1 knowledge and skills:

Understand that parallelism and verticality are two special positional relationships of two straight lines in the same plane, and initially understand parallel lines and perpendicular lines.

2 process and method:

In the process of observation, operation, comparison and generalization, we have experienced the process of exploring the characteristics of parallel lines and vertical lines and established the concepts of parallel lines and vertical lines.

3 Emotional attitudes and values:

Enrich students' activity experience and cultivate students' spatial concept and imagination.

Emphasis and difficulty in teaching

1 teaching points:

Correct understanding? Are the intersections parallel and perpendicular to each other? Concepts such as.

2 Teaching difficulties:

Understand the essential characteristics of the concepts of parallelism and verticality.

teaching tool

Multimedia equipment

teaching process

1 situational import, painting perception

1. Students imagine the positional relationship between two straight lines on an infinite plane.

Teacher: How do you feel when you touch the white paper lying flat on the table?

(1) student exchange report.

(2) An airplane like this is called an airplane. (blackboard writing: plane)

We can take this side of the white paper as a part of the plane. Please draw a straight line on this plane at will. Tell us what the characteristics of this straight line are.

(3) Close your eyes and think about it: the plane where the white paper is located is getting bigger and bigger and becomes infinite. On this infinite plane, the straight line also extends. At this time, another straight line appeared on the plane. What is the positional relationship between these two straight lines? What are the different situations?

2. Students draw various positional relationships of two straight lines in the same plane.

Draw your imagination on white paper. Pay attention to draw only one situation on a piece of paper, draw several kinds when you think of them, and don't draw the same type.

2 Observe the classification and feel the characteristics

1. Show works.

Teacher: Students' imagination is really rich! Take a look at each other. Do you think alike? The teacher selected several representative works, let's enjoy them together.

If you draw something different from these situations, you can add it to the blackboard.

In either case, the two straight lines we draw are on the same piece of white paper. Because we regard the surface of white paper as a plane, we can say that the two straight lines we draw are all on the same plane. (blackboard writing: same plane)

2. Classification discussion.

Teacher: The students' imagination is so rich that they draw so many scenes. Can you classify them? For the convenience of description, we use serial numbers to mark the works. How to divide it? According to what standard?

(1) Think independently first: How do I divide it? What kind?

(2) Reunion communication: how to divide it? Why is it so divided?

3. report and exchange.

Teacher: Which group will talk about your research results?

Academic presupposition:

(1) can be divided into two categories: intersecting and disjoint.

(2) Divided into three categories: crossed, non-crossed and about to cross.

(3) Divided into four categories: crossed, non-crossed, about to cross, right-angled crossed.

Teacher: The intersection you mentioned is called intersection in mathematics. (blackboard writing: intersection)

Question: Do two straight lines in two pictures intersect?

Students explain their ideas and reasons.

Courseware demonstration: Two straight lines extend and intersect at one point.

What kind of situation does Figure 6 belong to? (intersection)

Summary: In the same plane, there are two kinds of positional relationships between two straight lines: intersecting and non-intersecting. But when judging, we should not only look at the surface, but also look at its essence, that is, whether two straight lines intersect after extension.

3 independent inquiry, revealing concepts

1. Reveals the concept of parallelism.

(1) perceptual parallelism.

Teacher: Are these two straight lines really disjoint? How to verify?

Demonstrate the dynamic process that two straight lines will not intersect no matter how long they extend.

(2) Reveal the definition of parallelism.

Teacher: What is the mathematical name of the positional relationship between two straight lines as on the screen?

② Courseware demonstration: In the same plane, two disjoint straight lines are called parallel lines, or they are parallel to each other. (blackboard writing: parallel to each other)

Teacher: Which word do you think should be emphasized in this sentence? Why?

According to the students' answers, the teacher gave an example: Are these two straight lines parallel to each other? Why? (Show a cuboid)

Student experience? Same plane? And then what? Parallel to each other? Meaning of.

(3) Introduce parallel symbols.

① Courseware presents three groups of parallel lines in different positions.

Teacher: The straight lines A and B in these three pictures are parallel to each other. Shall we use symbols? ∥? Means parallel, a and b are parallel to each other, marked as a∨b, and read as a is parallel to B.

Teacher: What do you think of this way of indicating that A and B are parallel? Yes, it is vivid and convenient to show that two straight lines are parallel to each other like this.

(4) Experience the parallel phenomenon in life.

Teacher: We often encounter parallel phenomena in our life. Can you give some examples?

After students give examples, teachers can use multimedia courseware to supplement some real-life examples in time.

2. Reveal the concept of vertical.

(1) Perceived verticality.

Teacher: Just now, when the students drew the positional relationship between two straight lines, they also drew the intersection point. Let's take a look at these intersections together. (Courseware or physical projection presents several groups of typical works)

Teacher: Look at these intersections. What did you find? (all form four angles, some are acute and some are obtuse; Others are special, all four corners are right angles)

Teacher: How do you know that the angle formed by their intersection is a right angle? Please measure, what is the angle formed by the two intersecting straight lines just drawn? What new discoveries have you made through measurement?

Students can find a special situation through measurement, and the four angles formed are all 90? .

(2) Understand the definition of vertical.

Teacher: If two straight lines intersect at right angles, we say that they are perpendicular to each other, one of which is called the perpendicular of the other, and the intersection of these two straight lines is called the vertical foot.

The courseware presents three groups of vertical lines.

Teacher: Look at the three pictures here. What are their similarities and differences? According to the comparison just now, can you try to sum up your findings?

Default: Verticality depends on whether two lines intersect at right angles, regardless of how they are placed.

(3) Introduce vertical symbols.

Teacher: Vertical and parallel lines can also be represented by symbols, right? Line a and line b are perpendicular to each other and are called a? B, pronounced a perpendicular to B.

(4) Feel the vertical phenomenon in life.

Teacher: We often encounter verticality in our life. Can you give some examples about verticality in our life?

After the students give examples, the teacher supplements some examples with multimedia courseware.

Teacher: Students, this is the parallelism and verticality we learned today.

(blackboard title: parallel and vertical)

4 Practice consolidation, expansion and extension

1. Which of the following groups of straight lines are parallel to each other? Which groups are perpendicular to each other?

2. Which two line segments are parallel to each other in the picture below? Which two line segments are perpendicular to each other?

Using new knowledge to improve the understanding of rectangular characteristics.

5 class summary

What did you learn from learning this lesson today? Is there a problem?

1. Two straight lines that do not intersect in the same plane are called parallel lines, which can also be said to be parallel to each other.

2. If two straight lines intersect at right angles, they are said to be perpendicular to each other, one of which is called the perpendicular of the other, and the intersection of these two straight lines is called the vertical foot.

Summary after class

What did you learn from learning this lesson today? Is there a problem?

1. Two straight lines that do not intersect in the same plane are called parallel lines, which can also be said to be parallel to each other.

2. If two straight lines intersect at right angles, they are said to be perpendicular to each other, one of which is called the perpendicular of the other, and the intersection of these two straight lines is called the vertical foot.