Mathematics Teaching Plan: Diamond 1 Teaching Suggestions
Knowledge structure
Difficulties and difficulties analysis
This section focuses on the nature and judgment theorem of diamonds. A diamond is defined on the premise of a parallelogram. First of all, it is a parallelogram, but it is a special parallelogram with a special feature of "a group of adjacent sides are equal", which adds some special properties and judgment methods different from parallelogram. These properties and judgment theorems of rhombus are not only the continuation of parallelogram properties and judgments, but also the basis for learning squares in the future.
The difficulty of this section is the flexible application of diamond attributes. Because the diamond is a special parallelogram, it not only has the properties of parallelogram, but also has its own unique properties. If the parallelogram is a diamond, we can get many conditions about sides, angles and diagonals. In the actual problem solving, what conditions should be applied and how to apply them will often make many students at a loss, and teachers should pay enough attention to them in the teaching process.
Teaching suggestion
According to the characteristics of this section and its relationship with parallelogram, teachers are advised to pay attention to the following problems in the teaching process:
1, diamond-shaped knowledge, which students have been exposed to in primary school, can be introduced through what they have learned in primary school.
There are many examples of diamonds in reality. When explaining the nature and judgment of diamonds, teachers or students can prepare some life examples to judge which nature and judgment to apply, which not only increases students' sense of participation but also consolidates their knowledge.
3. If conditions permit, before teaching this lesson, teachers can instruct students to make a parallelogram as a prop in the teaching process, as shown in Figure 4-33 on page 148 of the textbook, which not only enhances students' hands-on ability and sense of participation, but also has a practical teaching style and is more convenient for students to master knowledge.
4. When explaining the nature, the teacher can divide the students into several groups, and each student will measure the edges, corners and diagonals of the graphs prepared in advance, and then sort them out and summarize them in groups.
5. Because the diamond and its property theorem are simple to prove, teachers can guide students to analyze ideas, and students can prove them in detail.
6. In the explanation of diamond-shaped application, teachers should pay attention to the hierarchical arrangement of topics, so as to facilitate understanding and mastering.
First, the teaching objectives
1. Master the concept of rhombus and know the relationship between rhombus and parallelogram.
2. Master the nature of diamonds.
3. By applying diamond knowledge to solve specific problems, improve analytical ability and observation ability.
4. Cultivate students' interest in learning through the demonstration of teaching AIDS.
5. According to the subordinate relationship of parallelogram, rectangle and diamond, the idea of set is infiltrated into students through drawing.
6. By studying the nature of diamonds, we can experience the graphic beauty of diamonds.
Second, the design of teaching methods
The method of combining observation, analysis and discussion
Three. Key points, difficulties, doubts and solutions
1. Teaching emphasis: the property theorem of diamonds.
2. Teaching difficulties: the comprehensive application of diamond nature and right triangle knowledge.
3. Doubt: The essential difference between a diamond and a rectangle.
Fourth, the class schedule
1 class hour
Verb (abbreviation for verb) Prepare teaching AIDS and learning tools.
Teaching AIDS (making a parallelogram with movable short sides), projectors and films, and common drawing tools.
Sixth, the design of teacher-student interaction activities.
Teachers demonstrate teaching AIDS, create situations, introduce new lessons, and students observe and discuss; Students analyze and demonstrate methods, and teachers give timely guidance.
Seven, teaching steps
Review questions
1. What is a parallelogram? What is a rectangle? What is the relationship between parallelogram and rectangle?
2. The angle between the diagonal of the rectangle and the big side is, and the angle between the two diagonal lines opposite to the small side is found.
3. The bisector of the rectangular corner divides the long side into two halves to find the perimeter of the rectangle.
Introduce a new course
We have learned a special parallelogram-rectangle, but there are other special parallelograms. At this time, we can demonstrate the teaching aid that a short side can be moved according to the textbook Figure 4-38. As shown in the figure, changing the side of a parallelogram to make a group of neighbors equal leads to the concept of diamond.
Explain a new lesson
1. Diamond Definition: A group of parallelograms with equal adjacent sides is called a diamond.
In explaining this definition, to grasp the essence of this concept, two points should be highlighted:
(1) emphasizes that the diamond is a parallelogram.
(2) A group of adjacent edges are equal.
2. The nature of diamonds:
The teacher emphasized that because the diamond is a special parallelogram, it has all the properties of a parallelogram. In addition, because it has more conditions of "a group of adjacent sides are equal" than parallelogram, it is similar to rectangle and has some special properties than parallelogram.
