Teaching design of the second volume of seventh grade mathematics

Instructional design represents the assumptions and expectations of seventh-grade math teachers for the classroom. The following is the teaching design of the second volume of seventh grade mathematics that I arranged for you. I hope you like it.

Teaching design under seventh grade mathematics

5. 1 intersection line

[Teaching objectives]

1. Through hands-on, operation, reasoning, communication and other activities, further develop the concept of space, and cultivate the ability of map reading, reasoning and orderly expression.

2. Knowing the adjacent complementary angle and antipodal angle in specific cases, we can find out the adjacent complementary angle and antipodal angle of an angle in a graph, understand that antipodal angles are equal, and use it to solve some simple problems.

[Teaching Emphasis and Difficulties]

Emphasis: the concepts of adjacent complementary angle and antipodal angle, the properties and applications of antipodal angle.

Difficulty: the exploration of understanding the nature of equal vertex angle.

[Instructional design]

First, create a situation to stimulate curiosity to observe the process of scissors cutting cloth, and introduce the angle formed by the intersection of two straight lines.

In the world we live in, there are a lot of intersecting lines and parallel lines. This chapter will study the angle formed by intersecting lines and its characteristics.

Observe the process of scissors cutting cloth and introduce the angle formed by two intersecting straight lines.

Students observe, think and answer questions.

The teacher showed a piece of cloth and a pair of scissors, performed the process of cloth cutting, and asked: When cutting cloth, hold the handle tightly. What is the angle between the two handles? How does the opening of scissors change?

Teacher's comment: If the structure of scissors is regarded as two intersecting straight lines, then the above is related to the angle formed by the intersection of the two straight lines.

2. Understand the adjacent complementary angle and antipodal angle, and explore the nature of antipodal angle.

1. Students draw a straight line where AB and CD intersect at point O and name the four corners in the picture. They match each other.

How many diagonal angles can * * * form? How to classify according to different positions?

Students think and communicate in groups, and the whole class communicates.

When students intuitively perceive the angle? Adjacent? 、? Opposite the top? Relationship, teachers guide students to use

Accurate expression of geometric language

;

There is a vertex O with a common * * *, and its two sides are extension lines with opposite sides.

2. Students use a protractor to measure the degree of each angle and find out the relationship between the degrees of each angle.

Students come to the conclusion that the two corners of the adjacent relationship are complementary and the top two corners are equal.

3 Students complete the following table according to observation and measurement:

The angular classification, positional relationship and quantitative relationship formed by the intersection of two straight lines

The teacher asked: If you change the size, will it change its position and quantity relationship with other corners?

4. Summarize the concepts of adjacent complementary angle and antipodal angle and the properties of antipodal angle.

Three. Preliminary application

Exercise:

Is the following statement true?

(1) Adjacent complementary angles can be regarded as two angles divided by rays passing through their vertices.

(2) Adjacent complementary angles are two complementary angles, and these two complementary angles are adjacent complementary angles.

(3) The antipodal angles are equal, and two equal angles are antipodal angles.

Students use the property of equal vertex angle to explain the phenomenon seen in the process of scissors cutting cloth.

Fourth, examples of consolidation application: As shown in the figure, straight lines A and B intersect to find the degree.

[Consolidation exercise] (exercise on page 5 of the textbook) is known, as shown in the figure, and the degree of: is found.

[Abstract]

Adjacent complementary angles, relative vertex angles.

[Homework] Textbooks P9- 1, 2p10-7,8

[Alternative questions]

True or false:

If two angles have a common vertex and a common vertex, and the two angles are complementary to each other, then they are complementary to each other ().

Two straight lines intersect, and if their adjacent complementary angles are equal, a pair of vertex angles are complementary ().

fill (up) a vacancy

1 As shown in the figure, straight lines AB, CD and EF intersect at point O, with antipodal angle of, and adjacent complementary angles of.

