The standard badminton in international competitions is composed of 16 feathers, and the weight is generally 5g. When the quality of badminton exceeds or exceeds the standard, add:. The international competition standard badminton is composed of 16 feathers, and the quality is generally 5g. When the quality of badminton exceeds or is lighter than the standard, we call it inferior. At present, there are 81 badminton balls, one of which is inferior and lighter. With the help of every day, at least several times, we can find this defective product. This paper analyzes the thinking process of solving this problem, and designs the main teaching process for the six-year mathematics expansion course in primary school.
6 times; The analysis should be carried out as few times as possible, and the number of scales required each time should be as large as possible. (Because it is certain to find out, so consider the worst case), then put 40 on both sides of the first time. If the weight is the same, it is the remaining one. If the weight is not the same, take the lighter side, and repeat the above operation again (if the number of badminton dealt with is an even number, it will be directly evenly divided; if the number is an odd number, it will randomly pick out the remaining one), so operate until the inferior product is found. The main process of teaching is to first let students try to do a few simple examples (the numbers are small and it is easy to enumerate all the cases), then guide them to find and summarize the rules (the number of examples can be determined according to the situation), and then use several more complex examples to let students verify the rules they found. Finally, use the existing knowledge to demonstrate this law and analyze the way to solve problems. In short, the ultimate goal is to let students learn a way to solve problems
81=27 X 3 Scales 27 of two
The 27 light ones can be judged
27=9 X 3 Weigh two of them
Judge the 9 light ones
9=3 X 3 Weigh two of them
Judge the three light ones
3 = 1 X 3
Weigh two of them
Judge which of the three is light!
So only four times
The first step is to divide them into three piles, 27 for each pile; Put two piles on the balance. If the two sides are equal, put them in the third pile. Otherwise, put them in the light pile of the two piles and weigh them for the first time;
The second step is to divide them into three piles, nine for each pile. The steps are as above, and the second time is to weigh them;
The third step is to divide them into three piles, three for each pile. The steps are as above, and the third time is called;
Step 4, divide them into three piles, one for each pile, as above, and weigh them for the fourth time;
I knew it was inferior! Primary school students are required to have a basic understanding of power. Be familiar with the 2nd power of a natural number within 20, and the 3rd power of a natural number within 10. The three numbers 2, 3, and 5 are the most frequently investigated!
