Here are the correct ticks for countable and uncountable nouns:

1. A lot of **children** like playing video games. (Countable)
2. There is not much **sugar** in the bowl. (Uncountable)
3. Would you like another **burger**? (Countable)
4. In the **mountain**, it's very cold in the winter. (Countable)
5. Help yourself to some more **rice**. (Uncountable)
6. Remember to close the **window** when you leave. (Countable)
7. Mary drinks **orange juice** for breakfast every day. (Uncountable)
8. The visitors arrived with a lot of **luggage**. (Uncountable)
9. Don't eat too much **food** before you go to bed. (Uncountable)
10. We need to buy some **toothpaste**. (Uncountable)

So, the correct ticks should be:

1. Countable nouns: children
2. Uncountable nouns: sugar
3. Countable nouns: burger
4. Countable nouns: mountain
5. Uncountable nouns: rice
6. Countable nouns: window
7. Uncountable nouns: orange juice
8. Uncountable nouns: luggage
9. Uncountable nouns: food
10. Uncountable nouns: toothpaste