scr888 test account id:scr888,test,account,锘,2018,Nin:锘?p>2018 Ninth grade book Mathematics East China Normal University version lesson plan 23.1 Proportional line segment data download 2018 Ninth grade book Mathematics East China Normal University version lesson plan 23.1 Proportional line s
锘?p>2018 Ninth grade book Mathematics East China Normal University version lesson plan 23.1 Proportional line segment data download 2018 Ninth grade book Mathematics East China Normal University version lesson plan 23.1 Proportional line segment 23.1 Proportional line segment 23. Proportional line segment [knowledge and skill] 1. Master the concept of proportional line segments and their properties. 2. Will find the ratio of the two line segments and determine whether the four line segments are proportional. [Process and method] can flexibly use the nature of the proportional line segment to solve the problem. [Emotional Attitude] The practical application of perceived knowledge, enhance the objective understanding of knowledge as power, and further strengthen the theoretical and practical learning methods. [teaching focus] the ratio of the line segment and the proportional line segment, and the basic nature of the proportional line segment. [Difficulties in teaching] Exploring the nature of the scale by introducing the ratio k. First, create a situation, introduce new knowledge. How to determine the proportion of four numbers? What are the basic properties of the proportional formula? 2. Are the two rectangles in the grid below similar? Second, cooperative exploration, understanding new knowledge exploration 1: proportional line segment 1. Do one (1) 1 In the above grid diagram, if the distance between two adjacent grid points of horizontal (or vertical) is 1, then AB=________, BC=________, A'B'=________ , B'C' = ________; 2 calculation = ________, = ________; 3 obviously AB, BC, A'B', B'C' are not equal, then what is the relationship between them? Through communication, the students draw conclusions: =. (2) Thinking: Is there a similar conclusion when changing to other line segments such as AD, CD, A'D', C'D'? If so, what is it? =.2. Conclusion Line ratio: If the same length unit is used to measure the length of two line segments AB and CD, their length ratio is the ratio of the two line segments. Proportional line segment: For four line segments a, b, c, d, if the ratio of the length of two line segments is equal to the ratio of the other two line segments, such as = (or a: b = c: d), then the four line segments It is called a proportional line segment, referred to as a proportional line segment. Also said that the four line segments are proportional. 3. Discussion (1) In the above grid diagram, if you remove the grid points, by metrics, can you still verify that the above conclusions are true? (2) If the length unit of AB is in centimeters and the length unit of A'B' is in decimeter when measuring, do their ratios change? (3) Does the ratio of the length of the two segments have any relationship with the length unit used? 4. Knowledge use example 1: Determine whether the following line segments a, b, c, and d are proportional line segments: (1) a=4, b=6, c=5, d=10; (2) a=2, b=, c=2, d=5. Analysis: Use the definition of proportional line segments. Solution: (1) 鈭?==, ==, 鈭粹墵. 鈭?line segments a, b, c, d are not proportional segments. (2) 鈭?==, ==, 鈭?=. 鈭?line segments a, b, c, d are proportional line segments. Example 2: Find the ratio of line segments according to the diagram: , , and point out the proportional line segments in the figure. Solution: It can be seen from the figure: AC=1cm, CD=2cm, DB=4cm, CB=CD+DB=6cm, so =,=,==. Then there is =. So AC, CD, CD, DB are proportional line segments. Inquiry 2: The nature of the ratio 1. In the proportional formula of the number, if the four numbers a, b, c, and d satisfy =, then we say that the four numbers are proportional, and if there is =, then there is ad=bc; if ad=bc, then = So if the line segment is proportional, is there any conclusion? Through the student analogy, the basic nature of the ratio is derived. 2. The basic property of the ratio is =, then ad=bc. If ad=bc (a, b, c, d are not equal to 0), then =.3. Discussion (1) Will you prove these two propositions? (Guide the students to prove from both positive and negative aspects) (2) By ad=bc, in addition to getting =, what proportions can you get? 4. Knowledge use example 3: Proof (1) If =, then =; (2) If = (a鈮燽), then =. Prove: (1) 鈭?