Sample notes for primary school mathematics lectures

Listening to lectures is one of the main forms of school teaching and research activities, and it is also a basic skill that teachers must possess. Below are some notes from primary school mathematics lectures, welcome to refer to them.

1

1. Divergent thinking and eliciting topics

Example: Divide -4, +3, +4, -3 into two groups.

1. Divide -4 and -3 into one group, and divide +4 and +3 into another group, that is, divide negative numbers into one group and positive numbers into another group.

2. I divided -4 and +4 into one group, and -3 and +3 into another group. I used the same number as the basis for grouping.

3·I put -4 and +3 in one group, and +4 and -3 in another group. The reason is that the signs of the two numbers are different, and the numbers behind the signs are also different.

2. Comparative summary and refined definition

Generally, a number consists of two parts, namely the symbol and the "number behind the symbol" just mentioned. Consider these two aspects , we also adopted three different classification methods. The two aspects are different is a kind of division method. Whether the "symbol" is the same is used as the basis for grouping. What is obtained is a group of positive numbers and a group of negative numbers that have been learned. Whether the "number behind the symbol" is the same is used as the grouping. Based on the above, we got pairs of numbers like -4 and +4, +3 and -3, so what numbers should they be called?

This is what we need you to learn in this lesson. Content: Opposite number.

Why are they called opposite numbers and not other numbers?

A positive number and a negative number have opposite meanings, so they are called opposite numbers.

Two numbers with different signs and the same number behind the signs are called opposite numbers.

The two numbers obtained by adding different symbols in front of a number are called opposite numbers.

Teacher: Please give an example.

For example, adding "+" and "-" in front of 5 results in +5 and -5 being opposite numbers.

The textbook says that "two numbers with only different signs are called mutually opposite numbers"

"only different signs" means that everything else is the same, including "the numbers behind the signs are the same " means.

Two numbers that have the same number after the symbol are called opposite numbers.

The implication of "Only the numbers behind the symbols are the same" is "the symbols are different", which is consistent with the statement in the textbook. It can be seen that the same meaning can be expressed in different languages. We should pay more attention to this in mathematics learning. It should be noted that the textbook uses "only the symbols are different" to include "the numbers behind the symbols are the same". The advantage is that it makes the concept of opposite numbers more refined and also avoids the confusion easily caused by using the statement "the numbers behind the symbols". Misunderstanding, we will see about this later.

Teacher: "Hu" means "mutual". For example, +4 is the opposite of -4. It can also be said that -4 is the opposite of +4, that is, +4 and -4 are the opposite of each other. number. Please make it more specific what "+3 and -3 are opposites of each other" means.

The textbook specifically points out that writing on the blackboard: the opposite of 0 is 0.

Oral answer practice: Say the opposite of each of the following numbers:

-7, -0.5, 0, 6, +1.5

3. Combination of numbers and shapes , discuss in depth

For example, please mark the point on the number axis that represents the opposite of +4.

0 4

From the number axis, the opposite of +4 Another feature is: it means that the distance between the points of each pair of opposite numbers and the origin is equal

In the concept of opposite numbers, "only the signs are different" includes other similarities, that is, "the numbers behind the signs are the same." On the number line, distances are equal.

Mastered the method of analyzing problems mentioned by the teacher. Regarding the opposite number, we study it from two aspects: "symbol" and "the number behind the symbol". The characteristics of these two aspects are not only included in the concept of opposite number, but also reflected on the number axis. Consider the two together. Will be helpful for future mathematics learning.

So far, what are the special aspects of zero?

Senior: Zero is neither a positive number nor a negative number; the opposite of zero is still zero; zero Cannot be used as a divisor.

Exercises and solutions

Attached is some blackboard writing

Two numbers with only different signs are called mutually opposite numbers. The opposite of zero is still zero.

The signs are opposite and separated on both sides of the origin

The distance to the origin is equal

Through this class taught by Teacher Li Hongge of Class 3, Grade 7, I discovered my own Not enough, come on!

May everyone be happy!!!

