SETS - EQUAL and EQUIVALENT

FOCUS QUESTION:

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

SPECIFIC OBJ.

Associate the members of a set with the properties of that set.

(Distinguish between equivalent and equal sets).

CONTENT SUMMARY

＝       Equal

≠        Not Equal

↔️       Is Equivalent

↮        Not Equivalent

ENGAGE 

Students, I want you to think about two words: EQUAL and EQUIVALENT. What is the meaning of the two words? They are both used to describe sets.

Ok I want you to use your dictionaries to help you.

Let's use the definition from the internet now. Can we read together?

                                 

equivalent

/ɪˈkwɪv(ə)l(ə)nt/

See definitions in:

all

mathematics

chemistry

adjective

adjective: equivalent

1. equal in value, amount, function, meaning, etc.

   "one unit is equivalent to one glass of wine"

   h

   Similar:

   equal

   identical

   similar

   parallel

   analogous

   comparable

   corresponding

   correspondent

   interchangeable

   like

   commensurate with

   the same as

   synonymous with

   much the same as

   amounting

   tantamount

   approximate

   near

   close

   of a kind

   of a piece

   coequal

   h

   Opposite:

   different

   dissimilar

   • having the same or a similar effect as.

     "some regulations are equivalent to censorship"
   • Mathematics

     belonging to the same equivalence class.

noun

noun: equivalent; plural noun: equivalents; noun: equivalent weight; plural noun: equivalent weights

1. 1.

   a person or thing that is equal to or corresponds with another in value, amount, function, meaning, etc.

   "the French equivalent of the Bank of England"

   h

   Similar:

   counterpart

   parallel

   alternative

   match

   complement

equal

/ˈiːkw(ə)l/

adjective

adjective: equal

1. 1.

   being the same in quantity, size, degree, or value.

   "add equal amounts of water and flour"

   h

   Similar:

   identical

   uniform

   alike

   like

   the same

   one and the same

Now would you say the two words mean the same?

Lets relate these words to sets. Give me your understanding of the two terms.

EXPLORE

Now I want you to examine the video clip below.

Look at this video clip. 

Let's do some re-cap now. Read the notes below.

EXPLAIN

Now you should be able to differentiate between EQUAL SETS and EQUIVALENT SETS.

Can you now provide examples of each type?

Write the symbols that represent the following.

 equal -----

 not equal _____

 equivalent ______

 not equivalent ____

EXTEND/ELABORATE

You can watch this video clip to glean more information.

EVALUATION

Task # 1

Indicate if the sets below are equal or equivalent.

1. Set A { vowels}

    Set B {a, e, i, o, u}

2. Set R { factors of 8}

    Set M { 1, 2, 4,}

3. Set C {Prime factors of 10}

    Set W {2, 5}

4. Set F { r, p, j, q}

    Set U {5, 9, 7}

5. Set O {odd numbers less than 10}

    Set L  {first 5 counting numbers}

Task #2

Write 3 examples of equivalent sets and 3 examples of equal sets below.

FOLLOW UP PRACTICE EXERCISES

ACTIVITY 1

ACTIVITY 2

ACTIVITY 3

ACTIVITY 4

ACTIVITY 5

ACTIVITY

ACTIVITY

ACTIVITY

ACTIVITY

Lesson Title: Understanding Equivalent and Inequivalent Sets

Grade Level: 6
Duration: 1 Hour
Strand: Sets
Focus Question: What are the special symbols and language I use when I work with sets?
Objectives:

1. Associate the members of a set with the properties of that set.

2. Distinguish between equivalent and equal sets.

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🌟 5E Lesson Model Plan

1. Engage (5-7 minutes)

Activity: "Mystery Bag Challenge"

• Teacher presents two "mystery bags" (physical or virtual) each with 4 random classroom objects.

• Students describe the objects and determine whether the bags have the same number of items and/or same items.

• Use this to introduce the terms:

  • Equivalent Sets: Same number of elements.

  • Equal Sets: Same number and identical elements.

