[Teaching content].
From the perspective of the "Curriculum Standards", an important part of the field of "graphics and geometry" is the translation, rotation, axisymmetry and similarity of figures. They are an effective tool for studying geometric problems and discovering geometric conclusions. Translation, rotation, and axis symmetry are the properties of a figure when it coincides with another figure through a certain motion. The learning of this part of the content makes the students' understanding of the relationship between graphs rise from static to dynamic, thus opening up a new perspective on the study of graphic problems. The textbook arranges the content of graphic transformations at different stages. Translation is a basic graphic transformation, and it is also the first graphic transformation introduced in this set of textbooks, the textbook arranges "translation" in the last section of Chapter 5 "Intersecting Lines and Parallel Lines", on the one hand, it is considered to be introduced as an application of parallel lines, and on the other hand, it is considered to introduce translational transformation, which can penetrate the idea of graphic transformation as soon as possible, so that students can try to use translation knowledge to analyze and solve problems as soon as possible. For the study of translation, the research methods also provide a reference for future research on axis symmetry and rotation.
[Learning Situation Analysis].
Grade 7 children are in the stage of active thinking, strong imitation ability, and full of desire to explore new things, and at the same time, they also have a certain learning ability, and under the guidance of the teacher, they can discuss and summarize a certain problem. However, the following problems often arise in mathematics learning: 1. The basic concepts and theorems are vague: concepts, formulas, and theorems cannot be seen in mathematical language. If you don't read the textbook, you can't explain the system of concepts, and you can't connect concepts with each other. 2. Students' self-learning ability is poor: they can't find out the key points and difficulties of the problem, can't answer the questions described in the textbook, can't say what they have mastered, can't ask questions, can't use the knowledge they have learned to solve problems, read slowly and easily interfered with the outside world, read passively, and have no consciousness. 3. Unable to grasp the key mathematical skills in problem solving, looking at each problem in isolation, and lacking the ability to draw inferences from one another. 4. When solving problems, there are too many small mistakes, and the problem can not be completely solved. 5. In class, they lack the motivation to think positively, refuse to use their brains, and are always careless and avoid answering. Therefore, in order to understand and grasp the concept and nature of translation, students should have some perceptual understanding of the translation phenomenon in life, and at the same time, they must have knowledge reserves such as the equality of line segments and the determination of parallel lines.
【Teaching Objectives】
1.Know what translation is. Will appreciate and analyze more complex translation patterns, and know that the essence of translation is the translation of points. A shape is panned as required.
2.Understand the importance of translation in daily life by observing translation patterns, clarify the purpose of translation, and improve learning translation.
Interest. On this basis, grasp the essence of translation, so as to learn a kind of appreciation and creation of beauty.
3.Through hands-on operation, observation, group cooperation and other activities, students cultivate students' practical ability, analysis and induction ability, enhance the awareness of cooperation and communication, penetrate the idea of graphic transformation as soon as possible, and try to analyze and solve problems from the perspective of movement.
【Teaching Focus】1.Analyze what kind of basic pattern the translation pattern is made of and how it is translated.
2.A graph can be easily translated as required.
[Teaching difficulties].1.Explore the translational essence of the graph. 2.Use your panning knowledge to create beautiful panning patterns.
[Teaching Preparation].Courseware, ruler, triangle.
[Teaching process].
First, the introduction of the situation, a preliminary understanding
Question 1 As shown in the figure, it can be seen that the "basic pattern" is obtained by translation.
Question 2 is shown in the figure, which is a graph of the fish before and after translation, pointing out the corresponding points of points a, b, and c, and pointing out the position relationship and size relationship between ad, be, and cf.
2. Think** and gain new knowledge
Reflection 1Is there only one answer to question 1?
2.What is the essence of graph translation?
3.What is the shape and size of the two figures before and after translation? What is the relationship between the line segments that connect the corresponding points before and after translation?
Inductive conclusions] 1There is no single answer to question 1.
2.The essence of graph translation is the translation of points.
3.Features of panning:
1) The shape and size of the two figures before and after translation are exactly the same;
2) Each point of the new shape is obtained by moving a point in the original shape. These two points are the corresponding points. The line segments that connect the corresponding points of each group are parallel (or on the same line) and equal.
4.The direction of translation of a graph is not necessarily horizontal.
5.There are a lot of beautiful patterns that can be created with panning.
Exercise: As shown in the figure, abc pans to the def position, then:
1) Corresponding points: points a and , point b and points, points c and points;
2) Corresponding angles: a and , 8 and , acb and
3) Corresponding line segments: line segments AB and , line segments BC and , line segments CA and .
4) Translation direction: Translation along the direction.
5) Translation distance: the length of the line segment.
Example: As shown in the figure, translate ABC so that point A moves to point A'to draw the panned a'b'c'
3. Use new knowledge to deepen understanding
1.As shown in the figure, it is a pattern of "Huba", which pattern is obtained by translating the pattern?
2.As shown in the figure, translate the quadrilateral ABCD so that the point A moves to the point A, and draw the translated quadrilateral A b c d
Fourth, teacher-student interaction, class summary
1.Translation: Move a figure as a whole in a certain straight direction to obtain a new shape, which is called translational transformation, referred to as translation.
2.Features of panning:
1) Before and after translation, the shape and size of the figure are exactly the same;
2) The lines of the corresponding points on the two graphs before and after the translation are parallel and equal.
Design Intent:Consolidate what you've learned through practice.
5. Assignment arrangement
Assignments: Exercise 5 from the textbook4".
[Teaching Reflection].
First of all, when teaching, I fully consider the cognitive level of students, look for the connection between new knowledge and students' existing experience, and select familiar life examples of students to intuitively import translation. At the same time, we select intuitive materials that can allow students to perceive translation, and through the observation of these materials, students can initially understand the characteristics of translation. I also guide students to use gestures and movements to express translation, and fully mobilize students' head, brain, hands, mouth and other senses to directly participate in learning activities, so that students can learn in an active situation, and students will actively participate and take the initiative, so as to have a deeper understanding of translation. Then, on the basis of observation, let the students use the perceptual experience, talk about the specific examples of translation in life, and then introduce the teaching of translation distance, from the textbook grid diagram intuitive observation, it is difficult for students to think of counting the number of squares of a figure translation, just to count the number of squares moving at a certain point. Here I let the students discover the way to move the numbers themselves. After experiencing the learning process of "conjecture verification one by one", the students knew the method of finding the corresponding point by translating the figure on graph paper, and were able to draw the shape of the simple figure after translation as required, and felt the geometric characteristics of the translation. It enables students to learn the methods of mathematical exploration while learning mathematical knowledge.
Judging from the effect of this lesson, students can quickly perceive and judge the translation phenomenon through specific examples based on the original life experience, and learn to draw the translated figure on graph paper. However, there are also some problems: first, students are promoted from the translation of the real thing to the translation on the graph paper, especially to say how many squares to reach the designated position, students are easy to misunderstand the movement of a few squares as a few squares apart, "the entry point is not obvious, so that the number of moving grids cannot be counted", "one point is wrong, the whole figure is wrong" phenomenon occurs from time to time. With a few exceptions, swings and fan rotation are not translational. You may also be interested: