the temperature map and ask them to say that the temperature in Beijing is "MINUS 4℃".
Among the lowest temperatures in the two cities just now, it happened that Nanjing was just 0 degrees Celsius. Shanghai, on the other hand, is over 0 degrees Celsius, which is 4 degrees Celsius above zero. Beijing is below 0 degrees Celsius, which is minus 4 degrees Celsius. This is a set of opposite quantities. Can you think of a clever way to record these two opposite temperatures?
Students discuss and exchange their ideas. The teacher selectively wrote on the blackboard: +4℃ or 4℃, -4℃ and so on. , and explains the negative sign, positive sign and their reading and writing.
6. Consolidate the exercises.
(1) Choose an appropriate number to represent the temperature in different places:
On the same day, the lowest temperatures in several cities and regions were recorded (the thermometer maps of Xining, Harbin, Hong Kong and other cities were displayed respectively). Can you write down their lowest temperatures separately in this way?
(2) Small weather recorder.
Let's make a weather recorder together, and record the temperature while listening to the weather forecast. Courseware demonstration: 40 degrees Celsius above zero at the equator, 26 degrees Celsius below zero at the North Pole and 40 degrees Celsius below zero at the South Pole.
(Design intention: In the process of introducing negative numbers, we should follow the problem of "reading the temperature with a thermometer" at the beginning of class, and gradually reduce the temperature in the three major cities of the motherland from high to low, so as to make the teaching smooth and natural. And what numbers can be used to represent and distinguish the two opposite temperatures "4 degrees Celsius above zero" and "4 degrees Celsius below zero" that are common in life? This problem not only makes students feel the limitations of numbers they have learned in the past in expressing quantities with opposite meanings, but also reminds them of the method of adding different symbols before the number "4" to express quantities with opposite meanings with the help of life experience.
(B) Teaching example 2, in-depth understanding of negative numbers.
1. (showing the map of Mount Everest) Does anyone know how high it is? What is the distance from this height to the top?
(After the students answer, add "altitude" before 8844 meters, and add the horizontal dotted line of sea level on the map)
Not every place in the world is above sea level. For example, Turpan Basin, the fifth great basin in China, is155m above sea level (the map of the basin is displayed next to the map of Mount Everest).
Can you be inspired by the way you just expressed the temperature and express these two heights in a more scientific way? (blackboard writing: +8844m- 155m)
3. Imitation exercises.
Textbook Exercise 1, page 6, 1, 2 questions.
4. Summary: Through the research just now, we can see that when the temperature is expressed, it is bounded by 0℃, when it is higher than 0℃, it is represented by a positive number, and when it is lower than 0℃, it is represented by a negative number; When the altitude is expressed, the sea level is taken as the boundary, above sea level is represented by a positive number, and below sea level by a negative number.
(Design intention: Using positive and negative numbers to represent altitude is the students' re-perception of the opposite number. Because the previous understanding of temperature is basic, this link tries to use the experience and paradigm of expressing temperature with positive and negative numbers obtained in the previous study to highlight the benchmark of "taking sea level as the boundary" and let students try to solve it. Under the influence of past experience, students can easily think of the counting rule of "positive above sea level and negative below sea level" (mastering the background of negative numbers and the essentials and methods of deep counting)
Thirdly, to promote and deepen the concept connotation by "comparative reflection"
1. We use these numbers to represent temperatures above and below zero and heights above and below sea level respectively. (The courseware presents thermometer and elevation map at the same time, in which 0℃ and sea level are marked with red lines. )
2. Observe these numbers (show the courseware). Can you classify them? According to what score? How many kinds are there? Group discussion. Summary: Numbers like+4,40 and +8844 are all positive numbers, and numbers like-4,7, 1 1, 155 are all negative numbers.
3. Discussion: Is 0 a positive or negative number? (Guide students to express their opinions in the set discussion forum through the Internet)
Guide the students to distinguish: from the thermometer, the number above 0 degrees Celsius is positive, and the number below 0 degrees Celsius is negative. The number above sea level is positive, and the number below sea level is negative.
With the help of courseware, teachers observe the mysterious line with arrows (that is, the number axis) and realize that 0 is the dividing line between the lower number and the negative number, and 0 is neither positive nor negative. Positive numbers are greater than 0 and negative numbers are less than 0.
4. Exercise-Complete the question L of "Exercise …— Exercise" on page 3 (add 0 to the original title).
Ask questions:
(1)0 Why not write it? (0 is neither positive nor negative)
(2) Observing these positive numbers, what do you find?
The numbers we have learned before are all positive numbers.
