"Hey, tomorrow's your half birthday! I know, let's make a cake to celebrate!"
Turns out the recipe called for 1 1/2 cups of flour. Since our cake was ingredient free due to multiple food allergies, we used even parts of two gluten free flours.
"Okay so we need one and one half cups of flour. How many halves in a whole?"
"Okay, so here is the 1/2 cup measuring cup. One scoop of the buckwheat, one of the rice... Now, we need 1/2 cup more flour, using both our flours. What's half of 1/2?"
"How'd you know that?"
"Oh, I just knew..."
Later in the morning, at the library.
"Hey look Mama! The [really big, red tiled] square is made up of smaller squares!"
"Very cool. How many small squares make up the big square?"
"So, you wanna hear something interesting? When you hear someone call a number 'square' that's what it means. Look, nine squares literally make a 'square' number! Isn't that cool?"
"Hey, it's time for cake!"
"But we can only eat half. How would you cut it in half?"
[Girl gestures a line from the middle of one side to the middle of the opposite/parallel side.]
"Well, that's one way. How else could you do it?"
[Girl pauses and then gestures diagonally from corner to corner.]
"Excellent! But I have one more idea. How many squares made up the big square at the library today?"
"So, I"m going to divide the cake into nine parts. Here's one for you, and one for me. We'll have more later, after dinner."
After dinner, and after one more piece each for the child and myself. (Papa doesn't like chocolate, so no cake for him!)
"Mama, can I have a little more cake?"
"Hmmm, maybe. We're only going to eat half of the cake -- let's see if there's any left.... How many pieces did we have to start?"
"What's half of nine?"
"Four and a half."
"So, together you and I have eaten four pieces. There's half a piece left and you can have it!"
Ladies and gentlemen, I present to you: half a cake!