What Is a Set?

A set is a collection of things that are clearly defined. The set of months in a year is a set because nobody argues about it. The set of beautiful flowers is not a set, because beauty is a matter of opinion. I start every sets lesson with that test, and it is also question 6 of this worksheet. If your child can say why "beautiful flowers" fails, the rest of the topic gets much easier.

Finite, Empty, Singleton and Infinite Sets

Sets come in four kinds your child must tell apart. A finite set ends, like the set of vowels in the word "cat". An empty set has nothing in it, written {}. A singleton set has exactly one member, like {0} or {Pakistan}. An infinite set goes on forever, like {1, 2, 3, 4, ...}. In this worksheet your child sorts sets into these kinds, including the set of dragons in a classroom and the set of months with 32 days. I love those two questions because they make children laugh and think at the same time.

What Is Inside This Worksheet?

This is a 5-page printable PDF. Section A has 6 multiple-choice questions on finite, singleton and empty sets. Section B has 8 fill-in-the-blanks questions, including the set of letters in the word MOON, written {M, O, N}. Section C asks students to identify the set type for 8 collections, labelled a to h. Section D matches 7 sets to their types. Section E has 7 short-answer Think and Write questions, including whether {0} is an empty set. Section F has 5 reasoning-based word problems, with the last one marked Challenging Level, including Rayan's birthday list and Omar's toy box.

Key Concepts Covered

• Well-defined collections and what counts as a set
• Finite sets from daily life
• Empty set {} and why {0} is not empty
• Singleton sets with exactly one member
• Infinite sets that never end
• Sorting and describing sets in words

How Students Learn

Students first pick the right set type in multiple-choice questions, then fill in missing words and sort collections themselves. Only after that do they match sets to types and explain their answers in writing, finishing with word problems about birthday lists and toy boxes. I find this order builds the vocabulary first and the reasoning second, which is how sets stick.

Try These Three Yourself

1. Is the set of tall students in your class well-defined? Answer: no, because "tall" is a matter of opinion.
2. Is {0} an empty set? Answer: no, it has one member, 0, so it is a singleton set.
3. Give one finite set and one infinite set from your daily life. Answers will vary; e.g. finite: days of the week; infinite: counting numbers.

Why Parents and Teachers Will Find It Useful

Use this worksheet for a first sets lesson, as homework, for homeschool or one-to-one tutoring, or as a quick check before set notation and Venn diagrams. Because the examples come from birthdays, toy boxes and classrooms, it quickly shows which students grasp the idea of a set and which ones are still guessing. For more Grade 6 worksheets, visit the grade page.