Bananas

My Beauties LOVE bananas. I mean they really LOVE them. We go through a good size bunch in less than 2 days around here. Today however, Chloe decided that she doesn't like the "stringy things" (as she named them) that sometimes stay on the banana instead in the peel. Yes she is my picky eater we all know. I peeled them off, making sure to get each and every "stinky thing" off the fruit. She insisted that she still tastes them. Her words tonight, "Mommy, I guess I don't really like bananas after all." Hmm...the perfect fruit...one of only three that she will actually eat (cantaloupe and apples (but not sour ones) being the other two.) Help! How do I convince her the strings are okay and the banana still tastes like the beloved bananas she has always eaten and loved so much?