Excellent lesson plan for the fourth grade primary school mathematics volume "The Positional Relationship of Straight Lines"

Teaching objectives:

1. In the activities of drawing, classifying, and analyzing, understand the positional relationship between two straight lines and understand the special positions of two straight lines in the same plane. Relationship-----parallel, perpendicular.

2. In the process of analyzing and understanding knowledge, initially establish the concept of parallel and vertical space and cultivate students' spatial imagination ability.

3. In the process of cooperation and inquiry, cultivate students’ awareness of active inquiry and independent learning.

Teaching focus:

In the activities of drawing, classifying, and analyzing, understand the two special positional relationships of two straight lines.

Teaching difficulties:

Understand the meaning of verticality and parallelism in the process of cooperation, exploration, and analysis.

Teaching preparation:

Question paper, triangle, small stick, marker

Teaching process:

1. With the help of reviewing old knowledge, elicit new knowledge.

(1) Review of relevant knowledge of a line.

1. Show and review old knowledge.

(1) Show (line segment).

Monitoring problem: This is (line segment). Who remembers its features?

(Student: The line segment has two endpoints and can be measured)

(2) Extend one end of the line segment to become a ray.

Monitoring question: now what? (ray), what are its characteristics?

(Study: The ray can be extended infinitely to one end and cannot be measured)

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

Monitoring problem:: It is also a (ray)

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

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

2. Summary: What lines can you find on this picture that we have learned? Let me tell you about it and point it out.

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

(2) Revealing the topic: Just now, we recalled the knowledge about a straight line. If two straight lines are drawn on this screen, what will be their positional relationship? This is what we are studying today. (Blackboard writing topic: The positional relationship between two straight lines)

Design intention: Through conversations with students, old knowledge is reviewed, thereby naturally eliciting new knowledge.

2. Understand the positional relationship between two straight lines with the help of classification and student analysis.

(1) Independently explore the positional relationship between two straight lines

1. Please imagine what the positional relationship between two straight lines will be. Draw it on paper, or you can use First place the small stick in your hand, and then draw it. Draw only one type on each piece of paper, and make it larger so everyone can see it. Just place as many as you can think of and draw as many as you can. start!

2. Students do hands-on operations, and teachers inspect and collect resources.

Monitoring: (1) This is what the students think. Take a look. Do you have anything to add? For the convenience of research, we mark this situation with a serial number. (label)

(2) Let’s take a look. Since they are all straight lines, and we know that straight lines can be extended infinitely to both ends, let’s extend these straight lines and see what happens. Woolen cloth? (Students will extend) (Change a color and let students extend)

(2) Group discussion and analyze the positional relationship between the two straight lines

1. Guide students to classify and analyze.

Monitoring problem: How do we study so many situations? (Classify first)

Ask everyone to 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 question paper, and we will discuss it together later, let’s get started!

2. Group discussion.

　①Intersection and non-intersection

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

(Write on the blackboard: Disjoint Intersect)

2. Establish related concepts with the help of analysis.

(1) Establish the concept of parallelism.

Monitoring questions:

①Teacher: Let’s first look at the positional relationship between two straight lines. Does anyone know what these two straight lines are called? Have you seen it in life? Where have you seen it? -----Does not intersect

②The positional relationship between these two straight lines in mathematics is parallel. Can anyone use their own words to say what is parallel?

③Let’s take a look at 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 in the book? (same plane), are these two straight lines on the same plane? Why? (All on this piece of paper) What about these two straight lines? (Draw a group on the blackboard), can you tell me more about parallelism?

④ Establish a representation method of parallel lines. "∥" a and b are parallel, which can be recorded as: a∥b, which is read as a is parallel to b or b is parallel to a

(2) Establish the concept of verticality.

Monitoring issues:

①We call this situation disjoint, that is, parallel. What do you think of this situation? Yes, intersect.

Question: Which of these intersections is the most special? What's so special about it?

②Establish a vertical concept.

A. Who can explain in their own words what verticality is?

B． Read the narrative in the book.

C. Learn vertical representation.

③Establish the concept of intersection and non-perpendicularity

What about this kind of thing? They intersect, but are not perpendicular, forming two sets of opposing vertex angles, and the opposing vertex angles of each set are equal. Follow-up question: What about verticality? After intersecting, two sets of opposing vertex angles are formed. What is special is that the opposing vertex angles of each group are equal, both are 90°. In fact, as long as they intersect, they will form opposing vertex angles. We will continue to learn this knowledge in middle school.

④Appreciate the parallels and perpendicularities in life. (ppt)

In fact, there are many parallels and perpendiculars in our lives. Let’s take a look. (Can we also find parallelism and perpendicularity in mathematics homework and textbooks?)

⑤Handling of overlap:

Default: A. If "overlap" occurs when students draw pictures < /p>

Monitoring question: The positional relationship between two straight lines in a plane drawn by this student is different from what we just studied. Do you know what this is? (Please introduce it to the students who drew the picture) Demonstration: the process of coincidence (two straight lines have countless intersections)

B. Why students do not appear in the picture, the teacher explains the "coincidence" of the picture.

(3) Summary: It seems that in a plane, the positional relationship between two straight lines may not only intersect or not intersect, but also overlap. Regarding two overlapping straight lines, we will further study such straight lines after we reach middle school.

Design intention: Through students’ independent exploration and collective analysis, the positional relationship of two straight lines in a plane was obtained, and classification research was conducted. In this process, students’ initiative and Be motivated and truly become the master of learning.

3. Consolidate new knowledge in different exercises.

1. Provide plane graphics and combined graphics.

Transitional language: We just learned about the positional relationship between two straight lines in the same plane, and we also saw examples of parallel and perpendicular in life. What if it is a plane figure? Can you still find parallel or perpendicular ones? Come on, let’s try it together! Requirements: Point out a set of perpendiculars and parallels in the figure below. (Students pointed and said)

(1) Parallel and perpendicular in plane graphics.

Follow-up question: Fifth, are there two sides that are perpendicular to each other?

Transitional language: You are amazing! The knowledge we learned today can also be found in plane graphics. What if it is a combined graphic? Is it okay? Come, let’s take a look!

(2) Look for parallelism and perpendicularity in the combined graphics.

It seems that if we want to verify whether it is vertical, the triangle plate helps us a lot. It is really a good helper for learning mathematics.

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

(1) Place the two small sticks parallel to the third small stick. See if the two small sticks are parallel to each other?

(2) Place the two small sticks perpendicular to the third small stick. Take a look at what these two little sticks have to do with each other?

Transitional language: We have looked and found it, so what if we let you show it off? OK? Come on, let’s work in groups. Please put your hands around as required, talk to each other, and see what you can discover? start!

Monitoring: ①Which group will bring up your display for all of us to enjoy! Now tell me, what did you find?

②Is there another one? Imagine it first and guess what! Then put your hands around to verify!

③Let’s talk to all of us! What was your first guess? What about after it’s done? Do you think the same as you all?

Summary: It seems that sometimes mathematical knowledge cannot be based solely on guessing. We need to verify it to know whether the answer is correct!

4. Summarize the whole lesson based on writing on the blackboard.

Teacher: In this lesson, we studied the positional relationship between two straight lines. We will apply this knowledge to learn more knowledge in the future.

5. Blackboard writing design:

The positional relationship of two straight lines

In the same plane

Do not intersect or overlap

Parallel “∥” (opposite corners)

Vertical but not vertical