Knowledge and skills

With the help of line graph, students can deepen their understanding of the concept of multiple, solve the practical problem of "how many times is a number" by multiplication, correctly distinguish two kinds of multiple problems, and cultivate students' ability to solve problems by using concepts. And in the process of solving problems, cultivate geometric intuition and infiltrate model ideas.

(2) Process and method

Cultivate students' abilities of observation, analysis, cooperation and communication, language expression and rigorous examination of questions, attach importance to the role of geometric intuition, help students understand mathematics through various intuitive forms, provide students with opportunities to participate in geometric intuitive activities, and accumulate experience in learning mathematics with pictures.

(3) Emotional attitudes and values

Experience the joy of success in the process of independent exploration, cooperation and communication, and problem solving.

Second, the diagnosis and analysis of teaching problems

The learning content of "how many times a number is a number" is still an abstract knowledge for the understanding ability of junior three students. Although children have a certain foundation in the concept of multiples and know the relationship between "1 weight" (standard quantity) and "comparative quantity", these mathematical languages are far from easy to understand. Rich practical problems should be designed in teaching, so that students can gain a lot of perceptual knowledge through practical operation, and then gradually transfer from the consolidation of old knowledge to the study of new knowledge. It is only necessary to abstract the "thing" studied as "figure", and then transform "the relationship between things" into "the relationship between figures", so the problem to be studied is "the number or position relationship of figures", and then think and analyze it. It is convenient for students to construct mathematical models in comparison and abstraction to solve such problems. Let students learn to draw a line diagram to express the quantitative relationship, understand the meaning of the problem, and let students clearly solve the problem of "how many times is a number" by multiplication. In the teaching of "how many times is a number" for students, in order to reduce the difficulty of students' understanding of knowledge, the number should be as few as possible, and students should use learning tools as much as possible to deepen their understanding of knowledge through intuitive images. Combining the knowledge of previous students, find the correct solution to achieve the teaching purpose of this class.

Third, teaching focuses on difficulties.

Teaching focus: The teaching focus of this course is to explore the calculation method of "how many times is a number" and the relationship between times.

Teaching difficulties: using the learned method of "seeking a few" to solve new problems and realize the transfer of knowledge.

Fourth, teaching preparation.

Courseware and practice cards

Teaching process of verbs (abbreviation of verb)

(A) dredge the concept and activate the original knowledge

Review old knowledge.

(1) See the formula in the figure.

①

Formula:

②

top row

Something prepared

How many times is the second line the first?

Formula:

2. Variant application

(2) Say and fill in.

① Six fives are () and two sevens are ().

②5×8= (), where () is () times of 8 and () times of 5.

③

The price is () times.

The design aims to link the systematization of knowledge with the follow-up of knowledge, find a breakthrough point for the study of new courses, and review the relationship between multiplication meaning and multiplication through intuitive diagrams, arouse students' experience, stimulate students' desire for learning and find the "starting point" for exploration.

(2) Transfer knowledge and build new knowledge.

1. Introduce the scene, analyze the information and understand the meaning of the question.

Teacher: Every student has the experience of shopping. Shopping has many math problems. What math problems did the following students encounter when shopping?

Courseware shows the theme map.

(1) Reading and understanding

Teacher: What information did you find?

Information on the blackboard: The price of military flag is 8 yuan, and the price of chess is four times that of military flag.

Question: What's the price of chess?

Show pictures in courseware

The design aims to introduce new lessons with things that students are familiar with, which can not only stimulate students' interest in learning, but also let students know that mathematics knowledge comes from life. With the help of courseware, students can abstract mathematical problems from concrete things, which conforms to students' cognitive characteristics and provides rich materials for the introduction of new knowledge.

(2) Analysis and answer.

Try to answer.

Some students may answer: the price of chess is 32 yuan, or the formula: 8×4=32.

The teacher asked: How do you know? How to verify whether his answer is correct?

