I have a group of girl friends that gets together about every 6 weeks. We call our time together “Ladies Learn”. To quote my awesome Sister-in-Law, Morgan (no, you met the OTHER Sister-in-Law, Maggie in past posts), “Ladies Learn is a monthly gathering of wonderful, wacky women. Each month is hosted by a different lady who chooses a theme for the afternoon. . . . What we do isn’t as important as the time we spend together away from work and other stressors.”
Anyhoo…. as soon as I heard what Septembers Ladies Learn shindig was, I KNEW I had to blog about it for Math IS Real Life!
First, I must mention that when Morgan entertains…. well, she goes over and beyond and then beyond some more! We all knew she was having an apple theme… but we had no idea what we were in store for!
Upon arriving, we were greeted with an awesome table full of goodies for us to take home! She made us each a homemade caramel-cream cheese dip for our apples, as well as a baked orange full of spices.
We had an awesome lunch of Waldorf salad, pork, onion and apple kabobs, apple pie “fries”, apple bourbon barbeque sauce, and homemade caramel dip.
Then she pointed to the apple and quart jars…. APPLE CIDER! I was so excited to take pictures of this entire process! I do hope you enjoy the pictures as much as I enjoyed the day!
The first step in the apple cider making process was to rough chop the apples. We rough chopped 8 bags of local apples plus another large basket. The basket carried about 3.5 bags of apples. All-in-all we had about 175 apples.
Oh, and before we start, here is some fun non-standard conversions you may want/need to know to continue…
1 bag of apples = 1/2 peck
4 pecks = 1 bushel
Next, we added the cheese cloth loosely to the barrel.
We then took our positions….
…for the record you don’t use both cranks at the same time but this pic was tooooooo cute to not post! Sister-in-law, Morgan on the right and her best friend Mandy on the right.
Then, someone, with lots of strength, cranked the handle to turn the churn where the apples were placed earlier.
While the cranking was taking place, two people held on to the cheese cloth so that the apples were contained without any spills!
Once 2 bags worth of apples had been cranked, we laid the cheese cloth over the bundle of apples and added the flat press on top of the cloth.
The person holding the jar had to be ready to transition another jar quickly so as not to lose any apple cider!
Our first two bags yielded a little over 1.5 quarts of cider. (this seemed to be our juiciest batch!)
A close-up of the cider dripping into the jar. It actually flows rather quickly, I just asked them to slow it a bit so that I could get a good picture!
11.5 bags of apples later we had 8 quarts of apple cider.
So other than the obvious, quarts… where’s the math? Well, Morgan is an awesome estimator! Originally 8 ladies had signed up for the Ladies Learn outing, for various reasons only 5 were able to attend. Morgan had to estimate the number of apples per quart needed… she was able to take her past experiences with campers and make a great estimated guess. But, what would she do if she didn’t have an background knowledge?
When you do the math, you can see that about 1.5 bags or 3/4 of a peck of apples is approximately 1 quart of apple cider. (please note that NOTHING was added to the juice, no sugar, no additives, no preservatives, etc…)
I’ll be honest with you, originally I had planned on writing about proportional reasoning to solve the “how many apples do I need to buy dilemma”, but the more I sat back and looked at the below data, the more I got a bit frustrated…
Proportion is tricky with juicing a fruit because of all the variance in the fruit itself. Some apples are juicer, some are larger, some are smaller. While all the bags are weighed, sometimes there are differences in the amount of juice you get from that bag – was the same amount of force used? was the full amount of juice extracted? too many factors to have a perfect proportion. However, you can use this data to get a pretty decent idea of what future batches will look like based on a linear regression.
y = 0.67x
or approx y = 2/3x
(in non-math terms… you get about 2/3 of a quart of cider for ever 1/4 peck of apples
Knowing that, I have a pretty decent estimate on how many apples to buy to make apple cider based on the amount of people attending my party.
So, making a table based off of that linear regression, you can see if I want to make 15 quarts (almost 4 gallons!) I would need 23 half-peck bags of apples. Knowing the equation of the line for the data can make your estimation much more exact!
If you don’t have a TI-83 calculator handy, you can search for “linear regression calculator” on your search engine of choice. I used this one.
Here are various math topics related to this tasty project: Measurement conversion, capacity, proportional reasoning. estimation. linear regression, measures of center (with the initial apples in each bag), force (to turn the crank to grind the apples), fractions (of usuble to unusable apples),