❓ Ask: “How can we describe sets that have the same number of items but not the same items?”
🔤 Highlight key vocabulary: Set, element, cardinality, equivalent (∼), equal (=), inequivalent

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2. Explore (10-15 minutes)

Activity: “Set Sorting STEM Task”

• In small groups, students are given a mix of image cards or objects related to STEM themes (e.g., types of energy sources, simple machines, planets, geometric shapes).

• Students group them into sets based on criteria (e.g., color, type, shape, use).

• Then they compare sets:

  • Count elements in each set.

  • Use symbols to label:
    A ∼ B (equivalent), A = B (equal), A ≁ B (inequivalent)

Materials: Printed cards or virtual slides with items, Venn diagrams, Set symbol posters.

🧠 Observation: Which sets are equivalent? Which are equal? Which are neither?

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3. Explain (10 minutes)

Mini-Lesson + Notes:

• Define:

  • Set: A collection of distinct objects.

  • Equivalent sets: Sets with the same number of elements. (Symbol: ∼)

  • Equal sets: Sets with the same elements. (Symbol: =)

  • Inequivalent sets: Sets with different numbers of elements. (Symbol: ≁)

• Use examples from previous activity.

• Highlight symbols and language used with sets.

💡 Write on board:
Set A = {1, 2, 3}, Set B = {a, b, c}, Set C = {1, 2, 3}
➤ A ∼ B, A = C

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4. Elaborate (15 minutes)

Activity: “Set Scenarios - Real-World STEM”

• Students complete a worksheet with scenarios (see examples below).

• For each pair of sets, students must:

  1. List the elements.

  2. Determine whether the sets are equal, equivalent, or inequivalent.

  3. Justify with a sentence using appropriate language/symbols.

Example Scenarios:

• Set A: planets in the solar system | Set B: days of the week

• Set C: types of energy (solar, wind, thermal) | Set D: {wind, solar, thermal}

🧠 Extension/Challenge: Students create their own sets from a STEM topic (e.g., animals with vertebrae vs. invertebrates) and compare them.

Differentiated Support:

• Tier 1: Use concrete objects or drawings.

• Tier 2: Provide sentence starters and vocabulary support.

• Tier 3: Students create and compare abstract sets independently.

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5. Evaluate (10 minutes)

Three-Tier Evaluation Task

Tier	Activity	Focus
Tier 1	Match sets with symbols: ∼, =, ≁	Recall and identification
Tier 2	Complete chart with sets and explain the relationship (equivalent, equal, inequivalent)	Understanding and explanation
Tier 3	Create 2 original sets: one that is equivalent but not equal, and one that is inequivalent; justify each	Application and analysis

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🌱 STEM Integration

• Sets drawn from Science (e.g., organs, planets, types of energy), Technology (e.g., devices, apps), Engineering (e.g., simple machines), and Math (e.g., types of angles, polygons).

• Students are encouraged to apply logical reasoning, categorize, and model their thinking using set notation.

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✏️ Materials Needed:

• Mystery bag items or cards

• Worksheets/slides

• Markers, chart paper, or digital whiteboard

• STEM-themed item cards or images

• Vocabulary posters with symbols: =, ∼, ≁

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🔁 Wrap-Up (2-3 minutes)

• Recap focus question:
  “What are the special symbols and language I use when I work with sets?”

• Ask for quick oral examples: “Give me two sets that are equivalent.”

• Share one new thing they learned today.

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.

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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.

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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.

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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.

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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.

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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).

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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.

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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

SETS/ DISJOINT

DISJOINT SETS

FOCUS QUESTION: 

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

 

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

1.  Name and list members in the intersection or union of two sets.

2.   Define “disjoint sets”.

 CONTENT SUMMARY

In other words, the two sets have no common elements/members.

ENGAGE

Students  I want you to examine the Venn diagrams below, then tell me what is the difference between the two representations of Sets A and B.

Why was there an overlap in the first Venn diagram?

Why was there no overlap in the second Venn diagram?

EXPLORE

Well by now you should have realized that the first  two sets had "a" and "b" as common elements and so there was an overlap of the two circles to show the elements common to both sets.

On the other hand, the second Venn diagram depicted two separate circles because the elements or members of the two sets A and B had no common elements.

Now this type of set is referred to as a  DISJOINT SET.

You can watch this video clip to glean more information.

