Can you provide a junior high school math lesson preparation model?

Subject 4.3.3 Complementary Angle and Complementary Angle Class 1

You Tingrong, Lecturer of Class 2 of Grade 08 Mathematics.

teach

study

eye

Standard knowledge and ability 1. In specific realistic situations, we should know the complementary angle and complementary angle of an angle and master their properties.

Knowing the position, you can determine the position of a specific object.

Process and method 1. Further improve students' abstract generalization ability, develop students' spatial concept and knowledge application ability, learn simple logical reasoning, and make reasonable guesses on the conclusion of the problem.

2. Discuss with your peers to understand the relationship between quantity and quantity.

Emotional attitude values 1. Experiential observation, induction and reasoning play an important role in obtaining mathematical conjecture and demonstration in mathematical knowledge.

2. The rigor of reasoning and the certainty of conclusions in preliminary mathematics can benefit from independent thinking and group communication.

Complementarity, complementarity and essential teaching are the keys to understanding the angle.

Teaching difficulties are summarized through simple reasoning, and the properties of complementary angle and complementary angle can be described in standardized language.

Teaching essentials Understanding the meaning and process of reasoning is the key to mastering the essence.

Research on School-based Teachers' Teaching and Group Cooperation

Making PPT courseware for teaching AIDS

teaching process

Teachers' intention of designing students' activities flexibly.

First, ask questions and introduce related concepts.

Do the students know the famous Italian building Leaning Tower of Pisa? (drawing with PPT)

The leaning tower of Pisa was built in 1 173. This project was interrupted twice and lasted for a long time, which took about 200 years to complete. It was designed to be built vertically, but due to uneven foundation and soft soil layer, it tilted shortly after the project started.

Second, the new lesson explanation:

1, explore the definition of complementary angle;

If the sum of two angles is 90 degrees (right angle), then these two angles are called complementary angles, and one angle is the complementary angle of the other angle. That is, ∠ 1 is the complementary angle of ∠2 or ∠2 is the complementary angle of ∠ 1

2. Exercise (1): (given by PPT)

What are the complementary angles of the angles given in the figure?

3. Explore the definition of complementary angle:

If the sum of two angles is 180 (flat angle), then these two angles are called complementary angles, and one angle is the complementary angle of the other. That is, ∠3 is the complementary angle of ∠4 or ∠4 is the complementary angle of ∠3.

4. Exercise 2: (given by PPT)

The angles given in the (1) diagram are mutual.

(2) Fill in the list (given by PPT):

The complementary angle of ∠ a ∠ a ∠ a.

five

32

45

77

62 23′

x

Conclusion: The complementary angle of the same acute angle is 90 larger than other angles.

(3) Fill in the blanks (given by PPT):

① The complementary angle of 70 is, and the complementary angle is.

②∠a(∠a & lt； 90 is its complementary angle, and its complementary angle is.

Important reminder: I (how to express the complementary angle and complementary angle of an angle)

The complementary angle of acute angle ∠a is (90-∠ A).

The complementary angle of ∠a is (180 —∠ a).

Ⅱ Complementarity and complementation are quantitative relations between two angles, which have nothing to do with their positions.

5. Explain examples:

Example 1: If the complementary angle of one angle is equal to 4 times of the other angles, find the degree of this angle.

Solution: Let this angle be x, then its complementary angle is (180-x) and its complementary angle is (90-x).

According to the meaning of the question:

( 180-x )= 4 (90-x)

Solution: x =60

The degree of this angle is 60 degrees.

6. Exercise (3):

The complementary angle of an angle is three times that of it. What's the angle?

7, explore the essence of complementary angle (PPT):

As shown in figure ∠ 1 and ∠2 are complementary, ∠3 and ∠4 are complementary. If ∠ 1 = ∠ 3, then ∠2 equals ∠4? Why?

The nature of complementary angle: the complementary angle of the same angle or equal angle is equal.

