No sugar cane in Old World (survival).

Hello. I recently started playing Minecraft a few weeks ago. I am playing the "old world" and noticed there are no sugar canes growing anywhere in my world. I have searched all the boundaries of the world and have no found any sugar canes (under water, along coastlne, on the ground, everywhere). I have created a "infinate" world and have seen them, but load back into the old world game, and still no sugar canes. Is this intended? Are there supposed to be no sugar canes in the old world version? Thank you for all your help =)