On the basis of the examination questions in the drawing class, the innovation and mathematical thinking method are highlighted. Throughout the country, there are situational, design, reading, open and grid types in the senior high school entrance examination of drawing courses, which are endless and dizzying. Compared with the traditional ruler drawing, the drawing problem is open, which requires students to explore in many directions, angles and levels, and examines the flexibility, divergence and innovation of students' thinking
First, the situational type
Example 1 (Guiyang city) As shown in the figure, there are two walls, and two students stand in A and B respectively. In which area does Xiao Ming move so as not to be found by these two students at the same time (indicated by shadows in the figure)?
Example 2 (Hebei) As the picture shows, Xiao Liang enjoys the cool in the square at night. In the figure, line AB represents the small lamp standing in the square, line PO represents the lamp pole standing upright in the square, and point P represents the lighting lamp. (1) Please draw the shadow of Xiao Liang in the picture under the illumination of the lighting lamp (P); (2) If the height of the lamp post is PO= 12m, the height of Liang Xiao is AB= 1.6m, and the distance from Liang Xiao to the lamp post is BO= 13m, find the length of Liang Xiaoyingzi.
Analysis:
Example 1 Xiaoming will not appear in the shadow area at the same time.
Example 2 in △CAB and △CPO,
∠∠b =∠c，∠ABC=POC=900，∴△CAB∽△CPO
∴
∴BC=2
Xiao Liang's shadow is 2 meters long.
Second, the design type
The schematic diagram of Example 3 (Anhui Province) (1) is a grid composed of 10× 10 squares. △ABC is a grid triangle (the vertex is at the intersection of the grid). Please complete the following two questions:
(1) Draw grid points △ a 1 b1c1and △A2B2C2, and △ A 1b 1 in the diagram (1).
(2) In Figure (2), use the same lattice triangles as △ABC, A 1B 1C 1 and △A2B2C2 (each triangle is used at least once) to spell out a familiar pattern, and provide appropriate comments for the pattern you designed.
Example 4 (Yancheng City) As shown in the picture, there are several square pieces of paper and several rectangular pieces of paper. Try to choose these pieces of paper (each piece of paper is used at least once) and make a rectangle in the dotted box below (there can be no overlap or gap between each two pieces of paper, and the spelled picture must keep the trace of the puzzle), so that the area of the spelled rectangle is, and the length and width of the rectangle are marked.
Analysis: Example 3
Example 4
Third, openness.
Example 5 (Guiyang) In a mathematical inquiry activity, Xiao Qiang divided the parallelogram ABCD into four parts with two straight lines, so that two figures with a set of diagonal angles were congruent.
(1) According to Xiao Qiang's segmentation method, you think that dividing an equilateral quadrilateral into straight lines satisfying the above congruence relationship has groups;
(2) Please draw a straight line satisfying the Xiao Qiang division method among the three parallelograms in the figure;
(3) From the above experimental operation, what rules do you find in the two drawn straight lines?
In example 6 (Ningxia Hui Autonomous Region), the side length of each small square is 1. Please draw an isosceles triangle with the grid point as the vertex and the area of 10 square unit, and draw two triangles that meet the requirements and are not congruent in the given grid (two triangles are considered as one).
Analysis: There are countless examples. These two straight lines pass through the center of symmetry of the parallelogram.
Example 6 Design part of the pattern as shown in the figure, in all possible situations.
Bottom 20 10 4 2 10
2
2
four
five
Height 1 2 5 10
2
five
2
2
No. 1 2 3 4 5 6 7 8 9
Fourth, reading.
Example 7 (Changchun City) Figures (1) and (2) are two bar graphs drawn by Jerry Lee according to the number of boys and girls in three grades in his school.
(1) Which of the two pictures can better reflect the total number of students in all grades of the school? Which chart can better compare the number of men and women in each grade?
(2) Please draw a fan-shaped statistical chart according to the number of students of all grades in our school.
Example 8 (Hainan Province) In order to understand the eyesight of primary and secondary school students, the relevant departments in a certain area randomly selected 300 students from primary schools, junior high schools and senior high schools in this area to conduct eyesight surveys, and drew a statistical chart as shown in the figure according to the survey data. Please answer the following questions according to the information provided by the statistical chart:
(1) Among the 300 junior high school students surveyed, there are boys with poor eyesight, girls with poor eyesight and boys and girls with poor eyesight, accounting for% of the students surveyed in this period. It is estimated that among the 1200 junior high school students in this area, the number of people with poor eyesight is about 1000;
(2) Please draw a broken-line statistical chart of students' poor eyesight rate in three learning periods;
(3) According to the survey results, it is estimated that the poor eyesight rate of primary and secondary school students in this area will increase with the increase of grade, and the poor eyesight rate of high school students is about twice that of primary school students. (The result is accurate to 0. 1 times)
Analysis:
Example 7 Figure (2) can better reflect the total number of students in all grades of the school, and Figure (2) can better compare the number of boys and girls in all grades of the school.
(2)
Example 8 (1) 65,79, 144, 12000× 48% = 5760,
(2)
(3) Increase, (103+110) ÷ (27+33) = 3.55 ≈ 3.6.
Verb (abbreviation for verb) grid type
Example 9 (Shanxi Province) As shown in the figure, the figure in the square paper is translated, so that the point A is translated to the position of A, and a figure with twice magnification is drawn. The line segments in the picture must be marked with a ruler and shaded. )
For example 10 (Jilin province), as shown in the figure, the coordinate of point A is (3,3). First, translate △ABC down by 4 units to get △ A' B' C, then rotate △ A' B' C counterclockwise around point O 180o to get △ A' B' C, please draw it.
Example 1 1 (Yunnan province) As shown in the figure, the trapezoid ABMN is a right-angled trapezoid.
(1) Please put a right-angled trapezoid in the drawing to form an isosceles trapezoid with the trapezoid ABMN;
(2) Take point M as the rotation center, rotate 180o counterclockwise, and then move up one grid to draw this right-angled trapezoid (no writing method is needed).
Analysis: Example 9 is as follows:
Example 10 is as follows:
Example 1 1 is as follows: