to someone's surprise

「to someone's surprise」是「令……吃驚、出乎預料」，例如：

To her surprise that the book she bought was wrapped in a dirty plastic bag.（令她吃驚的是，她買的這本書被包在一個髒兮兮的塑料袋裡。）

To the little boy’s surprise, the bathroom door was locked.（小男孩驚訝地發現，浴室的門被鎖上了。）

To the policeman’s surprise, the news soon got out.（出乎警方預料的是，這個消息很快就出來了。）

step by step

「step by step」是「一步走完再，走下一步」—「循序漸進」，例如：

I want to hear your whole story again, we’ll take it step by step.（我要你把整件事情再說一遍，我們按部就班地討論。）

Step by step, Alice knew the importance of it.（漸漸地，愛麗絲曉得了它的重要性。）

I am not rushing things and I’m taking it step by step.（我會循序漸進，不會倉促行事。）

underestimate

「underestimate」是「低估」，例如：

It was easy to underestimate him because of his occasionally ponderous manner.（由於他偶爾會出現笨拙的姿態，容易讓人小瞧了他。）

The worst thing you can do is underestimate an opponent.（最糟的錯誤就是低估對手。）

His cunning and guile were not attributes I would ever underestimate.（我不曾對他的狡詐掉以輕心。）