2

1. Create situations and initial perceptions

Conversation: Look at what the teacher is holding in his hand. A triangle, can you find out how many corners it has?

2. Organize activities and explore new knowledge

1. Understand the corners

p>

Projection display: Project the pictures in the textbook

Conversation: Look for it, which pictures look like corners? Student answers

Follow-up question: Corners have no role in our lives Everywhere, how many vertices and sides does an angle have? Can we find angles from the surfaces of some objects around us? Point out their vertices and sides after finding them.

2. Fold a corner

Conversation: We already know the corner, can we use our dexterous little hands to fold a corner? Let’s see who can fold it quickly and well. Use the prepared white paper to fold the corners

3. Comparison of corner sizes

1 Question: Can you make the corners you fold bigger? What did you do? Can Make it smaller? How to do it?

2 When the hour and minute hands on the clock face rotate, angles of different sizes are formed. Can the students compare which angle is larger? ?What method is used to compare?

3 Conversation: Observe the two triangles in the teacher’s hand. There are two triangles made of paper, one large and one small. Which triangle is larger? Or is it the same size? You know Is the size of the angle related to anything?

3. Solid application, expansion and extension

1. Textbook exercise question 1. Conversation: The clever little monkey found some shapes and wanted to test the children. Do you dare to accept its challenge? Projection display of the shapes: Which ones are angles and which ones are not angles? Can you point out the vertices and sides of the angles? Name them. answer.

2. Textbook exercise question 2. Conversation: The studious little cat felt that the children had learned well, so he came to ask us for advice. Projection display, how many corners are in each picture, tell your classmates.

3. Practice questions 3 and 5 in the textbook. Conversation: The smart little rabbit saw how good everyone was and finally couldn’t help but come to test us too, projecting the questions on display. Communicate within the class after discussion with classmates.

4. Textbook exercise question 4. Conversation: Teacher Goat was very satisfied with everyone and decided to take the children to play.

Pull and close the scissors with your hands. Talk about the changes you see in the corners

4. Summarize the whole lesson and assign homework

Conversation: What did you gain from studying this lesson? Go home and give it to your dad Mom, show me the skills you learned today. Find which objects in your house have horns.

Comments:

1. Guide students to be good at discovering teaching problems in daily life and use life experience.

Let students fully experience mathematical knowledge, understand mathematical knowledge, and apply mathematical knowledge to practical activities. By "looking for corners in common objects in life", students feel that mathematics is closely connected with life, which enhances students' understanding of the value and role of mathematics and stimulates students' enthusiasm for learning mathematics.

2. Guide students to practice and explore independently, and promote mathematical thinking.

Focus on guiding students to practice, understand knowledge and develop thinking during operation. Change the situation where teachers dominate the classroom, boldly let go, and change the past situation of simply watching teachers’ demonstrations to students doing it themselves, mobilizing students’ initiative. This lesson is designed with links of "finding", "speaking" and "doing" to help students understand the angle and understand the size of the angle in mathematical activities, which makes students more interested in learning and effectively cultivates students' observation and operation abilities. , expression ability and analysis and summary ability.

3

The first action teaching

......

1. Create scenarios

Teacher: classmates Have you read "Journey to the West"? Is the content in it exciting? Today the teacher will tell you a story about Sun Wukong dividing the peach.

After Sun Wukong came back from studying in the West, he couldn't wait to come to Huaguo Mountain to see his children. He brought gifts to the children - peaches. When he was dividing the peaches, he wanted to play with the children. Sun Wukong said: "Put 8 Share the peaches equally among the 2 monkeys!" The children below shook their heads repeatedly: "Too few! Too few!" Sun Wukong said, "Well, how about sharing the 80 peaches equally among the 20 monkeys? ?." The little monkeys took advantage of the situation, scratched their scalps, and said tentatively: "Your Majesty, can you give me more?" Sun Wukong patted his chest and showed his generosity: "Then divide the 800 peaches equally. 200 monkeys, you should be satisfied, right? The little monkeys smiled, and Sun Wukong also smiled.

Teacher: Which of the students smiled smarter, and why?

