〜の次の数は何？って英語でなんて言うの？

There are many ways of saying this, those above are best suited to a child. In mathematics numbers can also be referred to as numerals or integers.

There are so many way you can ask them to help you child count or check their progress.
What number comes after five?- This is a more direct way of asking them
Example
A:"What number comes after five?"
B: "6!"
1,2,3,4,?- This is a more fun way. You want them to fill in the missing number.
Example
A: "We say 1,2,3,4,?"
B: 5!

Let's count. 1, 2, what comes after 2?
How many cars do you have? 1, 2, 3, and what's next?
Let's count to five. 1, 2, 3 (pause to see if they answer)
Can you tell me your numbers? One.....(pause to see if they answer the next ones)

When you want to ask your child what number comes after a certain number; then you may say it in the following ways:
-What is the number after five?
-What comes after five?
-What is after five?

If you want to ask what the following number would be, you can say:
"What number comes after 10?"
"What is the number after 10?"

"What comes after (number)"
Is a commonly used question, ideally used when speaking to children, an educational question.
"Can you tell me what numbers after (ex.10)"
A more elongated way of asking this question, more formal and sounds like more of a question, this way it is phrased is asking an individual by emphasizing 'you'.

This is a fun game to play with a child and both of these questions will serve very well. THe verb in the first sentence is "come after" which can generally be accepted to mean "follows".