SETS/FINITE & INFINITE

FINITE AND INFINITE SETS

FOCUS QUESTION

What are the special symbols and language I use when I work with sets?

SPECIFIC OBJ. By the end of the lesson, students should be able to:

1. Identify members of finite and infinite.

CONTENT SUMMARY

ENGAGE

Students let's do some revision.

What do we call the elements of a set?

Let's consider the sets below:

EXAMPLE 1

What are the elements of  Set A? List them {                                                }

What are the elements of Set B? List them {                                                 }

What is A U B? Can you still list the members? {                                    }

What is A Ո B? Can you still list the members?  {                }

What is the cardinality of each set?

Now consider the sets below.

EXAMPLE 2

Set Y = {prime numbers between 0 and 10}

Set M= {counting numbers greater that 20}

Can you list all the elements/members of each set?

Which are you able to list?

EXPLORE

Well I hope you were able to answer the questions correctly. In a moment you will find out if you were correct.

If you remember when we did the first lesson on sets, you will recall that the cardinality of a set refers to the number of elements/members of the particular set.

Therefore, if all the members of the set were able to be listed, then we say that set is a FINITE SET.

On the other hand, if you are not able to list all the members/elements of the set, then that set is called an INFINITE SET.

Now look back at the sets above and identify which are finite and which are not.

👍👋 for your correct answers.

In example  1,  Both Sets A and B are finite

In example 2,   Only Set Y is finite. Set M is infinite as it is not possible to list all counting numbers.

EXPLAIN

Explain the difference between finite and infinite sets and write one example of each type.

EXTEND/ELABORATE

You can watch this video to glean more information.

Read pages 13-14 of Prime Mathematics Book 6 to glean further information on finite and infinite sets.

Complete the activities that follow.

EVALUATION

(1)

1.      David was given the table below, and asked to complete same with a ü in the appropriate column. He ticked as shown below.

STATEMENTS	FINITE	INFINITE
List of all prime numbers		ü
Even numbers between 20 and 500		ü
Set R {all squared numbers}		ü

i  Do you believe David was correct?    YES    NO

ii Justify your reason for the answer you chose.

2.      (2) Junior was asked to write an example of an infinite set. He wrote the following.

Set C {1, 2, 3, ……..9} David on the other hand, wrote the following to represent an infinite set:

Set B { 2, 4, 6, 8, 10, ……}

i  Who was correct?

ii Justify your answer for the question above.

3.       (3) List the members of the sets below then state if they are finite or infinite.

(a)    Set R { vowels} -----------------------                               (c) Set O { consonants in alphabet

(b)   Set P { counting numbers} _______                                (d) Set M {Months of the year}

FOLLOW UP PRACTICE EXERCISES

ACTIVITY 1

ACTIVITY 2

ACTIVITY 3

ACTIVITY 4

ACTIVITY 5

ACTIVITY 6

ACTIVITY 7

ACTIVITY8

Grade Level: 6

Topic: Sets – Finite and Infinite

Duration: 1 hour

Focus Question: “What are the special symbols and language I use when I work with sets?”

Objective:

• Students will identify members of a set as finite and infinite.

---

Materials:

Projector

Chromebooks

Teacher's blogsite

Model Lesson Plan

Engage (5–7 minutes)

Activity:

• Show two jars:

  1. Jar A with 10 marbles.

  2. Jar B labeled “Jar of Stars in the Sky.”

• Ask:

  “Can we count all the marbles in Jar A?”
  “Can we count all the stars in the sky?”

• Ask students to predict what makes one countable and the other not.

Purpose: To spark curiosity and activate prior knowledge about countable and uncountable items.

---

Explore (10 minutes)

Activity:

• Divide students into groups of 3. Give each group a Set Sorting STEM Task:

  • Sort the following into Finite and Infinite sets:
    A. Set of natural numbers
    B. Set of letters in the alphabet
    C. Set of stars in the universe
    D. Set of students in class
    E. Set of even numbers
    F. Set of days in a year

STEM Link:

• Groups briefly research (via tablet/text) why some sets are infinite (e.g., natural numbers never end due to patterns in number systems—linked to algorithms in computing or astronomy for stars).

Output: Each group writes their sorted sets on a mini whiteboard.

---

Explain (10–12 minutes)

Teacher Input:

• Define:

  • Finite Set: A set with countable or limited elements (e.g., {2, 4, 6})

  • Infinite Set: A set with unending elements (e.g., {1, 2, 3, ...})

• Discuss symbols and language:

  • { } to list elements

  • ... for continuing/infinite sets

  • ∈ (element of), ∉ (not an element of)

  • Example: 7 ∈ {1, 2, 3, 4, 5, 6, 7}

Visual Aid:

• Use a chart comparing finite and infinite sets with examples.

---

Elaborate (15–18 minutes)

Differentiated Task (Choice Board - Pick 1):
Students choose 1 activity based on their learning preference:

Visual Learners	Logical Learners	Kinesthetic Learners
Create a poster comparing finite vs infinite sets using symbols and diagrams.	Complete a worksheet with open-ended and true/false questions about set types, including justification.	Build physical sets using math manipulatives (beans, counters) to represent finite and infinite groups.

Peer Share:
Each group presents their work in 1–2 minutes.

---

Evaluate (10 minutes)

Three-Tier Evaluation Task:

Tier 1 – Basic (Below Mastery)	Tier 2 – Proficient (At Mastery)	Tier 3 – Advanced (Above Mastery)
Identify which of the following sets are finite: {1, 3, 5, 7}, {days of the week}, {natural numbers}	Explain why some sets are infinite and some are finite. Give at least two examples of each.	Write a paragraph using set notation and symbols to describe one finite and one infinite set in a real-world STEM context (e.g., computing, astronomy).

---

STEM Integration

• Science: Discuss how the concept of infinity is applied in astronomy (e.g., stars, galaxies).

• Technology: Relate to data structures—some programs use loops over infinite/finite sets.

• Engineering: Sorting components into countable and uncountable bins (used in factories).

• Math: Use of symbols, notation, and logical reasoning.

---

Differentiation Strategies

• Content: Tiered tasks, vocabulary support.

• Process: Choice board activities, group tasks, whiteboards.

• Product: Varied ways to show understanding—written, oral, visual, physical models.

1

H