Initially learn to raise and ask questions from the perspective of mathematics, comprehensively apply mathematical knowledge to solve simple practical problems, enhance application awareness and improve practical ability.
Get some basic methods to analyze and solve problems, experience the diversity of problem-solving methods, and cultivate innovative consciousness.
In mathematics examination questions, more and more attention is paid to the application of mathematics knowledge. Recently, students are studying the application of quadratic equation in one variable. In addition to the four types of questions given in the textbook, students will also encounter the problem of "communication" when doing problems, which will test their understanding ability. To sum up first:
Example 1.
Tracking exercise 1.
In order to help students understand, I made a picture of trunk, branch and twig with XMind. It is relatively easy for students to understand by explaining.
Then I gave another example 2:
Because of the infiltration of the above two topics, students can easily list the equation of 1+X+X2= 100. Is this right? What is the difference between this topic and the above two topics?
"After the trunk of a big tree has branches, there are no small branches anymore. Small branches sprout on the branches, right? "
"Right"
"If I am the first flu patient, I will infect five people in the first round, and will I continue to infect others in the second round?"
"Yes, it will continue to spread."
"How many sources of infection are there in total?"
" 1+5=6"
"How many people will be infected in the second round?"
"6×5=30"
"Assuming that the average number of infected people is X, how should this topic be formulated?"
" 1+x+( 1+x)x = 100 "
The answer to the equation is nine people.
Tracking exercise 2.
Solution: If an ordinary computer infects a workstation computer every turn, there is1+x+(1+x) x = 81. That is, (1+x)2=8 1.
The solution is x=8 and x2=- 10.
So after three rounds of infection, there are 8 1+8 1x8=729 infected computers.
A: A computer infects an average of 8 computers per round. After three rounds of infection, there were 729 infected computers.
Mathematics classroom needs teachers' guidance, and summarizes the problems that students encounter, so as to obtain some basic methods to analyze and solve problems and experience the diversity of problem-solving methods. It is our persistent task to be good at classification and summary and diligent in reflection and implementation.