乘法作为缩放（改变大小）

将乘法理解为一种缩放（改变大小）的过程：不通过计算，依据另一个因数的大小来比较乘积与某个因数的大小；并解释乘以大于1、等于1或小于1的分数时结果会如何变化。

Interpret multiplication as scaling (resizing): compare the size of a product to a factor based on the size of the other factor without computing; explain the effect of multiplying by fractions greater than, equal to, or less than 1

学习证据 / Evidence

• 不计算，预测3/4 × 7的结果比7大还是比7小。
• 解释为什么乘以5/3会使一个数变大，而乘以2/5会使它变小。
• 把 a/b 乘以 n/n = 1 与分数等值原理联系起来。

• Predict without calculating whether 3/4 × 7 is greater or less than 7
• Explain why multiplying by 5/3 makes a number larger and multiplying by 2/5 makes it smaller
• Relate multiplying a/b by n/n = 1 to the principle of fraction equivalence

评估问题 / Assessment

如果{{name}}计算20×1/4，能不能在计算前判断出答案比20大还是比20小，并解释为什么？

If {{name}} multiplies 20 by 1/4, can they predict whether the answer will be bigger or smaller than 20 — and explain why, before doing the calculation?