论文部分内容阅读
圆面积公式有三个认识层次,这一点在教学中应该引起我们的重视。第一个认识层次是:“S=πr~2”来自于“S=(πr)r。”因为圆通过分割、拼摆可以转化为一个长方形,借助于求长方形面积的方法求得圆面积。πr虽然表示圆周长的一半,但它充当了转化后的长方形的长;r虽然表示圆的半径,但它充当了转化后的长方形的宽。这样认识圆面积公式有助于理解其推导过程,利于学生掌握和运用公式解决有关实际问题。第二个认识层次是:“S=πr~2”不仅反映了半径与圆面积的关系,同时还派生出圆的直径乃至圆的周长与圆面积的关系。于是这个基本公式又可引伸出“S=π(d/2)~2”和“S=π(C/2π)~2”,这样就为学生灵活运用公式去解决有关实际问题打下了基础。第三个认识层次是:在“S=πr~2”中,
The circular area formula has three levels of understanding, which should be given our attention in teaching. The first level of understanding is: “S = πr ~ 2” comes from “S = (πr) r.” Because the circle can be converted into a rectangle by splitting and framing, the area of the circle can be obtained by finding the area of the rectangle. Although πr represents half the circumference of the circle, it serves as the length of the transformed rectangle; while r represents the radius of the circle, it acts as the width of the transformed rectangle. This understanding of the formula for the circle area helps to understand the derivation process, which helps students master and use formulas to solve practical problems. The second level of understanding is: “S = πr ~ 2” not only reflects the relationship between the radius and the area of the circle, but also derives the relationship between the diameter of the circle and the circumference of the circle and the area of the circle. So the basic formula can also be extended “S = π (d / 2) ~ 2” and “S = π (C / 2π) ~ 2”, so that students flexibly use the formula to solve the actual problems laid the foundation. The third level of understanding is: In “S=πr~2”,