Let's study the characteristics of diamonds:
Teacher: Students can guess the nature of diamonds according to their definition and figures (let students discuss and guide them to analyze from three aspects: edge, angle and diagonal).
Health: Because the diamond is a parallelogram with a set of equal adjacent sides, it can be obtained according to the property that parallel sides are equal.
Diamond property theorem 1: all four sides of a diamond are equal.
The four sides of the diamond are all equal. According to the diagonal of the parallelogram, we can get
Theorem 2: Diagonal lines of rhombus are perpendicular to each other, and each diagonal line bisects a set of diagonal lines.
Guide students to complete the normative proof of theorem.
Teacher: Please look at the picture on the right. What is the relationship between four right-angled triangles whose rhombus is divided diagonally?
Health: Full marks.
Teacher: What is the relationship between their base and height and the two diagonals?
Health: They are half of two diagonal lines.
Teacher: If the two diagonal lines of the diamond are respectively, what is the area of the diamond?
Health:
The teacher pointed out that when the diagonal length is difficult to find, the rhombic area is calculated by the general calculation method of parallelogram area.
Example 2 is known: As shown on the right, it is △, intersecting at, and intersecting at the angle bisector.
Prove that the quadrilateral is a diamond.
(Guide students to judge by the definition of diamond. )
Example 3 It is known that the side length of a diamond is diagonal and intersects with a point, as shown on the right. Find the diagonal length and area of this diamond.
(1) Find the area according to the textbook method.
(2) Students can also be guided to find the height of the delta side, that is, the height of the diamond, and then calculate the area of the diamond with the area formula of the parallelogram.
Summary and expansion
1. Summary: (Print projection) (Figure 4)
(1) subordination of rhombus, parallelogram and quadrilateral;
(2) Diamond properties: Figure 5
① It has all the properties of a parallelogram.
2 uniqueness: equality on all sides; Diagonal lines are perpendicular to each other and divide each diagonal line equally.
Eight, homework
6,7,8 in the textbook P 158 and 10 in P 196.
Nine, blackboard writing design
title
Definition of diamond ...
Example of diamond properties 2 ... Summary:
Property Theorem 1: ... Example 3 ........
Property Theorem 2: ...
X. Practice in class
Textbook P 15 1, 2, 3
supplement
1. If the diagonal length of the diamond is 3 and 4 respectively, the perimeter and area are _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
2. If the circumference of the diamond is 80 and a diagonal is 20, then the degrees of two adjacent angles are _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.
Mathematics Teaching Plan: Diamonds 2 I. Teaching Objectives
1. Master the decision of diamonds.
2. By using diamond knowledge to solve specific problems, improve analytical ability and observation ability.
3. Cultivate students' interest in learning through the demonstration of teaching AIDS.
4. According to the subordinate relationship of parallelogram, rectangle and diamond, the idea of set is infiltrated into students through drawing.
Second, the design of teaching methods
The method of combining observation, analysis and discussion
Three. Key points, difficulties, doubts and solutions
1. Teaching emphasis: diamond judgment method.
2. Teaching difficulty: the comprehensive application of diamond judgment method.
Fourth, the class schedule
1 class hour
Verb (abbreviation for verb) Prepare teaching AIDS and learning tools.
Teaching AIDS (making a parallelogram with movable short sides), projectors and films, and common drawing tools.
Sixth, the design of teacher-student interaction activities.
Teachers demonstrate teaching AIDS, create situations, introduce new lessons, and students observe and discuss; Students analyze and demonstrate methods, and teachers give timely guidance.
Seven, teaching steps
Review questions
1. Describe the definition and characteristics of diamonds.
2. The ratio of two adjacent angles of a diamond is 1: 2, and the longer diagonal is 0, so the distance from the intersection point of the diagonal to one side is _ _ _ _ _.
Introduce a new course
Teacher: What is the most basic way to judge whether a quadrilateral is a diamond?
A: Definition.
In addition, there are two other ways to judge. Let's learn these two methods.
Explain a new lesson
Diamond Decision Theorem 1: A quadrilateral with four equilateral sides is a diamond.
Diamond Decision Theorem 2: Parallelograms with mutually perpendicular diagonals are diamonds. Figure 1
Analysis and judgment 1: First prove that it is a parallelogram, and then prove that a group of adjacent sides are equal, which is a diamond in definition.
