Set, What!

Sets, Oh My!

Sets in Mathematics have always been confusing to me when looked at in depth.  On the surface, I understand that a set is grouping or collection of some sort that has identifiable characteristics.  However, I struggle answering questions about sets when they are filled with Set Theory jargon.  For example, when I see the symbols: ∩ and ∪, I often get them mixed up in my mind.  I have now memorized ∪ (union) because it is clearly a U shape, hence union.  This helps me remember ∩ must then mean Intersecting.  A Union is a when you take multiple sets and list all the elements in each set combined.  When you are considering the Intersection of multiple sets, you are looking for the common elements.

When I read about sets I realize that they are not as elusive as I once thought and I am capable of analyzing them.  I can often be a concrete thinker and it is beneficial to me to have definitions and examples as I work on math.  Therefore I have decided to find quick resources that I can study to familiarize myself with Set Theory language and meaning.  With practice, I believe I will eventually learn the process of identifying and comparing characteristics of sets.

All this talk about sets and I suppose you are wondering what a set looks like!  An example would be this set: {a, b, c, d, e, f, g}  A second example would be: {e, f, g, h, i, j, k}.  So what does the union of these two sets look like?  It's really quite simple, take all the letters in each set and list them like this: {a, b, c, d, e, f, g, h, i, j, k}.  How about the intersection of the sets?  Again, quite simple!  However, evaluate and compare each set carefully so you don't miss a shared element: {e, f, g}.

When considering mathematics for children, the concept of sets should be introduced as early as possible.  The level of complexity and detail can be adjusted to the level of the child.  You can introduce the concept by using objects rather than numbers and variables.  Use something fun and familiar like M&M's!

Borrowed from: http://www.mms.com/us/product/milk

Kids can make piles of different combinations of m&m colors and take an inventory of what the combined number of colors are and what colors each set has in common.

You can use your imagination and come up with any assortment of objects that is familiar to your student or child.  Some other ideas are different clothing objects, sports equipment, money, toys, etc.  

Here is another example using the sports equipment idea:

Set one {baseball, basketball, football}

Set two {football, catchers mitt, softball}

To make it more interactive you can use the actual items, kids love when they can use props!  An add on lesson would be to branch out into data collection.  How many baseballs total, how many footballs total, etc?

Check out this awesomely narrated video introducing Set Theory:

Some additional resources:

Quick reference guide to Set Theory symbols can be found here

Set Theory in depth descriptions can be found here