1. The basketball player threw the ball into the basket.

2. The basketball player threw the ball in the basket.

3. The basketball player threw the ball on the board so that it can go into the basket.

4. The basketball player threw the ball onto the basketball board and it came down through the basket.
(Which ones are grammatical? Would you check them? Do you have some more expressions related to the sentences mentioned above?)

1, 2, and 4 are OK, but 1and 2 are the best.

1. The basketball player threw the ball into the basket. (Grammatical)

2. The basketball player threw the ball in the basket. (Not grammatical - we use "into" instead of "in" when indicating movement from outside into something)

3. The basketball player threw the ball on the board so that it can go into the basket. (Grammatical, but the use of "on the board" is less common. It is more common to say "off the backboard" or "off the backboard and into the basket.")

4. The basketball player threw the ball onto the basketball board and it came down through the basket. (Grammatical, but the use of "onto the basketball board" is not the usual way to describe the action. It is more common to say "off the backboard and into the basket.")

It's important to note that when it comes to language, there can be multiple variations and expressions to convey the same meaning. Other expressions related to shooting a basketball can include:

- The basketball player sank the ball into the basket.
- The basketball player scored by tossing the ball into the basket.
- The basketball player made a successful shot by putting the ball through the hoop.
- The basketball player threw a perfect shot that went through the net.
- The basketball player nailed the shot, allowing the ball to make it into the basket.