When young students understand the concept of sets, they gain a foundation for future mathematical ideas. A set is a mathematical way to represent a group or collection, and elementary students understand sets better when they see, touch and experience them. When you introduce sets in your class, provide opportunities to manipulate and sort groups of objects before progressing to written exercises.
Familiar Territory

Children often collect items such as dolls, rocks or stuffed animals. When you engage them in a discussion about their collections, you lay the groundwork for helping students understand sets. Raise their awareness that all elements of a set must share certain attributes. Ask students whether they belong to any groups or sets. They might say “the human race” or “Mrs. Smith’s thirdgrade class.” Children can physically form sets in the classroom. All the boys wearing red shirts can stand together, or all the girls with blonde hair.
Concrete Objects

Students need to have handson experience forming sets with objects. The teacher can make shapes, such as squares or triangles, from foam or tag board so students can classify and sort them. Include at least three different shapes in three different sizes and colors. Children can work with partners to determine ways to classify the shapes into various sets. They can place a piece of yarn or string around the set of small triangles or the set of red shapes.
Venn Diagrams

Visual representations help students understand how elements of a set are related. Venn diagrams are used to represent sets. When students create Venn diagrams, it helps them organize their thinking. Draw two large, intersecting circles on the board. Tell students who have dogs as pets to write their names on the left circle. Those who have cats should write their names on the rightside circle. Those who have both cats and dogs write their names in the center where the circles intersect. Children can transfer this skill to create their own Venn diagrams to describe sets.
Paper and Pencil

Elementary students should learn how to indicate the bounds of a set with braces. Items inside the braces are members or elements of that set. Start with nonmathematical sets. Children could write the set of fourthgrade teachers: {Mr. Jones, Miss Garcia, Mrs. Taylor}. Next, progress to sets of numbers, such as the set of all prime numbers less than 8: {2, 3, 5, 7}. Ask students why 6 isn’t a member or element of the set. Create a set such as {3, 5, 7, 9} and ask students what it represents. They should recognize that it's the odd numbers between 1 and 10.
The Empty Set

Your students should also understand the meaning of the empty set. The empty or null set has no members. Show students how to represent the empty set with empty braces, { } or a zero with a diagonal line drawn through it, Ø. Examples of the empty set could be all cats with six legs or the set of triangles with five sides. These sets have no members. Children can work with partners to create their own empty sets and then share their results with classmates.