Student 1: The monkey king’s smile is a smart smile. The total number of peaches and the total number of monkeys have changed, but the number of peaches each little monkey received has not changed.

Student 2: The monkey king’s smile was a smart one. Because the monkey king deceived the little monkeys, each little monkey still got 4 peaches.

2. Explore the rules.

Teacher: Can you list the calculations? The teacher randomly wrote on the blackboard:

8÷2=4

80÷20=4

800÷200=4

Teacher: Please look at these three equations carefully and see what you found? Discuss them in the group.

Students start group activities. .

Student 1: Expand 10 times, and the quotient is still 4;

Teacher: How did you observe?

……

In the following reports, many students did not answer according to the ideas I prepared for the lesson. The entire arrangement was disrupted and a lot of time was wasted. Some students even made mistakes in the reports.

Reflection

According to my lesson preparation ideas, I think that the teaching in this link should be smooth, and students should be able to successfully complete this link of teaching. How can this happen in the actual teaching process? In reflection and this During the course evaluation process of the group of teachers, I gradually realized that my arrangements seemed reasonable, but in fact, I did not seriously consider the students' existing experience level, did not consider the students' perspective, and failed to communicate with the students' living world. The questions I raised were too big, which led to a lot of wasted time in teaching here. Even though I squatted down to "help the students" in class, the students were still "out of reach". It seems that there is a big gap between my understanding and that of students in some aspects.

Improvement strategies

Don’t rush to let students solve this problem. Give them a "crutch". It is necessary to combine the age characteristics and cognitive level of the students, and the throwing problems should be appropriately combined. Provide timely guidance and guidance. Because this was an observation class outside the school, I based on the opinions of the teachers in this group and combined with my own reflection. After active and independent thinking, I improved the first action plan again and carried out the second one. times teaching.

The second action teaching

After telling the story of Sun Wukong dividing the peach, he asked:

Teacher: Which of the students has a smart smile? Why?

Student 1: The Monkey King’s smile is a smart smile. The total number of peaches and the total number of monkeys have changed, but the number of peaches each little monkey gets each time has not changed.

Student 2: The monkey king’s smile is a smart smile. Because the monkey king deceived the little monkeys, each little monkey still got 4 peaches.

Teacher: Where did you see it?

※Guide students to list the calculation formula:

①8÷2=4

②80÷20=4

③800÷200=4

※Guide students to observe in an orderly manner and explore the rules: comparing the second equation with the first equation, the dividend and divisor have both expanded by 10 times, the quotient remains unchanged; comparing the third formula with the second formula, the dividend and divisor have expanded 10 times, and the quotient remains unchanged; comparing the third formula with the first formula, both the dividend and the divisor have expanded 100 times, looking from top to bottom, the dividend and The divisors are simultaneously multiplied by the same multiple and the quotient remains unchanged.

※Ask students: What else have been discovered? Looking from the bottom up, what are the patterns? This link allows students to communicate in groups.

Reflection on the entire lesson

In the following teaching, I got along very well with the children.

Students have gone through the process of analysis-synthesis-abstract summary, which not only helps students understand the rules, but also helps cultivate students' preliminary logical thinking ability and methods of learning mathematics. In the process of learning, I paid attention to the development of students' subjectivity, allowing students to explore independently and learn cooperatively, so that every child can be a discoverer, researcher, and explorer of new knowledge.

In these two consecutive teachings, my teaching quality has been improved as a whole. In future teaching practice, I will help students discover, organize and manage knowledge, guide them instead of "create" them; let students experience and understand with their own true feelings; let more students try the joy of success , allowing students to participate in the entire process of knowledge formation from beginning to end. Now, I deeply feel: Curriculum reform has no end; curriculum reform is always in the present tense.

People who have read the primary school mathematics lecture notes also read:

1. The experience of listening to the open class of primary school mathematics

2. The experience of listening to the high-quality primary school mathematics class Experience

3. Primary school mathematics teachers’ experience in listening to classes

4. Primary school mathematics teachers’ experience in listening to and evaluating classes

5. Primary school mathematics teachers’ experience in listening to classes