If: = 2: 3, then =

As shown in the figure, the straight lines AB and CD intersect at the O point.

rule

5. 1.2 vertical line

[Teaching objectives]

1. To understand the concepts of vertical line and vertical line segment, you will draw a vertical line with a known straight line with a triangular ruler or protractor.

2. Master the concept of distance from point to straight line and measure the distance from point to straight line.

3. Grasp the nature of the vertical line, and make simple reasoning by using the learned knowledge.

[Teaching Emphasis and Difficulties]

1. Teaching focus: the definition and nature of the vertical line.

2. Teaching difficulty: drawing vertical lines.

[Teaching process design]

First, review questions:

1, describing the definitions of adjacent complementary angle and vertex angle.

2. What is the essence of vertex angle?

2. New lesson:

Introduction:

Earlier we reviewed the angle formed by two intersecting lines. If two straight lines intersect at a special angle, what is the special positional relationship between them? Is there such an example in daily life? Let's take a look at this problem.

(A) the definition of vertical line

When one of the four angles where two straight lines intersect is a right angle, it is said that the two straight lines are perpendicular to each other, one of which is called the perpendicular of the other, and their intersection is called the vertical foot.

As shown in the figure, the straight lines AB and CD are perpendicular to each other, and the vertical foot is O. ..

Please give an example of two perpendicular straight lines in daily life.

note:

1. If line segments are perpendicular to each other, line segments and rays, rays and rays, line segments or rays are perpendicular to each other, indicating that their lines are perpendicular to each other.

2. Master the following reasoning process: (as shown above)

On the contrary,

(b) vertical drawing

Explore:

1. Draw a vertical line with a known straight line L with a triangular ruler or protractor. How many vertical lines can you draw?

2. How many vertical lines can you draw by drawing a vertical line of L through point A on the straight line?

3. Draw a vertical line of L through a point B outside the straight line L. How many vertical lines can you draw?

Painting method:

Let a right-angle side of a triangle plate coincide with a known straight line, move the triangle plate left and right along the straight line so that the other right-angle side passes through a known point, and draw a straight line along this right-angle side, then this straight line is the perpendicular of the known straight line.

Note: if you draw a little perpendicular to a ray or line segment, it means drawing a perpendicular to a straight line where they are, and the vertical foot is sometimes on the extension line.

(3) the nature of the vertical line

After passing a point (on or outside the known straight line), a vertical line of the known straight line can be drawn, and only one vertical line can be drawn, namely:

The attribute 1 has one and only one straight line perpendicular to the known straight line.

Exercise: Page 7 of the textbook.

Explore:

As shown in the figure, connect a point P outside the straight line L with each point O on the straight line L,

A, B, C,? , where (we call PO point to point p of a straight line.

L) of the vertical section. Compare line segments PO, pa, PB, PC? Which of these line segments is the shortest?

Property 2 Of all the line segments connecting a point outside a straight line with a point on a straight line, the vertical line segment is the shortest.

Simply put: the vertical line is the shortest.

(4) Distance from point to straight line

The length from a point outside a straight line to the vertical section of the straight line is called the distance from the point to the straight line.

As shown above, the length of PO is called the distance from point P to line L.

Example 1

(1)AB is perpendicular to AC;

(2)AD and AC are perpendicular to each other;

(3) The vertical line segment from point C to AB is line segment AB;

(4) The distance from point A to BC is line AD;

(5) The length of line AB is the distance from point B to AC;

(6) Line 6)AB is the distance from point B to AC.

The correct one is ()

A. 1 B.2

C.3 D. 4

Solution: a

Example 2 As shown in the figure, straight lines AB and CD intersect at point O,

Solution: Omit

Example 3 As shown in the picture, A is driving a car on the straight road AB.

Driving to b, m and n are villages on both sides of the road.

Let's assume that the car is closest to the village m when driving to point p,

When driving to point Q, it is closest to N village. Please draw two points, P and Q, on the AB highway in the picture.

Exercise:

1.

2. Textbook Page 9 3,4

Textbook page 10 9, 10,1,12.

