When you bite into a nice thick piece of chocolate cake, it’s hard to believe it was made from boring white flour and goopy eggs. Somehow, we mix flour, sugar, eggs, butter, and flavors like vanilla or chocolate, and the hot oven turns them into pound cake, brownies, and other yummy treats. So our fan Norah D. asked, if you made a cake and had only 1 tablespoon of flour, how small would the cake have to be? Well, the cake batter for a pan 9 inches by 13 inches long uses about 2 cups of flour. 1 cup has 16 tablespoons in it, so that’s 32 tablespoons. Your cake would be just 1/32 of the whole pan. Of course, to bake it right, you’d have to use only 1/32 as much sugar, 1/32 as much butter…and you’re probably going to want more than one slice.
Wee ones: 9-by-13 cake pans are rectangles. Find 4 rectangle shapes in your room.
Little kids: If you cut the cake into 5 rows of little brownies, which row is the second to last row? Count along your fingers if it helps! Bonus: Which row is the exact middle row?
Big kids: If you want to cut your cake into 32 equal rectangles – to show what 1 tablespoon of flour makes – how many rows across and down could you cut? Bonus: If you cut 4 rows across and 8 rows down, how many cake pieces are along the edges? Remember not to double-count any!
The sky’s the limit: What fraction of that same cake would use just one TEASPOON of flour? (Key fact: there are 3 teaspoons in a tablespoon). How many ways could you cut the cake to make that many pieces?
Wee ones: Items might include book covers, windows, Lego pieces, or your bed!
Little kids: The 4th row. Bonus: The 3rd row.
Big kids: You could cut 32 skinny rows down; 2 rows across and 16 teeny rows down, or switch them; and finally, 4 rows across and 8 rows down, or switch them. Bonus: 20 pieces. There are 8 across the top, 8 across the bottom, and then just 2 more on each short edge, since you already counted the corners.
The sky’s the limit: 1/96 of the cake, since there are 32 x 3 = 96 teaspoons in it. Lots of ways to slice it:
– 1 set of 96 skinny rows down
– 2 rows across by 48 rows down
– 3 rows across by 32 rows down
– 4 rows across by 24 rows down
– 6 rows across by 16 rows down
– 8 rows across by 12 rows down
…and then the reverse of each: 96 skinny rows across; 48 rows across by 2 rows down; and so on.
Laura Bilodeau Overdeck is founder and president of Bedtime Math Foundation. Her goal is to make math as playful for kids as it was for her when she was a child. Her mom had Laura baking before she could walk, and her dad had her using power tools at a very unsafe age, measuring lengths, widths and angles in the process. Armed with this early love of numbers, Laura went on to get a BA in astrophysics from Princeton University, and an MBA from the Wharton School of Business; she continues to star-gaze today. Laura’s other interests include her three lively children, chocolate, extreme vehicles, and Lego Mindstorms.