Мы взяли по куску дыни, а детям дали по куску арбуза.

We took a piece of melon each, and the children were given a piece of watermelon each.

Breakdown of Мы взяли по куску дыни, а детям дали по куску арбуза.

• мы: we
• дать: to give
• взять: to take
• ребёнок: the child

Questions & Answers about Мы взяли по куску дыни, а детям дали по куску арбуза.

What does по mean in this sentence?

Here по has a distributive meaning: one each / apiece / per person.

So:

• Мы взяли по куску дыни = We each took a piece of melon
• детям дали по куску арбуза = the children were given a piece of watermelon each

This is a very common Russian pattern:

• по яблоку = an apple each
• по билету = a ticket each
• по чашке чая = a cup of tea each

Why is it по куску, not по кусок?

Because after по in this distributive sense, Russian commonly uses the dative singular.

So:

• кусок = nominative
• куску = dative singular

That is why you get по куску.

This pattern is very common:

• по яблоку
• по подарку
• по вопросу
• по куску

Even though several people are involved, the thing distributed is still one item per person, so Russian uses the singular form.

Why are дыни and арбуза in different forms?