Venn and Carroll Diagrams  
Venn diagrams involve the use of rectangles and circles to show sets and the relationships between them. Each circle is one attribute (e.g. eveness, primeness, squareness, multiple of 3ness, etc.). The rectangle is the boundary. It represents the "universe"  everything being considered/included.
A Venn diagram involves yes/no thinking (belongs/does not belong). Suppose everything being considered/included consists of the numbers: 1, 2, 3, 4, 5, 6, 7. Suppose you count one attribute for this  evenness. The best Venn diagram to show this is: 

Note that there is only one circle. It represents evenness. You do not need another circle for oddness. By default, everything outside (not inside) the evenness circle must be odd. To put it another way, every number inside the circle is even. Every number outside the circle is odd.
For more detail, refer to: 

Early Years data display methods  
Try these:  
Make a Venn diagram for each situation. 

Everything under consideration/included is: 2, 3, 5, 9, 10, 15, 17, 21
Attribute #1 is primeness. Attribute #2 is oddness. 

Everything under consideration/included is: 5,10,15, 20, 25, 30, 35, 36
Attribute #1 is divisibility by 5ness. Attribute #2 is divisibility by 10ness. 

Everything under consideration/included is: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 Attribute #1 is primeness. Attribute #2 is evenness. Attribute #3 is multiple of 3ness. 



Carroll diagrams are rectangular tables that display data in a yes/no way. They are named in honour of Lewis Carroll, the pseudonym of the author of Alice in Wonderland. He was a mathematician who specialized in symbolic logic. Suppose you have 1, 2, 3, 4, 5, 6, 7, and one attribute  evenness. The Carroll diagram for this is: 



For detail on Carroll diagrams for two and three attributes/categories, refer to:  
Early Years data display methods  
Try these:  
Make a Carroll diagram for each situation. 

For 1, 2, 3, 4, 5, 6, 7, 8, 9, and the attributes/categories: primeness and oddness 

For 2, 5, 17, 30, 40, 41, 42, 43, 50, 55, and the attributes/categories: evenness, primeness, and divisible by 5ness 