∵ ∠ 1 +∠2= 180 , ∠3 +∠4= 180

∴ ∠2= 180 -∠ 1 , ∠4= 180 - ∠3

∵ ∠ 1 =∠3

∴ 180 -∠ 1 = 180 - ∠3

Namely: ∠2 =∠4

8. Explore the essence of complementary angle (PPT):

As shown in figure ∠ 1 and ∠2 are complementary, and ∠3 and ∠4 are complementary. If ∠ 1 = ∠ 3, are ∠2 and ∠4 equal? Why?

Complementary angle property: the complementary angle of the same angle or equal angle is equal.

∵ ∠ 1 +∠2=90 , ∠3 +∠4=90

∴ ∠2=90 -∠ 1 , ∠4=90 - ∠3

∵ ∠ 1 =∠3

∴ 90 -∠ 1 =90 - ∠3

Namely: ∠2 =∠4

9. Explain azimuth (given by PPT):

(1) Understanding positioning:

Due east, due south, due west, due north,

Southeast, southwest, northwest and northeast.

(2) looking for directions:

Azimuth from IB to A Azimuth from IIA to B.

10, give an example (given by PPT):

Example 3: Multiple choice questions:

(1)A looks at the direction of B, which is the northeast direction of 2 1, so B looks at the direction of A ().

A: 69 south east b: 69 south west c:2 1 south east d:2 1 south west.

(2) As shown in the figure, what is wrong in the following statement is ()

A: The direction of a:OC is 60 due east and north.

B: The direction of b:OC is 60 east-south.

C: The direction of ob is southwest.

D: the direction of d:OA is 22 north-west.

Example 4: As shown in the figure, during the voyage of cargo ship O, lighthouse A was found in the direction of 60 east of south, while passenger ship B, cargo ship C and island D were found in the directions of 40 east of north, west of south10 and northwest (i.e. 45 west of north) respectively. The rays representing the direction of passenger ship B, cargo ship C and island D are drawn according to the method of indicating the direction of the tower.

Third, the class summary:

1, this lesson learned complementary angles and complementary angles, and obtained the properties of complementary angles and complementary angles through simple reasoning.

2, understand the direction, learned to determine the direction of the object movement.

Fourth, homework:

①P 1 14 solving problems 9

② Choose 1 1 and 12 as a topic.

(3) Choose a topic as an assignment.

Let the students observe the leaning tower of Pisa, a famous Italian building, and listen to the teacher.

Student observation chart

Group communication after independent thinking.

Oral answer

Students observe the pictures, think independently and communicate in groups.

Peer discussion

come to a conclusion

Student training

Group exchange

Group exchange

Group exchange

Look at the pictures and actively participate in the teacher's explanation.

Student answers

Let the students pay attention to the tilt of the tower and introduce the topic

Cultivate students' ability to analyze problems

Consolidate the definition of complementary angle and deepen understanding.

Consolidate the definition of complementary angle and deepen understanding.

Cultivate students' ability to analyze problems

Apply what you have learned, sublimate

Test the mastery of knowledge.

Consolidate knowledge in the discussion and cultivate the awareness of cooperation and exchange. Improve students' learning enthusiasm

After knowing the definition of supplementary angle, increase the training of test sites.

blackboard-writing design

4.3.3 Complementary Angle and Complementary Angle

1, definition of complementary angle:

If the sum of two angles is 90 degrees (right angle), then these two angles are called complementary angles, and one angle is the complementary angle of the other angle.

2, the definition of complementary angle:

If the sum of two angles is 180 (flat angle), then these two angles are called complementary angles, and one angle is the complementary angle of the other.

3. The nature of complementary angle and complementary angle:

The complementary angles of the same angle or the same angle are equal.

4. Direction:

Orientation: as shown in the figure.

Azimuth: azimuth from B to A, azimuth from A to B.

4 class summary:

1, this lesson learned complementary angles and complementary angles, and obtained the properties of complementary angles and complementary angles through simple reasoning.

2, understand the direction, learned to determine the direction of the object movement.

Five tasks:

①P 1 14 solving problems 9

② Choose 1 1 and 12 as a topic.

(3) Choose a topic as an assignment.