Summary:

1. To master the concepts of vertical line, vertical line segment and distance from point to straight line;

2. Make clear the special situation that the vertical line is the intersection line, contact the previous knowledge, and draw the standard figure correctly with tools;

3. The nature of the vertical line lays a foundation for future knowledge learning and should be mastered skillfully.

Homework: Pages 9, 5 and 6.

0+0 parallel line

[Teaching objectives]

1. Understand the meaning of parallel lines and the positional relationship between two straight lines in the same plane;

2. Understand and master the content of parallel axioms and their inferences;

3. I can draw pictures according to geometric statements, and I can draw parallel lines with straightedge and triangle;

4. Do you understand? Three-line octagon? And can find the congruent angle, internal angle and internal angle of the same side in the specific figure;

4. Understand the application of parallel lines in real life and give examples.

[Teaching Emphasis and Difficulties]

1. Teaching emphasis: the concepts of parallel lines and parallel axioms;

2. Teaching difficulty: the understanding of parallel axioms.

[Teaching process]

First, review questions

How is the intersection defined?

Second, the introduction of new courses.

Apart from parallelism, what is the positional relationship between two straight lines in the plane?

Make teaching AIDS, and get the concepts of the positional relationship between two straight lines and parallel lines in the plane through demonstration.

Third, the positional relationship between two straight lines in the same plane.

1. The concept of parallel lines: In the same plane, two lines that do not intersect are called parallel lines. Line a and line b are parallel and marked as a ∨ B.

(Draw a chart)

2. There are two positional relationships between two straight lines in the same plane: (1) intersection; (2) parallel.

3. Understanding of the concept of parallel lines:

Two keys: one is? On the same plane? (for example); And second? Disjoint? .

One premise: for two straight lines.

4. Drawing of parallel lines

Drawing parallel lines is one of the basic skills of geometric drawing. In the future study, we will often encounter the problem of drawing parallel lines. The method is as follows: 1? Fall? (One side of a triangle falls on a known straight line), two? Shit? (Leaning on the other side of the triangle with a ruler), three? Moving? (move the triangle along the ruler until the side of the triangle that falls on the known straight line passes through the known point), 4? Painting? Draw a straight line through a known point along the edge of a triangle.

Fourth, the parallel axiom.

1. Explain with the previous teaching AIDS? Is there one and only one straight line parallel to the known straight line at a point outside the straight line? .

2. Parallelism axiom: After passing a point outside a straight line, there is one and only one straight line parallel to this straight line.

Ask questions and compare the properties of vertical lines.

3. Parallel axiom inference: If two straight lines are parallel to the third straight line, then the two straight lines are parallel to each other. That is to say, if B∨a, c∨a, then B ∨ C.

Five, three-line octagon

From the previous teaching aid demonstration.

As shown in the figure, Line A and Line B are cut by Line C, and among the eight angles formed, there are 4 pairs of congruent angles, 2 pairs of internal staggered angles and 2 pairs of internal angles on the same side.

Sixth, classroom exercises.

1. In the same plane, the possible positional relationship between two straight lines is.

2. In the same plane, the number of times three straight lines intersect may be.

3. The following statement is true ()

Only one straight line is parallel to the known straight line passing through a point.

B after a little, there are countless straight lines parallel to the known straight lines.

C there is a straight line parallel to the known straight line after a little.

D there is one and only one straight line parallel to the known straight line.

4. What if? With what? Is the ipsilateral inner corner, and? =50? And then what? The degree is ()

.50 caliber? B. 130？ C.50？ Or 130? D. uncertainty

5. The following proposition: (1) Straight lines on opposite sides of a rectangle are parallel; (2) After passing a point, a straight line parallel to the known straight line can be drawn; (3) In the same plane, if two straight lines are not parallel, the two straight lines intersect; (4) Make a straight line perpendicular to the known straight line after one point. The correct number is ()

A. 1

6. As shown in the figure, if straight lines AB and CD are cut by DE, then? The sum of 1 is the same angle. The sum of 1 is an interior angle. The sum of 1 is the inner angle of the same side. What if? 5=? What about 1? 1 ? 3.