Analysis and decision 2:
Teacher: How many conditions does this theorem have?
A: Two.
The teacher asked: which two?
Answer: (1) is a parallelogram. (2) The two diagonals are perpendicular to each other.
The teacher asked: What conditions are needed to prove that a parallelogram is a diamond?
Answer: Prove again that two adjacent edges are equal.
(Students' oral testimony)
Let students pay attention to the application of vertical line in line segment in proof.
Teacher: Are quadrilaterals with diagonal lines perpendicular to each other rhombic? Why?
You can draw a picture, which is diagonal, but not diamond.
The commonly used judgment methods of diamond are summarized as follows: (After the students discuss and summarize, the teacher writes on the blackboard):
Mathematics teaching plan: Diamond 3 I. Teaching purpose:
1, master the concept of rhombus and know the relationship between rhombus and parallelogram;
2. Understand and master the definition and properties of diamond 1 2; These properties will be used for related demonstration and calculation, and the area of rhombus will be calculated.
3. Use diamond knowledge to solve specific problems, improve analytical ability and observation ability;
4. According to the subordinate relationship of parallelogram, rectangle and diamond, the idea of set is infiltrated into students through drawing;
Second, the key points and difficulties
1, teaching focus: the nature of diamonds 1, 2;
2. Teaching difficulties: the nature of diamonds and the comprehensive application of diamond knowledge;
Third, the intention analysis of examples
There are two examples in this lesson. Example 1 is a supplementary question to consolidate the nature of diamonds. Example 2 is the example 2 in the textbook P 108, which is a practical application problem to calculate the rhombus area by using the knowledge of rhombus and right triangle. This topic can not only consolidate the nature of diamond, but also guide students to calculate the area of diamond in different ways, thus promoting students to use knowledge skillfully and flexibly.
Fourth, classroom introduction
1, (Review) What is a parallelogram? What is a rectangle? What is the relationship between parallelogram and rectangle?
2. (Introduction) We have learned a special parallelogram-rectangle. In fact, there are other special parallelograms. Please see the demonstration: (a set of teaching AIDS that can move in opposite directions as shown in the figure can be demonstrated in advance) As shown in the figure, change the sides of the parallelogram to make a group of adjacent sides equal, thus leading to the concept of diamond;
"18,2,2 diamonds" exercises contain answers;
5. In the same plane, use two equilateral triangular pieces of paper with a side length of a (the pieces of paper cannot be cut open), and the quadrilateral that can be assembled is ().
A, rectangle b, diamond c, square d, trapezoid
Answer: b
Knowledge points: the nature of equilateral triangle; Determination of diamond shape
Analysis:
Answer: a quadrilateral composed of two equilateral triangles with a side length of a, all four sides of which are a, which is a diamond according to the definition of diamond and a diamond according to the meaning of the question, so b,
Analysis: this question mainly examines the nature of equilateral triangle and the definition of diamond.
6. The quadrilateral composed of two equilateral triangular pieces of paper with side length A is ()
A, isosceles trapezoid b, square c, rectangle d, diamond
Answer: d
Knowledge points: the nature of equilateral triangle; Determination of diamond shape
Analysis:
Answer: since the sides of two equilateral triangles are equal, the four sides of the quadrilateral are also equal, that is, the diamond. From the meaning of the question, it can be concluded that the four sides of the quadrilateral are equal, that is, the diamond, so d,
Analysis: this question uses the concept of diamond: a quadrilateral with four equal sides is a diamond,
The Nature of Diamonds and Judgment Exercise
Multiple choice question:
1, the following quadrilateral is not necessarily a diamond ().
A, parallelogram b with equal diagonals, and a set of diagonal quadrangles bisected by each diagonal.
C, parallelogram D with diagonal lines perpendicular to each other, a quadrilateral formed by splicing two congruent equilateral triangles.
2, the following statement is correct ()
A quadrilateral with four equilateral sides is a diamond.
B, a set of quadrangles with equal opposite sides and another set of quadrangles with parallel opposite sides are diamonds.
C. The diagonal lines of quadrangles perpendicular to each other are diamonds.
The quadrilateral whose diagonal bisects each other is a diamond.
3. If the midpoints of the sides of the quadrilateral ABCD are connected in turn to get a rhombus, then the quadrilateral ABCD must be ().
Diamond B, quadrilateral C with vertical diagonal, rectangle D and quadrilateral with equal diagonal.