Fractions, put to use! (Math 1510)

My oldest daughter is 10 and in so many ways takes after her mother, which at times is quite scary.  We share a love of cooking.  I thought at first this common interest would be wonderful, but so far it has been quite a patience tester for this momma.  I have been cooking for about 25 years.  I am the oldest of 9 siblings and my mother absolutely despises the kitchen.  As soon as I was old enough to follow her directions, I was responsible for cooking.  It did not take long and I was creating my own "masterpieces" to share at the family table.  I have to remind myself often (like every 7 1/2 seconds! ) that my daughter is LEARNING.  It is going to take time for her to do things quickly and without the kitchen looking like a tornado went through it.  To get into the fractions lesson here, the other day I decided that we were going to make my grandmothers Lumberjack Molasses Cookies.  My children and I love these cookies.  My grandmother has been healing in a nursing home for almost 7 months now and we are planning a visit to southern Minnesota soon to visit, so I knew she would appreciate having this treat brought to her.  On a side note, these cookies freeze very well!  We started by measuring out the amount of molasses that I had in the cupboard and Aubrie (my daughter) said, "just a little more than 1 1/2 cups."  Great....this means we could make 1 1/2 bathes of these cookies.  Knowing this is what I wanted to do, I gave her the recipe and asked her to figure out the amounts for the rest of the ingredients to make 1 1/2 batches.

*The original recipe reads: 
2c. white sugar                      1tsp. salt
1c. shortening                        2tsp. cinnamon
1c. molasses                          2tsp. ginger
1c. sour cream                      1/2tsp. cloves
2tsp. baking soda                  6c. flour
2 beaten eggs
Mix as for a cake, refrigerate over night, roll out, cut, bake- 350° for 12-15 minutes
Lumberjack Frosting:
2 1/4 cups Powered Sugar, add 2 unbeaten egg whites and whip for 3 minutes.  While beating add 1/4 tsp. Cream of tarter and 1tsp. vanilla.  Beat for 3 or 4 more minutes.  Frost cooled cookies.

At first my daughter's solution to figuring out measurements was to only fill the measuring cups and spoons that she had used, 1/2 full this time.  While this is a creative solution, I explained that simply guessing what seems to be 1/2 full would not be exact enough and her cookies would probably not work out.  So we sat down together and started multiplying our measurements by 1/2 so that we would know exactly how much we needed of each ingredient.

Our multiplication of fractions began:
2c. sugar.... “easy mom, 1/2 of that is 1c”.....ok, no fraction needed :) (3c.)
1c. shortening..... “half of that is 1/2c.” (1 1/2c.)
1c. molasses....... “half of that is 1/2c.” (1 1/2c.)
1c. sour cream..... “half of that is also 1/2c.” (1 1/2c.)
2tsp. soda..... “half of that would be 1tsp.” (3tsp.)
2 beaten eggs.... “so, we need 1 more egg” (3 eggs)
1tsp salt........ “plus another 1/2 tsp” (1 1/2tsp.)
2tsp cinnamon..... “and another 1tsp.” (3 tsp.)
2tsp ginger..... “plus 1tsp.” (3tsp.)
1/2 tsp cloves..... “half of a half”.....ok, lets figure this one out.
  *We divided using the common denominator method.  We lucked out that our denominators were alike...  1/2 ÷ 1/2= 1/4....ok, so we need 1/2 tsp + 1/4 tsp,
finding a common denominator and then adding is the plan this time too!
1/2 + 1/4= 1/2 becomes 2/4 + 1/4= 3/4 , we need (3/4tsp.)
6c. flour.... “half of 6 is 3, 6+3=9” (9cups)

Frosting:
2 1/4c. Powered sugar....”well half of 2 is 1” and “half of 1/4....hmmmmm?”
again we will multiply using common denominators.  1/4 x1/2= 1x1=1, 4x2=8, = 1/8, so we need 2 1/4c. plus 1 1/8 cup....with the complexity of adding these two fractions we just left it at this, she added 3c+1/4c+ 1/8c. of powered sugar to the bowl (3c+1/4c+1/8c)
2 unbeaten egg whites “plus one more white”
1/4 tsp. Cream of Tarter “ugh, another 1/4? well half of 1/4 is 1/8”  * she did the same thing this time that she did with the powered sugar, (1/4tsp + 1/8tsp)
1tsp. vanilla “and another 1/2” (1 1/2 tsp.)

This entire process of converting took us a while, but I feel like she truly understood the method behind properly figuring out the halves. 

The cookies were then mixed and refrigerated, the next day baked, frosted and enjoyed them!! And....the half-batch we made is stored in the freezer for our special visit with Grandma next week!