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eighth grade math lesson plan arhombus
Learning Objectives (Learning Focus):
1. experience the process of exploring the identification of rhombus, in the activity of cultivating a sense of inquiry and the habit of cooperation and communication;
2. use the identification of rhombus to reason about.
Supplementary examples:
Example 1. As shown in the figure, in △ABC, AD is the angle bisector of △ABC. DE∥AC intersects AB at E, DF∥AB intersects AC at F. Is quadrilateral AEDF a rhombus? Explain your reasoning.
Example 2. As shown in the figure, the perpendicular bisector of the diagonal AC of the parallelogram ABCD intersects the sides AD and BC at E and F respectively.
Is the quadrilateral AFCE a rhombus? Explain.
Example 3. As shown in the figure , ABCD is a rectangular piece of paper, fold B, D, so that BC, AD fall exactly on AC, let F, H are B, D fall on AC at two points, E, G are the intersection of the crease CE, AG, and AB, CD, respectively
(1) Try to show that the quadrilateral AECG is a parallelogram;
(2) If AB = 4cm. BC=3cm, find the length of the line segment EF;
(3) Quadrilateral AECG is a rhombus when the two sides of the rectangle, AB and BC, possess what relation.
After class help:
I. Fill in the blanks
1. If quadrilateral ABCD is a parallelogram, plus the condition ___________________, it can be a rectangle; plus the condition _______________________, it can be a rhombus
2. As shown in the figure, D, E, F are points on the sides BC, CA and AB of △ABC respectively,
and DE∥BA, DF∥ CA
(1)To make quadrilateral AFDE is rhombus, add the condition ______________________
(2)To make quadrilateral AFDE is rectangle, add the condition ______________________
II. Answer questions
1. As shown in the figure, in □ABCD , if 2, determine whether □ABCD is a rectangle or a rhombus? And explain the reason.
2. As shown in the figure , the two diagonals AC,BD of parallelogram A BCD intersect at the point O,OA=4,OB=3,AB=5.
(1) Are AC,BD perpendicular to each other? Why?
(2) Is quadrilateral ABCD a rhombus?
3. As shown in the figure, in □ABCD, it is known that ADAB, the bisector of ABC intersects AD at E, EF∥AB intersects BC at F. Ask: Is quadrilateral ABFE a rhombus? Please give reasons.
4. As shown in the figure, fold a rectangular piece of paper ABCD along the diagonal BD, so that the point C falls at the point E, BE and AD intersect at the point F.
(1) Prove that: ABFì?ì_ì?_ì?ì_ì?_ì?_ì?_ì?_ì?_ì?_ì?_ì?_ì?_ì?_ì?_ì?_ì?_ì?_ì?_ì?_ì?_ì?_ì?_ì?_ì?_ì?_ì?_ì?_ì?_ì?_ì?_ì?_ì?ì_ì?_ì?_ì?_ì?_ì?_ì?_ì?_ì′?? (()，(1).
8th grade math lesson plan IIFluctuation of data
Teaching objectives:
1, experience the process of exploring the degree of dispersion of data
2, understand the three measures that portray the degree of dispersion of data polar deviation, standard deviation and variance, and be able to use a calculator to find out the corresponding values.
Teaching focus: can calculate the extreme deviation, standard deviation and variance of some data.
Teaching difficulties: understand the relationship between the degree of data dispersion and the three differences.
Teaching preparation: calculator, slide show
Teaching process:
I. Create a situation
1, projection textbook P138 examples.
(Through the solution of the problem string, so that students intuitively estimate the average quality of 20 chicken legs taken from A and B plants, while allowing students to initially appreciate the average level of similar, the degree of dispersion of the two may not be the same, so that the logical introduction of a measure to portray the degree of data dispersion of the extreme deviation)
2, the extreme deviation: refers to a set of data in the largest data and the smallest data difference, the extreme deviation is used to portray the degree of data dispersion. The extreme variance is a statistical measure used to characterize the degree of dispersion of data.
Second, activities and investigations
If the C plant also participated in the competition, a sample of 20 chicken legs from the plant, the data as shown in the figure (projection textbook page 159 figure)
Problems: 1, the C plant the 20 chicken legs of the quality of the average and the extreme deviation is what?
2, how to portray the difference between the mass of these 20 chicken legs and its average in factory C? Find the difference between the mass of the 20 chicken legs and the corresponding mean for factories A and C, respectively.
3. Which of the two factories, A and C, do you think has the better quality of chicken legs? Why?
(In the above scenario, it is easy for students to compare the extreme differences in the quality of chicken legs sampled in plants A and B to draw conclusions. Here to add a C plant, its average quality and extreme deviation is the same as the A plant, at this time leading to contradictions in the student's ideology and understanding, for the introduction of the other two portrayal of the degree of data dispersion of the measure of standard deviation and variance as a prelude.
Third, explain the concept:
variance: the average of the squares of the difference between the individual data and the mean, written as s2
Let there be a set of data: x1, x2, x3,, xn, the average of which is
then s2 = ,
and s = called the standard deviation of the data (both the arithmetic square root of the variance)
from above. From the above formula, it can be seen: the smaller the extreme deviation, variance or standard deviation of a set of data, the more stable that set of data is.
Fourth, do a do
Can you use a calculator to calculate the variance and standard deviation of the quality of the 20 chicken legs taken from factories A and C above? Do you think which factory to choose a better specification of chicken legs? How do you calculate?
(Through the solution of this problem, the students recalled the steps of the average with a calculator, and freely explore the detailed steps of the variance)
V. Consolidation exercises: textbook page 172 with the classroom exercises
VI. Classroom summary:
1, how to portray a set of data dispersion?
2, how to find the variance and standard deviation?
VII. Assign homework: Exercise 5.5, questions 1 and 2