Try to draw a picture to express the quantitative relationship.

Teacher: We know the quantitative relationship between the two prices. If we can show it as illustrated in the review question just now, we can see it more clearly.

Students discuss: how to express the relationship between these quantities concisely and clearly.

Guide students to express the quantitative relationship between military flag and chess with the length of line segment diagram.

The teacher explained that the length of the line segment should be used to represent the specific quantity in the line segment diagram, and the relationship between the line segment lengths in the diagram should conform to the quantitative relationship of the topic.

Let the students try to draw a picture on the draft paper and analyze it. After drawing, share your drawing methods at the same table.

③ Language expression, reporting and communication. (Platform display. )

④ Analyze and discuss the method of drawing line segments.

Draw a line segment to indicate the price of the flag (8 yuan). Then according to "chess is four times as long as a military flag", draw four continuous line segments with the same length as the first line segment to show the price of chess.

The teacher asked: Why are the number of military flags represented by shorter line segments? How to tell which line segment represents the military flag? How to see clearly that chess is four times that of military chess? How to express the problem in line segment diagram?

Teacher-student summary: The text in front of the picture shows that the weight of 1 (standard quantity) is short. When the "comparison quantity" is several times that of the "standard quantity", several paragraphs are drawn. The length of each paragraph should be consistent as far as possible, and the upper and lower numbers should correspond to each other.

⑤ Demonstrate the process of drawing a line segment diagram, so that students can improve their line segment diagram through comparative analysis.

The courseware shows each part of the line segment diagram in turn.

⑥ Understand the line diagram, analyze the meaning of the question and find the strategy to solve the problem.

Guide the students to see from the picture: If you want to know the price of chess, how much are the four eights? Calculate by multiplication "

8×4=32 (yuan)

Ask the students to talk about the meaning of the formula with the line graph.

Write on the blackboard: What is four times eight? How much are four eights? 8×4=32 (yuan).

Although the design intent diagram intuitively expresses the quantitative relationship with geometric line segments, it is abstract for students who are in contact for the first time. In the analysis and discussion, let students feel the simplicity of line drawing, and gradually guide them to draw vivid physical drawings or abstract line drawing, so that students can slowly transition to line drawing. It is necessary to strengthen the guidance of drawing line segments and pay attention to teaching requirements.

(3) Review and reflection.

Are you sure your calculation is correct? what do you think?

Show pictures in the courseware.

Explain the test method, which can be tested by division. Supplement answers, guide students to form the habit of answering questions completely, and reflect the standardization and integrity of mathematics.

(4) Variant exercises and strategies.

①

What is the price?

Students try to answer columns, report exchanges and write on the blackboard.

Write on the blackboard: What is three times nine? How much are three nines? 9×3=27 (yuan).

Teacher: There are many things in the sporting goods store. What else did you see?

② Courseware display information: the price of shuttlecock is 5 yuan, and the price of skipping rope is three times that of shuttlecock.

Teacher: Can you draw a line segment to represent the relationship between two quantities? Ask a math question? How much is skipping rope? )

Please try to draw a line diagram to represent the quantitative relationship and solve it.

The deskmates exchange lines with each other, and the whole class gives feedback. The teacher writes on the blackboard.

Write on the blackboard: What is the number of three times five? What's the number of three to five? 5×3= 15 (yuan).

(5) Summarize and compare abstract models

Compare the similarities and differences of 8×4=32, 9×3=27 and 5×3= 15. Further speculation on the essence of "Why do we all use multiplication"

In comparison and speculation, the relationship between the two quantities is gradually clarified, and the problem of "how many times is a number" is deepened, that is, how many times is a number, and the significance of multiplication is linked to understand the truth of multiplication calculation.

Write on the blackboard: How many times is a number? How many times?