Seven. abstract

Ask the students to summarize this part independently and describe the concept and conclusion of this part.

Eight, homework after class

1. textbook P 19 question 7;

2. Draw a picture to illustrate the positional relationship and intersection of three straight lines in the same plane.

[Supplementary content]

1. indicates that if two lines are parallel to the third line, then the two lines are parallel to each other.

2. In the same plane, there are only two positional relationships between two straight lines: intersecting or parallel, but the real space is three-dimensional.

Imagine the positional relationship between two straight lines in space. (Take a cuboid as an example)

5.2.2 Conditions of parallel lines (Grade 2)

First, the teaching objectives

(1) enables students to further understand and master the method of judging the parallelism of two lines;

(2) Understand the simple logical reasoning process.

Second, the teaching focus and difficulties

Key points: the application of the method for judging the parallelism of two straight lines;

Difficulties: simple logical reasoning process.

Three. teaching process

Review questions:

1. What are the methods to determine the parallelism of two straight lines?

2. As shown in the figure (1)

(1) What if? 1=? 4. According to _ _ _ _ _ _ _ _ _ _ _, AB ∨ CD can be obtained;

(2) What if? 1=? 2. According to _ _ _ _ _ _ _ _ _ _ _, AB ∨ CD can be obtained;

(3) What if? 1+? 3= 1800, according to _ _ _ _ _ _ _, AB∨CD can be obtained.

3. As shown in Figure (2)

(1) What if? 1=? D, then _ _ _ _ _ _ _ _ _ _;

(2) What if? 1=? B, then _ _ _ _ _ _ _ _ _ _;

(3) What if? A+？ B= 1800, then _ _ _ _ _ _ _ _;

(4) What if? A+？ D= 1800, then _ _ _ _ _ _ _ _;

New lesson:

Example 1 If two lines are perpendicular to the same line in the same plane, are they parallel? Why?

Analysis: Verticality is always associated with right angles. What methods have we learned to judge the parallelism of two straight lines?

These two straight lines are parallel.

As shown in the figure

The reasons are as follows: ∵b? a，c？ a

? 1=? 2=900 (vertical definition)

? B∑c (same angle, two straight lines are parallel)

Thinking:

This is a part of English copy paper made by Xiao Ming himself. Are the horizontal lines parallel to each other? How many ways do you judge?

Example 2 is shown in the figure. 1=? 2,? BAC=200，？ ACF=800。

(1) Q? 2 degrees;

(2) Are 2)FC and AD parallel? Why?

Consolidation exercise

1. Textbook exercises 19 pages

2. As shown in the figure, if? 1=470,? 2= 1330,? D=470, so BC is parallel to DE? Is AB parallel to CD?

3. As shown in the picture, you know? D=？ First,? B=？ Are FCB, ED and CF parallel?

4. As shown in the figure, 1=? 2,? 2=? 3,? 3+? 4= 1800, find the parallel lines in the figure.

Homework: Exercise 5.2, questions 7 and 8 on page 19 of the textbook.

Conditions of parallel lines (1)

[Teaching objectives]

3. Draw parallel lines with a ruler and a triangle, and get the conditions of parallel lines.

4. Parallel lines will be judged according to the situation of parallel lines.

5. Stimulate students' interest in learning mathematics.

[Teaching Emphasis and Difficulties]

Key point: understand the conditions of parallel lines.

Difficulties: application of parallel line conditions

[Instructional Design] Asking Questions

Review questions:

1. As shown in the figure, four straight lines AB, AC, DE and FG are known.

( 1)? 1 and? 2 is the _ _ _ _ _ angle formed by _ _ _ _ and a straight line.

(2) ? 3 and? 2 is the _ _ _ _ _ angle formed by _ _ _ _ and a straight line.

