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put on one’s thinking cap

努力地思考某件事情

“It’s a difficult riddle. If you want to solve it, you’ll have to put on your thinking cap.”

这是一个很难的谜语。如果你想解决它的话，你要非常努力地思考才行。

figure something out

弄明白或者解决某个问题

“I can’t figure out how to do the math homework.”

我弄不清该怎么做这个数学作业。

rack one’s brain

绞尽脑汁

“I racked my brain, but I couldn’t think of a good topic for my research paper.”

我绞尽脑汁了，但是我还是想不出一个好的研究论文话题。

be lost in thought

陷入沉思；沉浸在自己的思绪中

“When Dave is programming, he often gets lost in thought.”

当Dave在编程的时候，他经常陷入自己的思绪中。

daydream

做白日梦，开小差

“There’s no way you’ll learn calculus if you spend half the class daydreaming.”微积分

如果你半节课都用来开小差的话，你是学不好微积分的。

draw a blank 

记不起某件事情

“I know her name, but I can’t think of it right now. I’m drawing a blank.”

我知道她的名字，但是我现在想不起来了。