Vayetzei- Sorting, Sets, Subsets, and Unions related activity ideas

"[Lavan] said, 'What shall I give you?' And Yaakov said, 'Do not give me anything; if you will do this thing for me, I will resume pasturing and guarding your flocks: Let me pass through your whole flock today. Remove from there every speckled or dappled lamb, every brownish lamb among the sheep and the dappled or speckled among the goats- that will be my wage. Let my integrity testify for me in the future when it will come regarding my wage before you; any that is not speckled or dappled among the goats, or brownish among the sheep, is stolen in my possession.'
And Lavan said, 'Yes! If only it will be as you say.'
So he removed on that day the ringed and dappled he-goats and all the speckled and dappled goats- every one that had white on it, as well as all the brownish ones among the sheep- and he put them in the charge of his sons. And he put a distance of three days between himself and Yaakov; and Yaakov tended Lavan's flock that remained." ~Bereishit 30;27-36

In this week's parsha, we learn of how Lavan paid Yaakov for his years of work by separating his flocks into two groups. Lavan kept for himself all of the sheep and goats that were completely white or completely brown, and he gave to Yaakov all of the sheep and goats that had any kind of mixture of white and brown, regardless of the patterning- speckled, dappled, ringed, etc.

Activity Connections:
The concept of separating is a basic one that we begin working on with students at the preschool level. It is often thought of just as a primary skill, but the understanding of sorting, separating, and comparing groups is one that is necessary through higher levels of mathematics, as students work with logical thinking, and sets and subsets of information.

Activity ideas in increasing conceptual difficulty:
*The most basic level of sorting items is creating two or more simple categories and separating the items into the different categories. If I have a box of buttons, I might choose to sort them by color (green, blue, red, etc.), by size (large, medium, small), by shape (round, square, other), by number of holes (1, 2, 4, etc), or any other distinguishing feature that I notice. To make it even simpler, you can create just two categories- green & not green, large & small, round & not round, 1 or 2 holes & 3 or more holes. Sometimes it's easiest to just create two categories, and sometimes it's helpful to have the additional categories. This decision will be based on the items that you're using, if there's a purpose for the sorting beyond just sorting (do you need specific items for different projects?), and the way in which the students see the groupings of items that they're trying to sort. Even at an early age, you can see aspects of how each child processes information based on sorting decisions that they make when categorizing items in a group.

*The next step in sorting complexity is learning how to deal with items that might fall in two categories at the same time. The ultimate model for this situation is a Venn diagram. Students can practice sorting out actual items on an oversized mat that has a Venn diagram drawn onto it, or you can use string or hula-hoops to create overlapping circles for them the place objects into. This works for children as young as older preschool students. As students get up into early elementary classes, they should be able to record their work on a Venn diagram map, ultimately not needing to actually physically move items around. 
--When using Venn diagrams for sorting, you begin crossing categorizations. It could be straightforward- maybe some of your buttons are solid colors and others have multiple colors. Blue buttons go in one circle, red buttons in a second circle, and the buttons that have both red and blue will go in the overlapping section between the two circles. Or, you can begin crossing different attributes- you could sort buttons into green, 3 holes, and round. Different buttons will fit into different sections of the diagram- where will the green star with 2 holes go? what about the round, blue button with 3 holes? the round, green one with 3 holes?

*The next level of categorization is to identify sorted groups and then think about what the groups will look like if you subcategorize them or mix them in certain ways. This is where students begin thinking about subsets (a smaller group within a category), unions (combining of two categories), and intersections (what two different categories have in common). Really, this is an articulation of what they are drawing out on the Venn diagram, but as the concepts move from categories of items to categories of geometric attributes or categories of number types, the complexities increase. A Venn diagram showing categories and intersections of polygons, prisms, angle measures, etc. could have value into high school. Sorting numbers into sets, subsets, unions, and intersections- integers, prime numbers, factors of 26, multiples of 75- has applications in number theory into high school and beyond, depending on your field of study.