K12 Math Grade 7

This activity investigates how many subsets a set has.
What is a Subset?
A subset is a set contained in another set
It is like you can choose ice cream from the following flavors:
{banana, chocolate, vanilla}
You could choose any one flavor {banana}, {chocolate}, or {vanilla},
Or any two flavors: {banana, chocolate}, {banana, vanilla}, or {chocolate, vanilla},
Or all three flavors (no that isn't greedy),
Or you could say "none at all thanks", which is the "empty set": {} Example: The set {alex, billy, casey, dale}
Has the subsets: * {alex} * {billy} * etc ...
It also has the subsets: * {alex, billy} * {alex, casey} * {billy, dale} * etc ...
Also:
* {alex, billy, casey} * {alex, billy, dale} * etc ...
And also: * the whole set: {alex, billy, casey, dale} * the empty set: {}
Now let's start with the Empty Set and move on up ...
The Empty Set
How many subsets does the empty set have?
You could choose: * the whole set: {} * the empty set: {}
But, hang on a minute, in this case those are the same thing!
So the empty set really has just 1 subset (which is itself, the empty set).
It is like asking "There is nothing available, so what do you choose?" Answer "nothing". That is your only choice. Done.
A Set With One Element
The set could be anything, but let's just say it is:
{apple}
How many subsets does the set {apple} have? * the whole set: {apple} * the empty set: {}
And that's all. You can choose the one element, or nothing.
So any set with one element will have 2 subsets.
A Set With Two Elements
Let's add another element to our example set:
{apple, banana}
How many subsets does the set {apple, banana} have?
It could have {apple}, or {banana}, and don't forget: * the whole set: {apple, banana} * the empty set: {}
So a set with two elements has 4 subsets.
A Set With Three Elements
How about:
{apple, banana, cherry}
OK, let's be more systematic now, and