Example 1: In order to prevent sandstorms, the following figure shows the participation of four classes in tree planting:
(1) Which class has the largest number of participants? At least?
(2) What percentage of boys are more than those in Class Three? What percentage is all girls less than all boys?
(3) It is known that a * * * has planted 339 trees. How many trees does each person have?
(4) What are the benefits of afforestation? Talk about your opinion.
Analysis: This question mainly examines whether students can solve some valuable practical problems according to the information obtained by histogram. Cultivate students' ability to recognize drawings, process statistical information and comprehensively apply mathematical knowledge, and enhance students' awareness of environmental protection by combining science education.
Description: (1) I: 24+8=32 (person) II: 18+6=24 (person)
Class 3: 20+ 10=30 (people) Class 4: 15+ 12=27 (people)
Because of 32 > 30 > 27 > 24, Class One has the largest number of participants, while Class Two has the least. Give a brief answer
(2)(24-20)÷20=20%
24+ 18+20+ 15=77 (person) 8+6+ 10+ 12=36 (person) (77-36)÷77≈53.2%.
Give a brief answer
(3)339÷(77+36)=3 (tree)
(4) We can consider purifying air, improving air quality, conserving soil and water, and preventing sandstorms.
Example 2: A cuboid water tank with length, width and height of 50 cm, 40 cm and 60 cm respectively, equipped with two water inlets A and B..
Tube. Open pipe A first, and then both pipes will be opened at the same time after a period of time. The following line chart shows the water inflow. Please answer the following questions according to the chart.
(1) How many minutes does it take to open both tube A and tube B at the same time? What was the water depth at that time?
(2) The pipes A and B are fed with water at the same time. How many milliliters of water is injected every minute?
(3) According to the above table, what other questions can you ask? And answer.
Analysis: This question mainly examines students' ability to understand the characteristics of simple broken-line statistical charts and their ability to mine information. By observing and analyzing the simple broken-line statistical chart, we can understand the significance and function expressed by the broken-line statistical chart. In a general statistical graph of broken lines, each point on the broken line represents a quantity. In the above question, the vertical axis represents water depth and the horizontal axis represents time. There are obvious intersections between curves, and there is a straight line in front of the point, and the slope of the back straight line is obviously higher than that of the front straight line. Therefore, starting from this point, two measures are taken.
Solution: (1) 15 minutes later. The water depth was 20 cm at that time.
(2)50×40×(60-20)=8000 (cubic centimeter) 8000 cubic centimeter =8000 ml.
(3) We can get the following information: water inflow speed of pipe A, water inflow speed of pipe B and water inflow speed of two pipes.
Example 3: The following statistical table is the result sheet of a math exam in grade six. Please answer the following questions according to the information in the table below.
Student number
achievement
Student number
achievement
Student number
achievement
1
excellent
2
excellent
three
okay
four
okay
five
excellent
six
okay
seven
excellent
eight
excellent
nine
okay
10
excellent
1 1
excellent
12
qualified
13
excellent
14
titular
15
excellent
16
okay
17
okay
18
okay
(1) How many people in the class are qualified?
(2) What percentage of top students in the class are more than top students?
(3) Do you think the results of this class are good? Why? Talk about your opinion.
Analysis: This topic selects simple statistical tables that students are familiar with, and mainly examines students' understanding of the relationship between the quantities in the statistical tables, their understanding of the significance and function of the statistical tables, their ability to calculate relevant data from the known data in the tables, and their ability to observe, analyze, judge and reason.
Simple explanation: (1) 17 people.
(2)(9-7)÷7≈28.6%
(3) 17÷ 18≈94.4% is good. Among the students in class 18, 17 passed, with a passing rate of 94.4%.
From the above examples, we can see that the flexible and ingenious application of statistical graph knowledge can broaden our thinking and comprehensively apply the knowledge, skills and thinking methods we have learned to solve problems. This not only cultivates students' awareness of raising mathematical problems from real life, but also helps to cultivate students' ability to solve problems and their awareness of cooperation and communication.