1. On the basis of drawing an angle equal to the known angle with protractor and ruler, we can draw an angle equal to the known angle with compass and ruler;
2. Understand the concept of angular bisector, master the drawing method of angular bisector, and use the knowledge of angular bisector to solve some simple problems;
3. experience? Observe, practice, summarize and understand the rationality of ruler drawing? Further cultivate students' good habits of rational thinking and conscious reflection. Cultivate a rigorous learning attitude.
The focus of teaching is to master the drawing method of angle, the concept and simple application of angle bisector.
Teaching Difficulties Understanding and Mastering Using compasses and straightedge to draw an angle is equal to a known angle.
Teaching methods: induce thinking and explore teaching methods.
Teaching material analysis, this lesson is the second lesson in the second quarter of Chapter 6 of Grade 7 Mathematics (I) of Jiangsu Education Press. Before this, the students have got a preliminary understanding of the basic knowledge of some angles. This lesson focuses on the drawing of angle and the concept teaching of angle bisector. The textbook starts with guiding students to observe things, gradually abstracts the geometric figures they have learned, and uses the method of question inquiry to guide students to operate and explore independently, thus deepening their understanding and mastery of diagonal lines. Students' mastery of this part will lay a foundation for further study of geometric figures such as triangles, rectangles and squares, and play a role in connecting the past with the future.
Analysis of learning situation
Students' skill base: On the basis of the last lesson, students can basically understand the concept of angle, be familiar with the expression method of angle, measure the angle with a protractor, know the degree, minute and second, make a simple conversion, and write the relationship between the sum and difference of angle according to the figure.
Students' experience basis: Through observation, practice, summary and discussion, students can be familiar with it, and can compare the learning of angles with the learning of line segments to re-experience the mathematical analogy thought.
Prepare computers, courseware and projectors as teaching AIDS.
teaching process
First, self-exploration and doubt
20 10 Asian Games Women's Nine-Ball Competition (Video Play)
As shown in figure 1, do you know some basic knowledge of playing billiards? (Show graphics)
Known angle. So how do you draw an angle equal to a known angle?
The design aims to introduce the theme from billiards that students are interested in and stimulate their enthusiasm for learning. At the beginning of the class, first, ask questions around the teaching objectives, guide students to explore with questions, guide students to learn textbooks by themselves, solve problems by themselves, and consciously cultivate students' self-learning ability and spirit.
Second, explore and solve doubts together.
1. Think about it: place two triangles as shown. Can you calculate the angle in the picture?
2. Try it: Use a pair of triangular rulers and do it yourself to see what angle you can get.
The design intention is to let students feel the harmony and difference between the two angles from a special angle through practical operation.
Calculation, through the discussion at the same table, guide the students to sum up the drawing method of angles that are multiples of 15.
Do this:
As shown in the figure, known? Mona, can you draw with it? MON equiangular?
As shown in Figure 2, can the red ball hit the bag in the lower corner? To solve this problem, it is necessary to draw an angle, so that its design intention can be transformed from a special angle to a general angle, from the drawing of triangles and protractors to the drawing of straightedge and straightedge, and students' mathematical thinking will gradually rise from perceptual to rational. In the teaching process, teachers ask questions first, then ask questions, constantly deepen and expand, and induce students to explore deeply. It is necessary to let students fully contact painting.
If there are problems in the process, we should guide students to explore independently, take cooperation and exchange as the main line, be good at waiting and make suggestions in time.
practise
As shown in the figure, known? AOC, with OC as one side, draw? BOC，make？ BOC=？ AOC。 (ruler drawing)
What does it matter? Please use the equation.
The design intention is to let students draw a ruler and a ruler first.
Then analyze the relationship between the angles in the diagram,
Thus, the concept of angle bisector is obtained, which not only consolidates the process of making angles with a ruler, but also naturally transitions to new knowledge, which is reasonable and convenient for students to master.
Third, * * * to explore the problem
1. The door of thinking
As shown in the figure, if? AOD=80？ , OC is? A shot of AOD
Ok, OB is? The bisector of AOC, AOB=30? . Beg? Origin labeling
With what? Doctoral degree.
2. The Door of Misunderstanding
Known? AOD=60？ , ? AOB=20？ , OC is? Excuse me, the bisector of BOD? Degree of AOC.
3. The door of wisdom
(1) As shown in the figure, it is known that the line segment AB= 12cm, the point C is on AB, the point D is the midpoint of AC, and the point E is the midpoint of BC. Find the length of DE.
A b
(2) by angle? AOB analogy line segment AB, using the angle bisector analogy line segment midpoint, write a problem, put forward and solve the problem.
The design intention is to design three channels for the knowledge learned in this class, namely, the door of thinking, the door of exposition, the door of misunderstanding and the door of misunderstanding, so that students can freely choose questions, so as to fully understand the degree of students' mastery of new knowledge and reflect and summarize on this basis. The form of cooperation can be the cooperation of two people. Research shows that in classroom teaching, two people have the greatest opportunity to cooperate and the best effect is achieved. In addition, students can fill in the questions by hand and really explore by themselves. Enlightenment? Have a thorough understanding of mathematics.
Fourth, explore suspense again.
1. Summary: What did you learn from this class? What should I pay attention to? What other questions are there?
The design intention is to guide students to summarize, summarize and sort out the knowledge and internal thinking methods of this lesson, and then form a complete knowledge system and method system to pursue greater success.
2. Homework: Required Questions: Questions 4 and 6 of Exercise 6.2; Choose to do the problem: review problem 8.
Question: Can you make a bisector of an angle with the tools in your hand? Do you have any methods?
The design intention makes students have new questions, stimulates students' desire to climb to new knowledge goals, and then urges students to explore on the road of knowledge.
Teaching reflection can fully reflect students' initiative, combine independent answering with group cooperation and communication, and students keep thinking, using words and doing things, always in a kind of? Moving? Be in a state of. Fully embodies the new curriculum concept. Teachers guide students to actively participate in the inquiry process in the form of questions, timely reminders and timely discussions. Pay attention to induction and reflection after questions, and guide students' spatial imagination and abstract generalization ability through questions.