"The sum of two natural numbers is 350. If the last digit of a number is removed, it is equal to another number, then what is the larger of these two numbers? "
Why is it so challenging for students? Let's clear up the mathematical information in the topic:
First, the wrong thinking orientation
1, the concept of "natural number" is the learning link of Unit 1 "Multiplication and Factor" in the second volume of the fifth grade in the textbook of 20 13 edition of West Normal University (the same below), so the traction of this mathematical term is not involved in the daily teaching of the second grade.
2. The sentence "Remove the last number, it is equal to another number." It is easy to remind us that removing a zero at the end of an integer reduces it by 10 times, and adding a zero increases it by 10 times. What's more, we don't need the 10 relationship between decimal multiplication and decimal division in the first volume of the fifth grade. The difference between the two numbers is 9 times, and the sum of the two numbers is 165438+.
Second, the correct thinking orientation.
Think from the "three-digit addition" in this unit to guide students. The "natural number" in this topic refers to the number within three digits we have learned so far, and understand this concept as a number.
1, "If you remove the last digit of a number, it is equal to another number." Prove that one addend has three digits and the other addend has two digits. And it can be determined that the numbers on a larger number of hundreds of bits are the same as those on a smaller number of ten bits, and that the numbers on a larger number of ten bits are the same as those on a smaller number of bits.
2. "The sum of two numbers is 350", which proves that the sum of single digits of two numbers is either equal to 10 or equal to 0. According to the first item above, it can be comprehensively judged that the sum of single digits of two numbers must be 10.
3. Because the single digits of two numbers add up to 10, the decimal digits of two numbers add up to 1, the decimal digits of 350 add up to 5, and the original decimal digits of two numbers add up to 4. Therefore, it can be determined that the number on the hundredth digit of the larger number is 3, the number on the tenth digit of the smaller number is 3, and the number on the tenth digit of the larger number is 4-3= 1.
4. According to the first article, the number in the top ten is the same as the number in the bottom ten, and the number in the top ten of the third article is 1, so it is concluded that the decimal place is 3 1, so the decimal place is 350-3 1=3 19.
Finally, the answer can be determined: the larger number is 3 19 and the smaller number is 3 1.