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题目背景:四年级的期末试卷中有这样一道题:在圆圈中填上“>”、“<”或“=”号。85÷3○(85×3)÷(3×3)学生出现了两种答案:一部分学生填的是等于号,因为根据四年级学习的商不变的性质,被除数和除数同时扩大3倍,商不变。另一部分学生填的是小于号,因为他们通过列竖式计算发现虽然商的数值相等,但余数不相等。学生们的想法各有各的道理,这道题的答案到底应该填等于号还是小于号呢?有的学生怀疑商不变的性质是不是只适用于整除的算式,对有余数的除法适用吗?这道题又引起了老师们的争论。大家争相发言,各抒己见。
Title Background: The fourth-grade final papers have such a question: fill in the circle “> ”, “<” or “= ” sign. 85 ÷ 3 ○ (85 × 3) ÷ (3 × 3) The student has two kinds of answers: some students fill in equal sign because dividend and divisor expand 3 times at the same time according to the invariable nature of fourth-grade learning, Business unchanged. Another part of students fill in less than sign, because they find through column vertical calculation that although the quotient of quotient is equal, the remainder is not equal. Students’ ideas have their own truths. Should the answer to this question be equal to or less than the number? Some students doubt whether the invariant nature of the business applies only to the division of divisibility, and the division of the remainder? This issue has aroused the teachers’ arguments. Everyone vying to speak, express their opinions.