5. "You know what, show me? -China was the first country to use negative numbers. (Students can browse online resources freely)
(Design intention: This lesson is the first time that students know negative numbers. In order to let students have a complete understanding of the connotation and extension of negative numbers, thermometer and altitude map are displayed at the same time, so that students can intuitively feel that the zero scale line and sea level are the dividing point. With the help of intuitive scenarios, let students understand and accept the relationship between positive numbers, negative numbers and 0. At the same time, pay attention to let students realize that all the numbers they have learned in the past (except 0) are positive numbers to help students communicate the internal relationship between old and new knowledge)
Fourth, use "multi-layer exercises" to consolidate-expand the extension of negative numbers.
1. Basic exercises.
Write five positive numbers and five negative numbers and communicate with each other: read and write the numbers to determine whether they are correct.
2. Contrast exercises.
Choose the appropriate result and fill in the brackets:
In 2007, the Chang 'e satellite successfully launched by China, the sunny surface temperature in space was above (), while the sunny surface temperature was lower than (). However, through heat insulation and control, the temperature in the satellite cabin is always kept at (), which ensures the normal detection of the satellite.
①2 1℃② 100℃③- 100℃
3. Application exercises.
(1) Information Conference on "Negative Numbers in Life".
Say: What other situations in life can also be represented by positive or negative numbers?
Then the courseware shows related pictures.
(2) Summary: Things like above and below zero degrees Celsius, above and below sea level, above and below ground, deposits and withdrawals, scores and losses in competitions, stock ups and downs, etc. Both are quantities with opposite meanings, which can be expressed by positive numbers and negative numbers.
4. Expansion and extension.
Investigate your family's income and expenditure for one month and make records. After recording, analyze the data, talk to your family about your feelings, and write down your feelings and consumption suggestions in math diary.
Model essay on mathematics teaching plan in the second volume of the fifth grade of primary school (II) Teaching content: observation object.
Teaching objectives:
1. Let students experience the process of observation and realize that the shapes they see are different from different positions. Can recognize the shape of simple objects observed from the front, left and above.
2. Cultivate students' ability to observe and analyze things from different angles.
3. Cultivate students to construct simple spatial imagination.
Focus: Help students to establish their initial spatial imagination.
Difficulty: Help students to establish a preliminary spatial imagination.
Teaching process:
First, the riddle is introduced.
Let the students guess the riddle: "One is left, the other is right, tangible and intangible.". What is it? " (Ears) Why can you see other people's ears but not your own? Because we observe from different angles, today we will further study and observe objects (blackboard writing) together.
Second, cooperative exploration.
(1) Overall observation
1. The teacher held a cuboid with the same color on the back, and asked the students to observe and ask questions:
What is the cube you observe?
From your position, which side do you see?
2. Students report and communicate.
Students walk freely and observe. Report and communicate.
Explain the application
The teacher showed the three-dimensional pictures of two cubes, one with dotted lines and the other without.
Question: Who can explain why the cube is drawn like this with the knowledge just learned?
Students explain.
(2) Observe from three sides (example 1)
1. Teacher's question: Let's observe this figure from several different directions, see what shapes it has on the front, left and top, and draw them separately.
Students leave their seats to observe freely.
2. Communicate with each other among groups, and then communicate with the whole class. Students will show their communication in groups on the projection.
Summarize the students' speeches: From different directions, the shapes you see are different.
Third, expand applications.
1. Example 2 of Making Textbooks
2. Intelligence game: Two students play games in groups, one draws lots and the other guesses. The students in charge of guessing should try to determine what this object is through the questions you ask. Take it out and verify it after guessing, and see if it's right.
Students play games and teachers guide them.
Fourth, summary.
What did you learn in this class?
Verb (abbreviation for verb) assignment
Explore your interests and find out what is opposite to 1, what is opposite to 2 and what is opposite to 3 according to the pictures below.
1. When you look at an object from different angles, all the faces you see are two or three adjacent faces, so it is impossible to see both sides of a cuboid or cube at once.
When you see the shape of an object from a surface, you can express it in many different ways.
3. Knowing the shape of the object seen from both sides, we can determine the number range of small cubes.
Model essay on mathematics teaching plan in the second volume of the fifth grade of primary school (3) Teaching requirements
① Make students understand the significance of grouping and compiling statistical tables;
(2) Learn the method of grouping and sorting the original data;
③ Learn to fill in simple statistical tables.
Teaching focus
The method of grouping and sorting the original data.
training/teaching aid
Enlarge two statistical tables of Example 2.
teaching process
First, create a situation
1. Let's review the simple data collation and some statistics we have learned.
2. The following is a statistical table of girls' height measurement in a class math interest group.
Name:
Average value:
Height: (cm)
Thinking and answering questions after independence:
① How to find the average height of this group of female students?
What are the characteristics of the height of these female students?
How many centimeters is the tallest female classmate taller than the shortest female classmate?
