- Understanding how an item can be part of a set and how that set can be part of another set.
It is useful if pupils have completed KS2 Syntax, Sorting and, Sets Intermediate level before attempting this exercise.
Adding more and more circles does not increase the difficulty, although the practicality of using string circles becomes harder. So what we will aim to do in this advanced level activity is to show how embedded sets work.
An embedded set is a further classification of a set within a set. Going back to the trusty library example, we might have sets of books, sorted by genre: e.g Fiction or Non-fiction. Embedded groups within the fiction genre may be: Science Fiction, Fantasy, Crime, Historical, Romance etc. or in Non-fiction there may be embedded groups such as Reference books, Biographies, Travel, text books etc.
In order to create an embedded set, simply place a set within another set. The ‘inner’ embedded set has 2 sets of properties – Its own properties and the properties of the set it is contained in. (This is sometimes referred to as ‘inheritance’).
As with the initial use of the Venn Diagram with 2 sets. Set out the exercise and try and tease out of the pupils what the significance of a set inside a set is. At this stage it would be expected that the pupils are familiar enough with the NOT, AND, OR rules to be able to identify sets (or in this case – embedded sets) without needing to go through several instances of using the simple sets.
Embedded sets can also form part of a Venn system as before. By embedding a set then intersecting the embedded set with a ANOTHER set. We can create quite complex systems through this method:
Again, run through these exercises with tell me, show me and, odd one out format to ensure that the pupils have understanding of how the system is working.
Advanced Diagrams to try!
Here are a few more diagrams to try and play with, see if you can work out where these might be appropriate!