Could fractions and Christmas be at further ends of the fun spectrum? Personally, I don’t see how it’s possible. What is possible is learning fractions while partaking in one of the most fun–and delicious–Christmas traditions there is…baking Christmas cookies!
If you’ve already baked your Christmas cookies, have no fear! You can teach math while baking anything at any time of year! Let’s get to it.
Get out the measuring cups and spoons!
Let’s go with a traditional holiday favorite for our recipe–classic sugar cookies, courtesy of Food Network. In preparation, gather all the ingredients as well as measuring cups and spoons that you’ll need–not only to bake but to teach fractions!
- 2-1/2 cups all-purpose flour
- 1/4 teaspoon baking powder
- 1/4 teaspoon fine salt
- 3/4 cup superfine sugar
- 1-1/2 sticks (3/4 cup) unsalted butter, cut into small pieces, at room temperature
- 1 large egg, lightly beaten
- 1 teaspoon pure vanilla extract
- 4 cups confectioners’ sugar
- 1/4 cup meringue powder
- Food coloring, optional
- Decorating sugar, for topping, optional
- Sprinkles, for topping, optional
Now that you’ve got everything ready…it’s time to do some math! Why? Because you just got a text from your…cousin (just play along here…) and she’s dropping by for the holidays. With her four kids. So now you have to double your recipe!
Doubling the cookies
It’s math time! Show the list of ingredients to your junior baker and have him or her figure out the new measurements by multiplying each number and/or fraction by two. So, how do we do that?
- Multiply the numerators from each fraction (the numbers on top) by each other. The result is the numerator of the answer.
- Multiply the denominators of each fraction (the numbers on the bottom) by each other.
- Simplify or reduce the answer.
Let’s start with the flour. First, we need to turn the mixed number (a whole number plus a fraction) into an improper fraction (a fraction with a larger numerator than denominator). This is done by multiplying the whole number with the denominator of the proper fraction. Add the numerator of the proper fraction to this product to obtain the numerator of the improper fraction.
Doing this turns 2-½ into the improper fraction of 5/2. Now we can double our flour by multiplying:
5/2 x 2 (which we will change to the fraction of 2/1). So, multiplying the numerators of 5 and 2 gives us 10. Multiplying the denominators of 2 and 1 gives us 2. The new fraction is 10/2. Now we can turn that into a whole number by dividing 10 by 2. That gives us 5 cups of flour. Let’s try the same for the baking powder and salt.
Each requires ¼ teaspoon for the recipe. We’ll need to multiply ¼ by 2 as well, in the same way we did for the flour. Multiplying the numerators 1 and 2 equals 2. The denominators 4 and 1 give us 4. That leaves us with the fraction 2/4–reduce that, and we have ½. Twice the amount of baking powder and salt is ½ teaspoon!
Let’s finish up with the sugar and butter (the egg and vanilla extract are easy enough to figure out).
The recipe calls for ¾ cup of sugar. Using the same process, we’ll multiply the numerators (3 x 2 = 6) and denominators (4 x 1 = 4). That gives us 6/4 cups. Uh oh. Improper fraction! Now we have to convert that into a mixed number so we know how much sugar to add–because you’re not going to find a 6/4 measuring cup in your drawer. We already performed the reverse operation and turned a mixed number into an improper fraction by multiplying. So, now we’ll divide to turn the improper fraction into a mixed number. We’ll do that by dividing 6 by 4, which gives us 1-2/4. We can reduce the 2/4 so we get 1-½ cups!
Now the butter. Back to turning a mixed number into an improper fraction! By multiplying, we can turn 1-½ into 3/2. And now we multiply the numerators 3 and 2 (since we’re doubling) to get 6. The denominators 2 x 1 = 2. That gives us 6/2, which we can divide to turn into a whole number of 3–we’ll need 3 sticks of butter!
So, now that you’ve done all that math, let’s look at the updated ingredients list for a double batch of classic sugar cookies!
2-½ x 2 = 5 cups all-purpose flour
¼ x 2 = ½ teaspoon baking powder
¼ x 2 = ½ teaspoon fine salt
¾ x 2 = 1-½ cups superfine sugar
1-1/2 (3/4 cup) x 2 = 3 sticks of unsalted butter, cut into small pieces, at room temperature
1 x 2 = 2 large eggs, lightly beaten
1 x 2 = 2 teaspoons pure vanilla extract
Doubling the icing
Only two math problems to solve here…easy as pie. Or cookies. The recipe calls for 4 cups of confectioners’ sugar. Simple enough. 4 x 2 = 8 cups of confectioners’ sugar. As for the meringue powder, the recipe needs ¼ cup. Doubling that equals 2/4 cup (just like the doubling of ¼ teaspoon for the cookies). Reduce that, and you’ll need ½ cup of meringue powder.
Time to bake!
- For the cookies: Whisk together the flour, baking powder, and salt in a small bowl.
- Beat the superfine sugar and butter with an electric mixer on medium speed in a large bowl until light and fluffy, about 5 minutes; beat in the egg, then the vanilla. Add the flour mixture and mix on medium-low speed until completely incorporated. Divide the dough in half, pat into 2 discs about ¼ inch thick, wrap in plastic wrap, and refrigerate until firm, about 1 hour.
- Position oven racks in the top and bottom thirds of the oven and preheat to 350 degrees F. Line two baking sheets with parchment paper.
- Let the dough sit at room temperature for a few minutes to make rolling easier. Roll out one disc of dough at a time between two pieces of parchment paper until ⅛ inch thick. Cut out shapes with cookie cutters and arrange about 2 inches apart on the prepared baking sheets.
- Bake until the cookies are golden brown on the bottom, 10 to 12 minutes. Let the cookies cool on the baking sheets until firm enough to transfer to a wire rack; let cool completely.
- Gently gather any scraps of dough into a ball and press into a disc; wrap in plastic wrap and refrigerate the disc until firm enough to roll, about 1 hour. Cut out as many cookies as possible and bake.
- For the royal icing: Beat the confectioners’ sugar, meringue powder, and ⅓ cup water with an electric mixer on medium-high speed in a large bowl until stiff peaks form. Beat in the food coloring if using. (The icing can be stored in an airtight container at room temperature for up to two days.)
- Decorate the cookies with the icing; top with decorating sugar and sprinkles if using.
Now comes the fun part…
Eat! Enjoy your cookies with the family…and also those cousins for whom you doubled the recipe! See, fractions actually can be fun–especially when the result of the math is a batch of delicious sugar cookies. So, go ahead and mix some math into your baking–that’s Today’s Lesson!