(3) ? 5 and? 6 is the included angle formed by _ _ _ _ _ and _ _ _ _ _.

(4) ? 4 and? 7 is the included angle formed by the line _ _ _ _ _ and _ _ _ _ _.

(5) ? 8 and? 2 is the _ _ _ _ _ angle formed by _ _ _ _ and a straight line.

2. The following statement is true ().

(1) In the same plane, there are three positional relationships between two straight lines: intersecting, parallel and vertical.

(2) In the same plane, two non-vertical straight lines must be parallel.

(3) In the same plane, two non-parallel straight lines must be vertical.

(4) In the same plane, two disjoint straight lines must not be perpendicular.

3. If a∨b, b∨c, then _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.

Introduction:

Last class, we learned the meaning of parallel lines, the positional relationship between two straight lines in the same plane, and the axiom of parallelism.

On this basis, we will study the conditions of parallel lines.

New lesson:

Conditions of parallel lines

Demonstrate the process of drawing parallel lines with straightedge and triangle.

What if? 4+? 2= 180? ，a∨b？

Three methods can be simply described as:

Examples are known: As shown in the figure, straight lines AB, CD and EF are cut by MN. 1=? 2, ? 3+? 1= 180? Please explain CD∑EF.

Solution: Because? 1=? 2,

So AB∨CD

Because again? 3+? 1= 180? ,

So AB∨EF.

So CD∨EF (why? ).

Classroom exercises:

1. The following judgment is correct ().

A. because? 1 and? 2 is the same side inner angle, so? 1+? 2= 180?

Because of what? 1 and? 2 is the inner corner, so? 1=? 2

C. because? 1 and? 2 is a conformal angle, so? 1=? 2

D. because? 1 and? 2 is a supplementary angle, so? 1+? 2= 180?

2. As shown in the figure: (1) Known? 1=65? , ? 2=65? Are DE and BC parallel? Why?

(2) What if? 1=65? , ? 3= 1 15? Are AB and DF parallel?

Why?

(3)) What if? 4=60? , ? 2=65? Are DE and BC parallel?

Why?

3.

4. As shown in the figure:

(1) If you know? 1=? 3. It can be judged that AB ∨_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _；

(2) If known? 4+? 5= 180? , you can determine the location of _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.

(3) If known? 1+? 2= 180? , you can determine the location of _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.

(4) Is it known? 5+? 2= 180? So, according to the vertex angle, is it equal? 2=__,

Do you know that?/You know what? 4+? 5 = _ _ _ _ _ _, so it can be determined that _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.

(5) If you know? 1=? 6. It can be judged as _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.

Figure 4, Figure 5

5. As shown in the figure, (1) What if? 1= _ _ _ _ _, then de ∑ ac;

(2) What if? 1= _ _ _ _ _, then ef ∨ BC;

(3) What if? FED+？ ________= 180? , then AC ∑ ed;

(4) What if? 2+ ? ________= 180? , then AB∑DF.

6.

7.

Homework after class: Exercise 5.2, Question 1, 2, 4.

Supplementary exercises:

Known: As shown in the figure, AB∑CD and EF are given to AB and CD respectively.

Divide it equally between e, f and EG AEF，

FH split? Are EFD EG and FH parallel? Why?

New Mathematics Curriculum Teaching in Junior Middle School

First, make the introduction of the topic more interesting.

People's feelings are very rich, and humorous words can leave a deep impression on people and make the classroom full of vitality. For example, when teaching algebraic expression addition and subtraction, the teacher can tell a joke to the students first. Aunt Wang raised three sheep and nine pigs, but Xiaojun counted 12 pigs. Do students know why? After listening, the students will answer with a smile: Is that because he counted sheep? Why do students laugh? That's because they know that pigs and sheep are different kinds, so they can't add up the numbers like this. At this point, teachers can introduce the focus of teaching, that is, the merger of similar items means that different kinds of things cannot be merged. This teaching method not only enlivens the classroom atmosphere, but also deepens students' understanding of similar items, killing two birds with one stone.