1 quantity (standard quantity) × multiple = comparison quantity

The modeling process of "how many times is a number" is the difficulty of this lesson. Starting from the above steps, let students gradually abstract this model through comparison and induction with the help of analyzing and understanding the line segment diagram in specific situations. This process not only enables students to clearly understand the basic strategies of analyzing practical problems, accumulate experience in solving problems, but also improves students' interest in learning mathematics and their awareness of application.

(C) comprehensive application, enhance capacity

1. Consolidate applications and enhance capabilities.

(1) Exercise 1 1 Question 5 (courseware presentation)

Let the students finish it independently. When communicating and reporting, focus on the meaning of the formula "7×3=2 1". "Why multiply by 3?"

(2) Exercise 1 1, Question 6 (Show Courseware)

① Read the materials, use strategies and explain the process.

② Peer help each other and deepen understanding.

Design intention: two exercises: design highlights progressive thinking. The first question, let students look at the diagram combining schematic diagram and line segment diagram, improve the ability of examining questions and reading drawings, gradually learn to see and express quantitative relations with line segment diagram, and cultivate geometric intuition; The second question, let the students describe the problem about time completely in the same question type, and cultivate their ability to express it in mathematical language.

2. communication expansion.

Exercise 1 1 question 7 (courseware demonstration)

① Situation creation: The courseware presents the situation diagram of Question 7, and the information and questions appear first: Wang Ping only kicked three, and Li Fang kicked 18.

② Question (1) How many times did Li Fang kick Wang Ping? Ask students to answer independently. 18÷6=3. Tell the meaning of the formula.

The teacher asked: whose number is the standard quantity?

Question (2) Liu Mei kicks twice as often as Wang Ping. How many did Liu Mei kick?

③ Analysis question: Whose number is the standard quantity, and how to express the relationship between Liu Mei and Wang Ping? .

(4) Drawing a line diagram for analysis:

Students try to answer columns, report exchanges and write on the blackboard.

3×2=6 (piece)

⑤ Comparison: Question A. How many times did Li Fang kick Wang Ping? Formula: 18÷6=3.

Liu Mei plays twice as often as Wang Ping. How many did Liu Mei kick? 3×2=6。

Teacher: These two questions are related to the knowledge of multiplication. One is division calculation, and the other is multiplication calculation. what do you think?

Students discuss, report and communicate.

Teachers and students sum up: when solving "how many times is one number another", it is to find out how many numbers a number has and calculate it by division; In solving the problem of "how many times is a number", it is to find out how many times a number is and calculate it by multiplication.

Although it is not difficult for students to design the method of solving problems by columns, they still need a lot of concrete examples to compare, speculate and model, to perceive the process of knowledge formation, to gradually internalize the method of solving problems, to constantly trigger cognitive conflicts and to stimulate the rigor of examination. From shallow to deep, from simple to complex, from intuitive to analytical reasoning, we follow students' cognitive laws and explore the essence of solving problems through physical representation, operational representation, language representation, graphic representation and symbolic formula representation.

(d) Flexible use, expansion and extension

1. Look at the formula.

What's the number of (1)?

(2) How many?

2. Tell me about it.

(1) Draw 2 in the first line ☆ The number of △ in the second line is 6 times that of ☆, and the second line has () △.

(2) The first line is 15 ☆, the number of the first line is three times that of △, and the second line is () △.

3. Exercise 1 1, Question 9 (Show Courseware)

(1) Students try to do it by themselves.

(2) report and exchange collective analysis.

The design intention is to connect the old and new knowledge seamlessly through layered exercises, and let students know the situation in life through intuitive charts and abstract words, so as to make the construction of various knowledge problem models more clear on the basis of intuitive understanding. Let students use what they have learned to solve practical problems in specific life situations and problem situations, so as to consolidate and improve what they have learned, reflect the application value of mathematics and enhance students' learning confidence.

(5) Review, summarize and improve the classroom.

Teacher: What did you learn in this class? What did you get? Can you give an example?