=, add 1 to both sides of the equation, 鈭?+1 = +1,鈭?.(2)鈭?,鈭碼d=bc. Add ac to both sides of the equation, 鈭碼d+ac=bc+ac.鈭碼c-ad=ac-bc,a(c-d)=c(a -b), 鈭礱鈮燽, from = get c鈮燿, 鈭碼-b鈮?, and c-d鈮?. Both sides are divided by (a-b)(c-d), 鈭?. Exercise: Known =, the value of the sum. Guide students to practice, sum up the solution method, and finally the teacher summarizes the problem related to the scale by setting the value of k. Third, try to practice, master the new knowledge. If x is a ratio of 3 and 12, then the fourth proportional term of 3, x, and 8 is __卤16__. 2. Known: 3a = 4b, then = ____. 3. If ===(b+2d-3f鈮?), find the value. (Answer:) 4. If ===k(a+b+c鈮?), try to find the value of k. (Answer: 2) 5. As shown in the figure, ===, and the circumference of 鈻矨BC is 36cm, and the circumference of 鈻矨DE is obtained. (Answer: 24cm) 6. Ask the students to complete the 'Inquiry Online and Efficient Classroom' section. Fourth, the class summary, combing the new knowledge of this class, what are your gains and confusion? 1. Summary of contents (1) Proportional line segment: In the four line segments, if the ratio of two line segments is equal to the ratio of the other two line segments, the four line segments are said to be proportional segments. (2) Basic properties of the ratio: If =, then ad=bc. If ad=bc (a, b, c, d are not equal to 0), then =.2. Method summary (1) In the solution of the proportional problem, use the method of setting the value of k; (2) determine whether the four line segments are proportional, as long as the four line segments are arranged in order of magnitude, determine the ratio of the first two segments and the last two Whether the ratio of line segments is equal, equal is proportional, otherwise it is not proportional. 3. Points to pay attention to (1) When seeking the ratio of two line segments, the units must be unified; (2) Line segments a, b, c, and d are proportional, and the representation method is sequential, that is, =. V. Deep practice, consolidation Xinzhi asked the students to complete the 'Internship and Effective Classroom' 'Classwork' section. The first to sixth questions of the exercises on page 55 of the textbook. twenty three. Parallel line segmentation is proportional [knowledge and skill] On the basis of understanding, grasp the nature of the parallel line on one side of the triangle, the proportionality theorem of the parallel line segment and the bisector of the parallel line, and apply it flexibly. Will make the known line segment into the known ratio and divide the line segment into the drawing problem. [Process and Method] Through the learning theorem, the mathematics of analogy can be exercised again. A slightly complicated graph can be divided into several basic graphs, and the ability to recognize and push the theory can be applied through the application of exercise. [Emotional Attitude] Through the study of theorem, we know that the general law of understanding things is from special to general, and can appreciate the symmetrical beauty of mathematical expressions. [Key points of teaching] Understand and grasp the proportionality theorem of parallel line segmentation and the property theorem of parallel lines on one side of the triangle, and apply the theorem to solve related problems. [Difficulties in teaching] Exploring and summarizing the proportional theorem of parallel line segments and the property theorem of parallel lines on one side of the triangle, and how to decompose complex graphics into simple basic graphs. First, create a situation, introduce new knowledge [warming and new] problem: a set of equidistant parallel line intercept line a is equal to the line segment, then what is the relationship between the line segment intercepted on the line b? (Please ask the students to watch the verification process in the courseware) [Student Activities] Students observe, analyze, think, explore and communicate with classmates. [Teacher Activities] Teacher organizations guide students to conduct independent research and communication. [Summary] The teacher guides the students to conclude that a set of equidistant parallel lines are equal in line segment on line a, then the line segments intercepted on line b are also equal. [Teacher Dial] This is the parallel line bisectoral theorem we learned earlier. It discusses the case where the line segments intercepted by parallel lines are equal, so what if the intercepted line segments are not equal? This is what we are going to learn today: the proportionality theorem of