There are many female students on this list. What should I do if I can't see the height distribution clearly? In this lesson, we learn to divide raw data into several groups according to the size of quantity, and then make statistical tables.
Second, exploration and research.
1. Method of grouping and sorting original data.
(1) The teacher shows the record sheet and the students think independently.
Who is the tallest? How tall are you?
② Who is the shortest? How tall are you?
③ What is the height range? (It's hard to see, it needs to be sorted out in groups)
(2) Group discussion:
How to organize in groups? Tell me what you think.
(3) The specific practice of grouping (comparison):
① Find out the range of original data (students find out the range of original data in the record sheet). 130~ 154 cm.
② Divide the data range into several groups, arrange them in a certain order, and make a table. (A group of 5cm can be divided into five groups, and then divided into two columns of "height" and "number of people" to make a table, resulting in the statistical table of Example 2)
③ Count the number of people in each group and fill in the statistical table (collect data by orthography and ask students to fill in the statistical table).
(4) Reading and answering questions:
Look at the third page of the textbook and answer the following three questions.
② Look at page 4 of the textbook. What about "think about it"? (explain the importance of the original data on the record sheet, and don't throw it away casually)
Third, classroom practice.
1. Make a weight survey of the students with the student number of 1~32 in this class, and sort out the survey results according to the grouping method.
2. Classroom assignments
Do questions 4 and 5 in exercise 1
Reflection after class:
Collecting and sorting out information is the most basic requirement of modern society, and it is also one of the necessary skills for everyone. The best way to stimulate students' learning motivation is to make them feel the significance of collecting and sorting out information.
Model essay on mathematics teaching plan in the fifth grade of primary school (4) 1. Speaking of teaching materials
1. Teaching content: the significance of the score on pages 73-74 of the tenth volume of Mathematics published by Jiangsu Education Publishing House.
2. Teaching objectives
Knowledge goal: to make students understand the generation of the score, the unit "1" and the meaning of the score, and explain the practical meaning of a score.
Ability goal: through some intuitive demonstrations and practical operations, cultivate students' hands-on operation ability and analysis and induction ability.
Emotional goal: let students actively participate and cooperate, and fully experience and feel the close relationship between mathematics and life in a relaxed and harmonious atmosphere.
3. teaching material analysis
The meaning of fractions is taught on the basis that the fourth-grade students have preliminarily understood fractions, mainly to make students understand that not only an object, but also a unit of measurement can be expressed by the unit "1", and a whole composed of many objects can also be expressed by the unit "1", thus summarizing the meaning of fractions.
4. Teaching emphases and difficulties
Establish the concept of unit "1" and understand the meaning of score.
Second, oral teaching methods
In teaching, the methods of creating situations, group cooperation and independent inquiry are mainly adopted to create a relaxed and democratic learning atmosphere for students, fully mobilize the participation of students' various senses, deepen their understanding of knowledge and feel the joy of learning.
Third, the design ideas
This lesson focuses on the meaning of fractions. The main design idea is to let students practice as much as possible, so as to get the meaning of fractions by themselves. In order to prepare for this class, I will try my best to think of the students. What materials do students need to prepare for operation? What materials can make students operate simply and learn effectively? Finally, it is decided to divide a round piece of paper, a rectangular piece of paper, a one-meter-long line segment into 10 pieces, some triangular pieces of paper and some match sticks to organize students to study in groups and improve their communication and cooperative learning ability. Try to let every mathematical knowledge take root in students' minds after they have experienced the process of knowledge generation and happy learning. Let students learn valuable mathematics and let them develop.
In classroom teaching, students use the materials I prepared for them to conduct special research. In the process of group cooperation, students get many different scores, and then gradually get the meaning of the score from these different scores. Especially when students operate with triangular pieces of paper and match sticks, they can experience many objects as a whole, that is, the unit "1", which breaks through the teaching difficulties of this course and enables students to deeply understand the meaning of fractions.
Fourth, the teaching process
(1) review
What does 1. integer division mean?
2. According to the multiplication formula 13438=5092, write two corresponding division formulas.
3. What do you mean by multiplying a fraction by an integer and a number by a fraction?
The above review questions can be answered by name.
(2) New curriculum
1. The significance of fractional division teaching.
The teacher showed five and a half pieces of moon cake teaching AIDS and asked:
(1) Everyone eats half a moon cake. How many moon cakes do five people eat? How to form? how much is it?
(2) Two and a half moon cakes are distributed to five people on average. How many moon cakes are distributed per person?
The teacher showed two and a half moon cakes, which were divided into five and a half moon cakes on average. Students are required to make formulaic calculations according to the demonstration process of teaching AIDS.
(3) Each person will be given two and a half mooncakes. How many people can you give?
