Teaching content: People's Education Publishing House, the fifth grade of primary school mathematics, Volume II, "Expressing quantitative relations with formulas containing letters"

Analysis of learning situation: most of the knowledge in this unit is abstract, so we should make full use of students' original relevant knowledge and pay attention to the abstract generalization process from concrete examples to general meaning. When learning to express quantitative relations, equation concepts or equation properties by letters, we should not only give full play to the supporting role of concrete examples in abstract generalization, but also guide students to get rid of the concreteness of examples in time and make necessary abstract generalization.

Teaching objectives

Knowledge and skills: On the basis of understanding the quantitative relationship, students will use formulas containing letters to express the quantitative relationship.

Process and method: On the basis of understanding the specific meaning of the formula containing letters, students can work out the value of the formula containing letters according to the value of letters.

Emotion, attitude and values: cultivate students' abstract thinking ability and inductive generalization ability.

Teaching emphasis: quantitative relations will be expressed by formulas containing letters.

Teaching difficulty: understanding the meaning of expressing quantitative relations with formulas containing letters.

Teaching Preparation: Micro-course and Teaching Courseware of "Expressing Quantitative Relationship with Formulas Containing Letters"

teaching process

First, check the import.

1. Fill in the appropriate name in the () below.

Projection demonstration exercise.

() × time = distance

Single output × () = total output

Work efficiency × time = ()

() × () = total price

2. introduction

Teacher: Your math textbook is 14.5 yuan. How much does it cost to buy a math textbook and a math extracurricular reading?

Students will definitely ask how much the textbooks for math extracurricular reading are. Teachers can point out that when we don't know the price of math extracurricular reading, we will use the letter X.

Now who can tell how much it costs to buy a math textbook and a math extracurricular reading?

Ask the students to answer: What does 14.5+x mean?

Teacher: This formula with letters can also express quantitative relations. Today we will discuss this problem.

2. Teaching implementation

1. Name the students and tell their ages.

Li Mingbao 1 1 year old.

Teacher: The teacher is 25 years older than Li Ming. What's the age of the teacher? Please calculate the teacher's age when Li Ming 1, 2, 3 years old ... and now he 1 1 year old.

The teacher wrote on the blackboard:

Li Ming's age, the teacher's age

1 ? 1+25=26

2 2+25=27

3 3+25=28

4 4+25=29

Question: Have you finished asking the teacher's age? (No) Why? Because Li Ming is growing up, every year Li Ming's age increases, and so does the teacher's age. What do these formulas mean? [The above formula indicates that when Li Ming 1 year old, the teacher is (1+25) years old; When Li Ming was 2 years old, his teacher was (2+25) years old ... When Li Ming 1 1+25 years old, his teacher was (1 1+25) years old ...] Although Li Minghe's age is changing, what hasn't changed? (The teacher is 25 years older than Li Ming)

We have learned to use letters to represent numbers. Can you use a concise formula to express the age of teachers?

Use the letter A to indicate Li Ming's age, so the teacher's age is a+25. (Other letters are acceptable)

The teacher continued to write on the blackboard: A and a+25.

What information do you know from formula a+25?

Students discuss at the same table or in groups, then exchange reports. A+25 not only shows the age of the teacher, but also shows that the teacher is 25 years older than Li Ming. Therefore, as long as we know Li Ming's age A, we can use this quantitative relationship to calculate the teacher's age.

Teacher: Yes, as long as we know Li Ming's age, we can know the teacher's age. We can calculate; How old was Li Ming 12 when he graduated from primary school?

The students answered, and the teacher wrote on the blackboard: When a= 12, a+25= 12+25=37.

Teacher: How old was the teacher when Li Ming 19 was admitted to the university?

The students answered, and the teacher wrote on the blackboard: When a= 19, a+25= 19+25=44.

Thinking: We have learned to use a formula containing letters to express quantitative relations. What are its advantages?

Through discussion, students realize that letters can express the relationship between quantities.

2. Show the example on page 52 of the textbook 1:

(1) Ask the students to read the questions silently and understand the meaning of the questions.

(2) Students describe the meaning of the question in their own language.

(3) Students solve problems independently.

(4) Students exchange and revise collectively.

3. Play the micro lesson to explain Example 2 on page 53 of the textbook.

On the moon, the mass that people can lift is six times that of the earth.

(1) Read the questions and guide the students to make their own calculations according to the following process, and fill in the table below.

Mass of objects that can be lifted on the earth/kg

Mass of objects that can be lifted on the moon/kg

1

1×6=6

2

2×6= 12

three

3×6= 18

(2) ask questions.

Teacher: If the letter X is used to represent the mass that people can lift on the earth, can the formula containing letters be used to represent the mass that people can lift on the moon?

(3) Calculation: What is the weight that the child in the illustration in the textbook can lift on the moon?

Students communicate after calculation, and the teacher writes on the blackboard: 6x = 6x 15 = 90 (kg).

(4) Tell what numbers the letters in Example 2 can represent.

Note: People's life span is limited, and the weight they can lift is also limited, so the numbers represented by A and X are also limited.

Third, classroom exercises.

1. formula calculation.

There are m cars in the parking lot. Take eight cars.

(1) When m=24, how many cars are left?

(2) When m=32, how many cars are left?

2. Think about it and fill it in.

When x= (), 8 ÷ x =1; When x= (), 8÷x=8;

When x; 8; When x> (), 8 x

Teaching reflection

1. Modify the examples appropriately and choose examples that are close to students' real life.

For primary school students, it is abstract to express the quantitative relationship with a formula containing letters. Students are often not used to treating "a+25" as a quantity, and often think it is a formula, not a result. Replacing "the age relationship between Xiaohong and his father" in the textbook with "the age relationship between students and teachers" makes the textbook closer to the teaching practice and easier to stimulate their interest in learning.

2. Play micro-lessons, give students the initiative to learn, and let them find and solve problems by themselves.

Using micro-class teaching can improve students' initiative and interest in learning mathematics, and establish an interactive learning model.

When solving the problem that "teachers are 25 years older than their classmates", students are required to simply express the age of teachers in any year with a formula, and the learning task is given to students, so that students can discuss how to express this formula themselves, which is simple and clear, so that students can deeply understand the significance and superiority of the formula "a+25" in two discussions and give full play to their main role in class.