In a Japanese Junior High School textbook it is written:
"A kendama is a toy"
and then there is a question:
"Do you play kendama everyday?"

Many people ask why it is not "Do you play a kendama everyday?"

Please explain why the textbook is correct.

Also which one is correct: Can you play the piano? Can you play a piano? Can you play piano?
The following are all correct:

For a toy:

a doll, a top, a kendama, a yo-yo

A doll is a toy. A top is a toy. A kendama is a toy. A yo-yo is a toy.

She played with a doll. He played with the top. You played with a kendama.

For a game:

checkers, chess, kendama, tennis

Do you play checkers? Do you play chess? Do you play kendama? Do you play tennis?

For an instrument:

piano, guitar, flute, violin

Can you play the piano? Can you play the flute? Can you play the violin?

So if kendama refers to the object as a piece of equipment, it is "a kendama"; if kendama is considered a game, it is "kendama".

This is not different from other cases, such as baseball: If baseball refers to the object that is thrown, it is "a baseball"; if baseball is considered a game, it is "baseball".

I threw a baseball. I played baseball.

Hope that helped. Emotion: smile
Thorough coverage, Jim. Well done.

A 'kendama' is a wooden toy looking something like a small mallet, in one of whose three shallow cups you try to catch its tethered ball. 'He often played with his kendama.'
Students: Are you brave enough to let our tutors analyse your pronunciation?
Guest"Do you play kendama everyday?"

Note also the more egregious error: it is 'every day' (two words).

Site Hint: Check out our list of pronunciation videos.

A kendama is a toy, right?!
Which means you play with it; it's a personal item!
So, a reasonable statement would be , "I play with my kendama every day."
Now, if it's a group game and there are rules ; winners or losers, or points included, then it will be ,"we're playing 'kendama.
The textbook isn't correct! I know the textbook you're referencing your info from, and next to the picture of a kendama it has a picture of a yo-yo which is pretty strange considering the sentences would be different as well as the question as to what are you doing with either toy.

 Mister Micawber's reply was promoted to an answer.