1. In the activities of drawing, classification and discrimination, understand the positional relationship between two straight lines, and understand the special positional relationship between two straight lines in the same plane-parallel and vertical.

2. In the process of discriminating and understanding knowledge, the parallel and vertical spatial concepts are initially established to cultivate students' spatial imagination ability.

3. In the process of cooperative inquiry, cultivate students' awareness of active inquiry and independent learning.

Teaching focus:

Understand two special positional relationships of two straight lines in drawing, classifying and discriminating activities.

Teaching difficulties:

Understand the meaning of vertical and parallel in the process of cooperation, exploration and analysis.

Teaching preparation:

Title paper, triangle, stick, marker

Teaching process:

First, introduce new knowledge by reviewing old knowledge.

(1) Review of line-related knowledge.

1. Show and review old knowledge.

(1) display (line segment).

Monitoring problem: This is (line segment). Who remembers what features it has?

(health: the line segment has two endpoints, which can be measured)

(2) One end of the extended line segment becomes a ray.

Monitoring question: What about now? (Ray), what are its characteristics?

(health: rays can extend to one end indefinitely and cannot be measured)

Operation: Restore the light to a line segment and then extend the other end of the line segment.

Monitoring problem:: Also (thunder)

(3) Restore the ray to a line segment and extend both ends of the line segment into a straight line.

Monitoring problem: This is a straight line. What are its characteristics? A straight line has no end and cannot be measured. )

2. induction: what lines can you find in this picture that we have learned? Let's talk to you and point.

It seems that both line segments and rays are part of a straight line.

(2) Reveal the theme: Just now we recalled the knowledge about a straight line. If you draw two straight lines on this screen, what is the positional relationship? This is what we are learning today. (Title on the blackboard: the positional relationship between two straight lines)

Design intention: By talking with students, reviewing old knowledge will naturally lead to new knowledge.

Second, with the help of classification and students' discrimination, understand the positional relationship between two straight lines.

(A) independently explore the positional relationship between two straight lines

1. Please imagine the positional relationship between two straight lines. Draw them on paper, or put them on before drawing with the help of a stick in your hand. Draw only one kind on each piece of paper, and enlarge it for everyone to see. You can post several kinds and draw several kinds. Let's go

2. Students begin to operate, teachers patrol and collect resources.

Monitoring: (1) This is what students think. Take a look. Do you have anything to add? In order to facilitate the study, we use the serial number to mark this situation. (label)

(2) Let's take a look. Since they are all straight lines, and we know that straight lines can extend to both ends indefinitely, let's extend these straight lines and see what happens. (Students to extend) (Change the color for students to extend)

(B) collective discussion, the difference between two straight lines.

1. Guide students to classify and identify.

Monitoring question: How to study such diverse situations? (classify first)

Please work in pairs and classify the two straight lines according to their positional relationship. You can write the serial number on the back of the title paper. Let's discuss it later. Let's go!

2. Collective discussion.

① Intersection and non-intersection.

② Guide students to classify, establish the concepts of intersection and non-intersection, and write them on the blackboard.

(blackboard writing: disjoint and intersecting)

2. Establish related concepts through discrimination.

(1) Establish the concept of parallelism.

Monitoring problems:

Teacher: Let's look at this positional relationship between two straight lines first. Does anyone know what these two straight lines are called? Have you ever seen it in your life? Where have you seen it? -disjoint.

② The positional relationship between these two straight lines in mathematics is parallel. Who can use their own? What is parallelism?

Let's see what the book says. (Show the concept of parallel lines)

Question: Is it similar to what we said? Is there any difference between what we just said and what is written in the book? (same plane), are these two straight lines on the same plane? Why? (Both on this paper) What about these two straight lines? (Draw a group on the blackboard), can you say a little more about comparison?

④ Establish the representation method of parallel lines. "∨" A is parallel to B, which can be written as: A∨B, which is read as A is parallel to B or B is parallel to A..

(2) Establish a vertical concept.

Monitoring problems:

We call this situation disjoint, or parallel. What do you say about this situation? Yes, the intersection.

Question: In this case of intersection, which is the most special? What's so special about it?

② Establish a vertical concept.

A. Who will say what is vertical in their own words?

B. the narrative in the book.

C. learn the vertical representation.

(3) Establish the concept that intersection is not vertical.

How's this? They intersect, but are not perpendicular to each other, forming two pairs of antipodal angles, each of which is equal. Follow-up: vertical? After the intersection, two groups of antipodal angles are formed, which is unique in that each group of antipodal angles is equal, both of which are 90 degrees. In fact, as long as they intersect, they will form an antipodal angle. We will continue to learn this knowledge in middle school.

④ Appreciate the parallelism and verticality in life. (ppt)

In fact, there are many parallels and verticals in our life. Let's have a look. Can you find parallelism and verticality in math homework and textbooks? )

(5) overlapping processing:

Default: A. If there is a "coincidence" when students draw.

Monitoring problem: the positional relationship between two straight lines in a plane drawn by this classmate is different from what we just learned. What do you think this is (please introduce it to the students who drew the picture)? Demonstration: the process of coincidence (two straight lines have countless intersections)

B. How do students not appear in the picture? The teacher gives the picture a "coincidence" understanding.

(3) Summary: It seems that in a plane, the positional relationship between two straight lines will overlap except intersection and non-intersection. For two overlapping straight lines, we will do further research on such straight lines when we get to middle school.

Design intention: Through students' independent exploration and collective analysis, the positional relationship between two straight lines in the plane is obtained and classified. In this process, students' initiative and enthusiasm are brought into full play and they really become the masters of learning.

Third, consolidate new knowledge in different exercises.

1, which displays planar graphics and composite graphics.

Transition: Just now we learned the positional relationship between two straight lines in the same plane, and we also saw examples of parallelism and verticality in life. What if it's a flat figure? Can you still find a parallel or vertical one? Come on, let's try it together! Requirements: point out a set of verticality and parallelism in the figure below. (Students point to say)

(1) Parallelism and verticality in plane graphics.

Follow-up: Fifth, are there two vertical sides?

Transition: You are amazing! We can also find the knowledge we have learned today in plane graphics. What if it's a combination graph? Is it okay? Come on, let's see!

(2) Find the parallelism and verticality in the combination diagram.

It seems that if we want to verify whether it is vertical, the triangle has helped us a lot and is really a good helper in math learning.

2. In-depth study of parallel and vertical transitivity.

(1) swing. Parallel the two sticks to the third stick. See if these two sticks are parallel to each other?

(2) Make two sticks perpendicular to the third stick. What is the relationship between these two sticks?

Transition: We looked and looked. What if we let you do it? Is it okay? Come on, work in groups. Please pose as required, talk to each other and see what you find. Let's go

Monitoring: ① Which group will bring you up for all of us to enjoy! Tell me again what you found.

(2) There is another one? Imagine first, guess! Then put it on your hand to verify!

Tell everyone about it! What is your first guess? What about after the show? Like all of you?

Summary: It seems that sometimes mathematics knowledge can't be just guessed, and it needs to be verified to know whether the answer is correct!

Fourth, combine the blackboard writing to summarize the whole class.

Teacher: In this class, we learned the positional relationship between two straight lines together, and we will apply this knowledge to learn more knowledge in the future.

Five, the blackboard design:

The positional relationship between two straight lines

On the same plane

Disjoint, intersection and coincidence

Parallel "∩" (with opposite vertex angles)

Vertical or not vertical