parallel line segments. [Teaching Instruction] Through the review of the bisector line theorem of parallel lines, it will pave the way for the students to summarize the proportionality theorem of parallel line segments in the new lesson. Second, cooperation and exploration, understanding of new knowledge [teacher-student cooperation inquiry] Teacher: Students, please open the math homework, we can find that each page is composed of parallel lines with equal spacing, please ask the students first in the homework Arbitrarily draw a straight line m, as shown in the figure: Teacher: From the graph we can see that the line m intersects with three adjacent parallel lines at three points A, B, and C. The parallel line aliquot line theorem knows AB. =BC. If you draw a straight line n and intersect this set of parallel lines, then you can also know that DE=EF. So we can get =.[Thinking improvement] If you change the adjacent three parallel lines on the jobbook to not Adjacent three parallel lines, arbitrarily draw two lines m, n and they intersect, as shown in the figure, when the two lines of m and n are parallel, observe and consider the four line segments AD, DB, FE, and EC obtained at this time. What is the relationship between the length? If the two lines m and n are not parallel, you can observe it again, or you can calculate the amount and see if they have a similar relationship. [Student Activities] Students explore and communicate with their students. [Teacher Activities] Teacher organizations guide students to conduct independent research and communication. [Summary] The teacher guides the students to explore and conclude the following conclusion: Parallel line segmentation proportional theorem: The two straight lines are intercepted by a set of parallel lines, and the corresponding corresponding line segments are proportional. Expressed in geometric language: 鈭礎D鈭E鈭F,鈭?.[teacher dial] dial one: When point A and point F in the above figure coincide, as shown in the figure, AD, DB, AE, EC four What is the relationship between the line segments? Dial 2: As shown in the figure, when the lines m and n intersect at a certain point on the second parallel line, is there a similar proportional line segment? [Summary] The teacher guides the students to conclude the following: the property theorem of the parallel line on one side of the triangle: the line parallel to one side of the triangle intercepts the other two sides (or the extension of the two sides), and the corresponding corresponding line segment is proportional. Expressed in geometric language: 鈭礑E鈭C,鈭?. 鈭礑E鈭C,鈭?.[teacher dial] The two figures can be simply referred to as 鈥淎鈥?and 鈥淴鈥? Example explanation example 1: As shown in the figure, l1鈭2鈭3, AB=4, DE=3, EF=6, find the length of BC. Analysis: Considering that there is a set of parallel lines in the problem, you can try to solve the problem by using the proportional theorem of parallel line segmentation. Solution: 鈭祃1鈭2鈭3,鈭?(parallel line segmentation is proportional). 鈭礎B=4, DE=3, EF=6, 鈭?.鈭碆C=8. Example 2: As shown in the figure, E is a point on the extension CD of the side CD of ABCD, link BE, AC at point O, pay AD At point F. Prove: =. Analysis: Since the line segments in the proportional formula are all on the same line, the parallel line segmentation proportional theorem should be used to find the sum of the values. Proof: 鈭?Quadrilateral ABCD is a parallelogram, 鈭碅B鈭D, AD鈭C.鈭礎B鈭D,鈭?.鈭礎D鈭C,鈭?.鈭?.3, try to practice, master the new knowledge. Exercise on page 55 of the textbook. 2. As shown in the figure, DE鈭F鈭C, try to find a proportional line in the picture, compare it with your companion, see who is looking fast, find more. Question 2 Figure 3 Figure 3. Known: As shown, l1鈭2鈭3,=, verify:=.4. Ask the students to complete the 'Inquiry Online and Efficient Classroom' section. Fourth, the class summary, combing new knowledge 1. This lesson mainly learns the properties of parallel lines parallel to one side of a triangle, the proportionality theorem of parallel line segments and the aliquot line theorem of parallel lines. The proof of the parallel line segmentation theorem is transformed into parallel to the side of the triangle. The nature of the parallel lines to solve. 2. Use the parallel line segmentation proportional theorem, one must see the parallel line group, the second to find the corresponding line segment of the quasi-parallel line group, otherwise it will produce an error. .
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