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.
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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
Guest"Do you play kendama everyday?"
Note also the more egregious error: it is 'every day' (two words).