My sister Tali loves capers. She snacks on them by the jar. I don’t mind them and even periodically sprinkle a few on my bagel. Last week, my mom went food shopping and brought home a huge jar of capers. As we were sitting down at the breakfast table to have some fresh hot bagels, I reached for the jar to fill my spoon and then I got to thinking: was there a way to calculate the number of capers in the jar without actually counting them one by one?

I asked my dad how many capers he thought were in the jar. He said he didn’t know exactly but that he could estimate the amount.

**Doing the Math**

He grabbed a pencil and a nearby napkin and started calculating. He tried solving the problem by figuring out the volume of the jar and the amount of __capers__ per a cubic inch. This wasn't a particularly difficult method but it required several steps and calculations.

There had to be a faster way! I picked up the jar and looked at the nutritional information on the back of it and then the answer jumped out at me. On the label it said that one serving size was 1 tablespoon and the total number of servings per container was approximately 155. Estimating around 25 capers per tablespoon, I simply multiplied 20 x 155 and came up with 3100 capers in the jar. My dad was just finishing his calculation (he came up with 3500 capers), and he was surprised to hear how quickly I arrived at my estimate so I explained how I got my number.

Then dad suggested that we actually count every caper one by one to see who was closer (the winner’s prize to be determined at a later time).

**The Great Count**

Yes, it’s true. We actually did count every single tiny caper in that enormous jar. We started by emptying the jar into a large stainless steel bowl. Each one of us (my mom, dad, and me) took approximately one third of the jar and proceeded to count. The counting took close to 10 minutes and finally when the last caper was accounted for, my mom tallied each of our numbers and came up with 3428 - 72 capers fewer than what my dad had estimated.

I thought that this was a very interesting, because it shows that there are several ways to __estimate__ the number of capers in the jar without actually counting them. In addition to the volume and servings per container method that my dad and I used, I could have also used either of the following 2 methods:

**By Weight**

- Weigh the stainless steel bowl before adding the capers
- Add the capers (without the juice) and then weigh the bowl again
- Subtract the weight of the bowl from the measurement in step 2 (This will give us the weight of the capers).
- Weigh 3 capers and calculate their average weight
- Divide the total weight of the capers in step 3 by the average single caper weight

**By Displacement**

- Fill a bucket with water (to a height slightly greater than the caper jar)
- Mark the height of the water with a marker
- empty the capers into the bucket (make sure you drain the liquid first) Note the height the water rose to
- calculate the amount of
__water displaced__by the capers using the formula: - Calculate the
__volume__of one caper using the formula: - Divide the total capers volume you got in step 4 by the average caper volume you got in step 5 (you will need to average the volume of 3 capers)

I must say, after this fun exercise, I don’t think I’ll ever be able to sprinkle capers on my bagel again without instinctively counting each and every one.

That is just cool beyond words!

ReplyDeleteyou have an incredible thought process, impressive ... maths MUST be one of your strongest subjects at school right?! I take my hat off to you Sheva :D

ReplyDeleteLOVE your post!

Thank you soooo much for the great feedback! I do like math very much, especially when I don’t have to count hundreds of capers :-)

ReplyDeleteWhy? do not make a book....? will be fun..so much in your head..I enjoy it!! Keep the good job!

ReplyDeleteMe I just do and fix and Recycle Jewelry...you are a Genius...in the Bottle!!

Patricia