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题目:用1×1×2,1×1×3、1×2×2三种木块拼成3×3×3的正方体。现有足够多的1×2×2木块,还有14块1×1×3的木块,要拼成10个3×3×3的正方体,最少需要1×1×2的木块____块。(1994小学数学奥林匹克决赛第8题)此题突出空间形体在位置发生变化时,形体相应变化规律的理解和应用,且该题较为抽象,尤其是对“足够多的1×2×2的木块”的理解,“14块1×1×3木块”如何恰当地分配组拼难以把握。所以要较为顺利地解答此类竞赛题,就有必要对学生进行强化空间意识,透彻理解题意的多种综合能力的训练。现就此题解答思路剖析如下。1.三种木块各自不同的空间位置表现形式①1×1×2木块的空间形体:
Title: Use 1 × 1 × 2, 1 × 1 × 3, 1 × 2 × 2 three pieces of wood into 3 × 3 × 3 cube. There are enough 1 × 2 × 2 pieces of wood and 14 pieces of 1 × 1 × 3 pieces of wood to make up 10 pieces of 3 × 3 × 3 cubes with a minimum of 1 × 1 × 2 pieces of wood _ ___Piece. (1994 Elementary School Mathematical Olympiad, Problem 8) This question highlights the understanding and application of changes in the shape of a body when its position changes, and the question is rather abstract, especially for an “adequate number of 1 × 2 × 2 Wood block ”understanding,“ ”14 1 × 1 × 3 wood block" How to properly assign the group difficult to grasp. Therefore, in order to answer such competition questions more smoothly, it is necessary to train students to strengthen their spatial awareness and thoroughly understand the various comprehensive abilities of the questions. Analysis of the problem is now answering this question as follows. 1. Three kinds of wood in different spatial positions of their manifestations ① 1 × 1 × 2 wood space shape: