## Chapter 1: Sets

**BIG IDEAS**

You can form, describe, and compare collections of objects such as numbers by means of sets.

**CHAPTER OVERVIEW**

This chapter deals with sets and operations involving sets. Lesson 1 begins with the notion of a set and its representations. The lesson defines and illustrates equal sets, finite sets, equivalent sets, empty sets, universal sets, and subsets. Lesson 2, on the other hand, tackles set operations such as union and intersection and representing them through Venn diagrams. Other operations such as complement of a set and set difference are also discussed.

**DESIRED RESULTS**

**Content Standards**

The learner demonstrates understanding of the key concepts on sets.

**Performance Standard/s**

The learner is able to formulate challenging situations involving sets and solve these in a variety of strategies.

**CHAPTER OBJECTIVES**

At the end of the chapter, the students should be able to . . .

• describe, represent, and illustrate sets;

• define and illustrate equal sets, equivalent sets, finite sets, universal sets, empty sets, and subset and proper subset of a set;

• perform operations on sets;

• use Venn diagrams to represent set relations and operations; and

• solve problems involving sets.

• describe, represent, and illustrate sets;

• define and illustrate equal sets, equivalent sets, finite sets, universal sets, empty sets, and subset and proper subset of a set;

• perform operations on sets;

• use Venn diagrams to represent set relations and operations; and

• solve problems involving sets.

**PERFORMANCE TASKS**

Create examples found in everyday living that illustrate set relations and operations: universal set, empty set, subset of a set, complement of a set, union of sets, intersection of sets, and set difference.

**HOW TO INTRODUCE THE CHAPTER**

1. Assess students’ prior knowledge about the concepts on sets. Proceed by writing the names of the days of the week on the board and enclosing them in a circle. Ask: What can you say about the names inside the circle? What characteristic do they have in common? Let the students fill in the blank in the sentence: It is the collection of ______. Then ask: Can you give one object that does not belong to the collection? Have you had prior ideas about sets? If so, have them state a word or two that you can associate with the given set. Have them cite things that they encounter in their everyday life.

2. Ask: Why do you think it is useful to collect or group objects that share a common property? Let the students write their answers on a sheet of paper. Discuss their answers in class.

3. Tell the students the topics that they will learn in chapter 1.

4. Discuss with the students the performance task for the chapter. Discuss with them the rubric for assessment of the performance task. (Please see Culmination/Transfer on pages 9 and 10 of this TLG.)

2. Ask: Why do you think it is useful to collect or group objects that share a common property? Let the students write their answers on a sheet of paper. Discuss their answers in class.

3. Tell the students the topics that they will learn in chapter 1.

4. Discuss with the students the performance task for the chapter. Discuss with them the rubric for assessment of the performance task. (Please see Culmination/Transfer on pages 9 and 10 of this TLG.)