Second, establish equal teacher-student relationship.

The ancients said:? Kiss his teacher and believe in his way. ? This requires teachers to abandon the old habit of learning from others, establish a personality equality with students, walk beside students, enter their hearts and communicate with students on an equal footing; Explore and discuss with students, encourage students to actively think, choose and ask questions, and actively participate in their free communication; Establish friendly relations with students, so that students will no longer resist teachers. If this new relationship between teachers and students is established, classroom teaching can be carried out and completed in a relaxed and harmonious atmosphere. In order to establish an interactive relationship between teachers and students, teachers should not only consider students' actual life and knowledge, but also consider how to let students acquire relevant skills through their own learning. In addition, teachers should respect every student in the classroom, let students explore and ask questions actively, encourage students to actively explore ways to solve problems, and participate in students' learning activities when they need it, give necessary guidance, and become learning partners and close friends with students.

Third, set the level of the problem.

The core of mathematics teaching is the problem. Teachers should not only consider students' cognitive level, but also consider the characteristics of knowledge itself when setting questions. If the questions set are too big, it will make students think too much and even make students with learning difficulties lack confidence. But if the problem is too small, it will lack the value of thinking, which is not conducive to the all-round development of students. Therefore, when preparing lessons, teachers should think about how to set the appropriate difficulty so that most students can clearly understand the knowledge points in depth questions. For example, when teaching the relationship between roots and coefficients, I first give four equations: ① x2-5x-6 = 0; ②x2+3x+2 = 0； ③x2-x-6 = 0； ④x2-3x+7=0. Then, I asked the students to calculate the values of A, B and C respectively, solve the equation and calculate the sum and product of the two roots of each equation. Students soon found that Equation 4 could not find the answer. What caused this? Because △ < 0, the equation has no solution. Then, I asked students to observe the relationship between the sum and product of the first three equations and the original equations A, B and C. Students can easily find that when the quadratic coefficient a= 1, the sum of the two roots is exactly the reciprocal of the linear coefficient B, and the product of the two roots is also a constant term. At this point, I will give the equation 2x2-6x-7=0, and students will know how to change the quadratic coefficient into 1 according to the basic properties of the equation, thus transforming the special into the general.

Fourth, train diversified ways of thinking.

1. Train your thinking speed. This is mainly done in class. Therefore, teachers should arrange teaching contents reasonably and use vivid teaching mode to train students' thinking speed, so as to improve the quality of mathematics teaching. For example, after teaching a new lesson, the teacher should arrange the exercises in the textbook as quick calculation questions for inspection. Teachers can also carefully compile multiple-choice questions, true-false questions and short-answer questions with strong concepts, high flexibility and wide coverage, and carry out special training, thus improving students' ability to answer questions quickly.

2. Train the thinking quality. Teachers can fully organize students to discuss the characteristics of some problem-solving ideas and methods. This will help students think positively, thus effectively improving their ability to analyze and solve problems.

3. Train reverse thinking. Enlightening students to think from opposite angles and cultivating the habit of reverse thinking will help to expand students' thinking, find solutions to problems and effectively cultivate students' thinking ability.

4. Train divergent thinking. This can fully stimulate students' thirst for knowledge and curiosity, let students think independently, constantly explore new knowledge and try their best to solve problems. In classroom teaching, teachers should take solving problems as the starting point, focus on conclusion and reconstruct the open teaching mode with inquiry as the key.

Verb (abbreviation of verb) conclusion

In a word, as long as teachers practice hard, think seriously, make continuous progress in mathematics teaching, adhere to the new curriculum concept, and use it to guide classroom teaching, with the help of various teaching methods, students can actively participate in teaching activities and enjoy learning mathematics, thus greatly increasing their enthusiasm and initiative in learning mathematics.

Author: Li Unit: No.5 Middle School in Zhangye City, Gansu Province