Beijing design courses
definition of straight lines and perpendicular to the plane and determine the case of
Jiangxi,UGG boots, Jiangsu Province, Huai-school
horse of a high school, teaching case describes
teaching objectives
1. from the familiar things of life to extract, generalize the definition of straight line and perpendicular to the plane and the decision theorem, and then combined with graphical summary of abstract mathematical language, presentation these contents;
2. students of abstraction, the rational speculative argument quickly recognized the essence of things spiritual and intuitive ability;
3. through the formation of mathematical knowledge and practical application to enable students to Recognizing that truth comes from practice, and applied to practice this philosophy;
4. mathematical concepts students can consciously use and improve learning in the process interest in mathematics.
teachers teaching goal is to be expected, in the teaching process-fulfilling content. cover educational intent is the best way to achieve educational intent, but also add the art of science the embodiment of art education, the author has never used these elements before making a new lesson to the students demonstrate the practice, but in the teaching process to achieve these goals in unconsciously.
teaching
1. Introduction
We live in three-dimensional space, on a straight line and plane is very familiar, took the altar in the school flag pole, it's relationship with the ground to give us the impression that perpendicular to each other as a straight line l,Discount UGG boots, the ground (which is also representative of many things) as plane, line l today to study the knowledge and the plane perpendicular to 2.. the new class as shown in Figure 1,UGG shoes, the straight line l on behalf of the flag on behalf of the ground plane, then Do you think with the line l What is the relationship? Students to use life experience and prior knowledge can determine the into a flagpole, the ground plane as the intention is to use a combination of abstract and concrete, to guide students to a smooth and rapid completion of the interaction between the abstract and the specific conversion. In teaching, teach those trying to determine and set square to measure the line is vertical, students often will be issued knowing laughter, education wrote: 'thinking' out. ) and (ground) are perpendicular to the line, then l and what is the relationship? Require students to read books not summarize the premise of the definition of straight line and perpendicular to the plane, although the summary of the language is likely not ideal to teach those who do not vertical. people in the process of research and problem solving is always a convenient way to take, and now we are pursuing is to find a simple and feasible to determine the method of straight lines and perpendicular to the plane. Here we have to simulate the tree planting activity, a student up demonstration, on the desk while other students presentations, observe to determine how to determine the a series of questions:
(1) a straight line with the plane perpendicular to this line can be determined with the plane perpendicular to it?
(2) two straight lines with the vertical plane, can determine this line and the plane perpendicular to it?
(3) straight line and plane straight line perpendicular to ten thousand, can determine this line and the plane perpendicular to it?
(4) straight line and plane perpendicular to the countless straight line, to determine this line and the plane perpendicular to it?
(5) To get a straight line and the plane perpendicular to this line at least a few lines with the vertical plane?
(6) To get a straight line and the plane perpendicular to this line with the plane of the vertical line two what?
On the basis of the above proposed conjecture: If a straight line with a plane perpendicular to two intersecting lines, then this line perpendicular to the plane.
through the presentation and the range of issues The seminar, students gradually realize determine the nature of straight lines and perpendicular to the plane: if a straight line perpendicular to the plane of countless straight line, it can not determine this line perpendicular to this plane. because there may be many straight line parallel to each other, then This line only represents a myriad directions, it is only two different directions, people planting trees to determine whether the ground when the vertical applied to this principle. guess not a substitute for proof, we need to use rigorous logical reasoning to justify this conclusion. ... through the transformation problem is reduced to: If the lines l two lines with the plane perpendicular to prove that line l and any line perpendicular to the plane, and then into (Figure 2): such a treatment by the
intention: to seize the essence, eliminate interference, so that The following goals can focus concentrated on the proof of ⊥. specific process slightly. in teaching must be noted that this application is to construct a congruent triangle method and the knowledge of the most simple geometry, eliminating the mystery of students.
3. Summary:
(1) the definition of straight line perpendicular to the plane;
If l ⊥ m, l ⊥ n, intersecting lines m,UGG boots clearance,
n determine the plane, then l ⊥. and g is the arbitrary straight line, then l ⊥ g
(2) straight line perpendicular to the plane of the decision theorem (compiled witty formulas: essence of the problem);
(3) will (1) and (2) together, an important mathematical model was right:
the so-called mathematical model to reveal the nature of things, with the mathematical form of a relatively fixed format. model because of its simplicity of form, depth of content, so very beneficial to understand, remember, master, assembly, retrieval, extraction and use. The teaching model in the future, but also many repetition, reinforcement, and assembled with the knowledge of the organic integration of knowledge systems. The model will be a three-dimensional geometry of the most important and the most frequent effective Three explicit language and the brain's internal language of efforts to make the model become obvious on the intuitive students to be more flexible and comfortable use of its capability.
4.A group exercises
(1 ) will be opened a little book, upright on the table (not shown), then the spine What is the relationship with the desktop? Why?
(2) roof is composed of two rectangles (not shown), then the plane of the gable roof and what is the relationship? Why? (3) Let △ ABC, if the line l ⊥ AB, l ⊥ BC, Prove: l ⊥ CA. (4) to make a tripod, so that the three legs of any two legs perpendicular to each other (Figure 3), then PA and BC, PB and CA, PC and AB, respectively, what is the relationship? Why?
above series of exercises implemented progressively, from concrete to abstract, interlocking,
progressive layers, forming a steady growth in student ability to make the training chain.
In teaching, the use of a variety of means to enhance the effectiveness of training.
described as the first port, and then demonstrate the process of writing specifications, and then wipe the blackboard fuzzy graphics polished
Some require very clear in this case does not demonstrate the process say. If the students a good foundation, you can wipe off all the graphics and letters, by means of imagination, action and language expressions using the argument process. You can also use
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