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The teacher send home an assignment labelled "Irregular plurals". The instructions say "Fill in the blanks with the correct form of the verb"

Question........

Today, Edward ______________ about his new trophy. We have to put in the correct form of the verb think. I don't know if the answer is thinks or thought!

The next one is "Yesterday, Edward __________ about his new trophy.

I don't think the teacher meant plurals, I think she meant tense (past, present, future). Any thoughts?
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This seems to be nothing to do with irregular plurals. It seems, as you say, to be about tenses.

Several verb forms fit each sentence, and there isn't enough context to decide between them. For example:

"Today, Edward thinks* / is thinking / thought / was thinking / has been thinking about his new trophy."

"Yesterday, Edward thought / was thinking / had been thinking about his new trophy."

*uncommon; people don't often talk like this in the simple present tense.
Comments  
Today, Edward ______________ about his new trophy. We have to put in the correct form of the verb think. I don't know if the answer is thinks or thought!

The first one is not as easy as it looks.

Today can be past, present, or future.

We can say:

I did my English homework today. (meaning before now, in the past)

I'm doing my English homework today. (meaning either right now in the present or later today in the future)
I'm going to do my English today. (meaning later today, in the future)

What we can't say is "*I do my English homework today" because the present simple tense (do) is used for a repetitive or habitual action, ie "I do my English homework every day."

Now the word think is a special case because it has two different meanings.

When think means to have an opinion, we use it in the simple present tense.
Edward thinks his new trophy is beautiful.

When think means to perform a mental activity, we use it in the present continuous tense.
Edward is smiling because he is thinking about his new trophy.

Edward thinks about his new trophy today doesn't make a lot of sense to a native speaker.

Edward thought about his new trophy today is correct.

But does your teacher know this?

You have to ask yourself, "How well does my teacher know English?"
Because if your teacher doesn't know the difference between nouns and verbs, is he going to know the difference between action (is thinking) and non-action (thinks)
verbs?

The second one is easy.
Yesterday is a specified time in the past.
Use a past simple verb (thought) with a specified time in the past.

The Linguist (and retired ESL teacher)