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在四年级下册长方体和正方体的体积单元测试中,有这样一个问题:一个长方体空盒,长8 cm,宽6 cm,高12 cm,最多可以放()个棱长4 cm的小正方体。同类型的题目已经讲解练习过,但本次依然有部分学生给出如下答案:(8×6×12)÷(4×4×4)=9(个),而正确的应该是:8÷4=2(个),6÷4≈1(个),12÷4=3(个)2×1×3=6(个)。反思整个过程,把一个长方体切割成若干个正方体,想让学生明白如果长、宽、高都是棱长的整数倍,两种方法解决:方法一,大体积÷小体积;方法二,用长、宽、高分别除以棱长,再把得数相乘。但只要有一个量不是棱长的整数倍,只能使用方法二,并且是去尾型。在处理练习十四的第7题时(同类型问题),通过尝试,使用了大半节课解决这个问题。但课后练习依然反映出不小的问题。
In the fourth-grade volumetric cuboid and cube test, there is such a problem: a cuboid empty box with a length of 8 cm, a width of 6 cm and a height of 12 cm can hold up to (4) small cubes of 4 cm long. The same type of topics have been explained practice, but this time there are still some students give the following answer: (8 × 6 × 12) ÷ (4 × 4 × 4) = 9 (a), and the correct should be: 8 ÷ 4 = 2, 6 ÷ 4 ≈ 1, 12 ÷ 4 = 3 (pieces) 2 × 1 × 3 = 6 pieces. Rethink the whole process, a rectangular box cut into a number of cubes, want students to understand if the length, width, height are all multiples of the prism length, two methods to solve: Method One, large volume ÷ small size; Divide the width and height by the length of the prism and multiply them by the number. But as long as there is an amount is not an integer multiple of the edge length, can only use the second method, and is to tail type. In dealing with Question 14 of Practice XIV (of the same type), I tried most of the lesson to solve the problem. But after-school practice still reflects no small problem.