The teacher asked the students to demonstrate the teaching AIDS in front of the blackboard and then calculate them in columns.
The teacher asked the students to observe and compare the known number and the obtained number of formulas in the above three questions, and then answered the following questions:
(1) What is the first known formula? Ask for what? What method is used to calculate? (Given two factors: and 5, find their product as; Calculate by multiplication. )
(2) What about the second formula? It is known that one factor of the product sum is 5, and the other factor is calculated by division. )
(3) Which of the above formulas is similar to the third formula? (Similar to the second formula, we also know that the product is and one factor is and the other factor is 5, which is calculated by division. )
Teacher: What does fractional division mean? Is it as different as integer division? (The meaning of fractional division is the same as integer division, and it is an operation to find another factor by knowing the product of two factors and one of them. )
2. Do the problem on page 30 of the textbook.
The teacher asked the students to read and do the questions by themselves. When they are finished, they should ask students how to use the meanings of multiplication and fractional division to fill in the numbers of the division formula.
3. Divide the teaching achievement by an integer.
The teacher gave an example of 1: divide the rice noodle into two sections on average. How long is each part? Teacher: according to the meaning of the question, what operation is needed to find the number? And list the formulas. (It should be fractional division, and the formula is 2. )
Teacher: What does this formula mean? How many meters is rice? How should I calculate it? Give it a try. Divide the rice into two parts equally. The meter is 6 meters. In fact, six meters is divided into two parts on average. How many meters is each part? You can list the following formulas (the teacher writes on the blackboard). )
Teacher: How do you calculate a fraction divided by an integer? A fraction divisible by an integer can be divisible by the numerator of the fraction. )
Teacher: Divide the rice into two parts equally and work out how much each part costs. What else can I do? Can you convert it into an algorithm that you have already learned? Divide the rice into two parts equally. How many meters is each section? How many meters can be counted as meters? Can be calculated by multiplication. )
Teacher: Divide the rice noodles into four sections. How long is each part? Calculate in two ways. Ask the students to calculate by themselves and name two students to act out. )
After you finish, let the students discuss which method is feasible. Which method is not feasible? Why?
(The second method is feasible. The first method is not feasible, because the numerator of the dividend cannot be divisible by the dividend. )
Teacher: Fractions divided by integers can be divided by the numerator of fractions, but the quotient of integers may not be obtained, so fractions are usually divided by integers, and the number of components is multiplied by the reciprocal of integers.
Teacher: In fractional division, can all integers be divisible? Read the textbook page 3 1 while thinking.
On the law of dividing fractions by integers.
Teacher: Why divide by integer in the conclusion to exclude 0? What does this rule have to do with the division of integers and decimals that we have learned before? (In the division operation, 0 cannot be divided, which is the same; In the operation of dividing a fraction by an integer (except 0), the number of components to be converted is multiplied by the reciprocal of this integer. )
4. Do the title on page 3 1 of the textbook.
Let the students do the questions independently, and the teacher will patrol. Pay attention to students' calculation errors when patrolling. Collective revision
Let the students talk about the wrong way. Generally speaking, there are:
Let the students talk about the reasons for the mistakes.
(1) After the divisor is changed to a multiplier, the divisor is not changed to its reciprocal accordingly.
(2) After the divisor is changed to its reciprocal, the divisor is not changed to a multiplier.
The teacher added the following exercises:
Fill in the appropriate operation symbols or numbers in ○.
(3) Consolidate exercises
1. Do the 1 question in Exercise 8.
Let the students do it independently, and the teacher reminds them to do the questions according to the rules. If they can do it orally, they should do it orally. When patrolling, we should pay attention to helping students with difficulties and correct mistakes in time. Collective modification after completion.
2. Do the second question in Exercise 8.
Let the students finish it independently. When revising collectively, ask the students to talk about the topic corresponding to the second line for each item in line 1.
What is the connection? It is clear that the dividend in each column division formula is the product of the above multiplication formula, while the divisor is one factor in the multiplication formula and the divisor is another factor in the multiplication formula.
3. Do exercise 8, question 3 1 column.
Let the students explain the basic method of the equation first, then finish it independently, and then modify it collectively.
4. Do Question 5 of Exercise 8.
Ask the students to read the questions carefully and analyze the quantitative relationship before doing them. After finishing, let the students talk about the quantitative relationship and algorithm of the questions. Let the students know the weight of eight eggs, and how many kilograms each egg weighs on average, that is, divide the kilograms into eight parts on average, so it should be calculated by division.
(4) Summary
Teacher: Today we learned the meaning of fractional division and the calculation method of fractional division by integer. These contents are the basis of this unit. When reviewing, you should read the contents of the textbook on pages 30 ~ 3 1 with examples to further understand what you have learned.