EXPLAIN

Now can you explain what a disjoint set is?

EXTEND

Write a scenario that would be represented by disjoint sets.

EVALUATION

1. Examine the diagram below carefully, then answer the question that follows:

Which of the following represents the Venn diagram above?

(a) U= {1, 2, 3, 4, 5, 6, 7, 8, 9}

      A={1, 2, 5, 6}

      B={3, 9}

(b) U=(4, 7, 8}

      A={1, 2, 6, 5, 8}

      B={3,4,9}

(c) U={ 7, 8, 9}

      A={1, 2, 3, 4, 5, 6, 7, 8, 9}

      B={3,  4, 7, 8}

2. Consider the sets below:

    M={odd numbers between 0 and 10}

    V= {prime numbers between 1 and 12}

                      and

    J= {1, 4, 6, 13}

   K= {2, 5, 7, 10}

Draw the two Venn diagrams to represent the sets. Which is the example of a disjoint set?

Follow up Practice Exercises

Activity 1

Activity 2

Activity 3

Activity 4

Activity 5

Activity 4

🧠 Lesson Overview

• Grade: 6

• Subject: Mathematics

• Theme: Disjoint Sets

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

• Duration: 1 hour

• Objectives:

  1. Name and list members in the intersection or union of two sets.

  2. Define “disjoint sets.”

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🔎 5E Lesson Plan

1. Engage (10 minutes)

Activity: Set Sort and Compare

• Present students with two different bags (real or virtual) containing labeled cards:

  • Bag A: {apple, banana, orange}

  • Bag B: {carrot, potato, cabbage}

• Ask:

  • What do you notice about the items in both bags?

  • Are there any items that appear in both bags?

• Guide students to conclude there are no common elements → lead into the concept of disjoint sets.

STEM Integration: Technology — Use an online Venn diagram simulator (e.g., mathisfun.com) to drag and drop items interactively.

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2. Explore (10 minutes)

Activity: Hands-On Set Building

• In small groups, students receive two sets of cards with mixed elements (numbers, letters, or objects).

• Task:

  • Create two sets that intersect (e.g., Set X: {1, 2, 3}, Set Y: {3, 4, 5})

  • Then create two disjoint sets (e.g., Set A: {a, b}, Set B: {x, y})

• Students draw Venn diagrams to represent these relationships.

Differentiation:

• Tier 1: Teacher support with word cards and visual cues.

• Tier 2: Moderate scaffolding with guiding questions.

• Tier 3: Independent creation of set examples with symbols.

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3. Explain (15 minutes)

Mini-lesson:

• Define:

  • Set: a group of objects/elements.

  • Union (∪): all elements from both sets.

  • Intersection (∩): common elements.

  • Disjoint sets: sets with no elements in common.

• Introduce symbols:

  • ∩ = intersection

  • ∪ = union

  • ∅ = empty set

• Use board/visual to show:

  • Set A = {1, 2, 3}, Set B = {4, 5, 6}

  • A ∩ B = ∅ → Disjoint Sets

• Guide students in recording definitions and drawing examples.

STEM Integration: Math Language + Logical Thinking (Computational Science: Classifying/Grouping Data Sets)

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4. Elaborate (15 minutes)

Activity: STEM Challenge – Sorting Data

• Scenario: Students are software designers building a filter for a streaming platform. They must:

  • Create two sets of user preferences (e.g., Set A: {Action, Sci-Fi}, Set B: {Romance, Drama})

  • Determine if the sets overlap or are disjoint.

  • Represent them using Venn diagrams and write:

    • A ∩ B = ?

    • A ∪ B = ?

Differentiation:

• Visual learners: Use color-coded diagrams.

• Kinesthetic learners: Use set circles with physical cut-out images.

• Advanced learners: Add a third set and analyze.

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5. Evaluate (10 minutes)

Three-Tier Evaluation Activity:

Tier	Activity	Evaluation Focus
1	Match sets using cut-outs or visuals to identify if they are disjoint, overlapping, or equal	Recognize disjoint sets visually
2	Given Set A and Set B, write A ∪ B and A ∩ B. Indicate if the sets are disjoint	Apply union and intersection correctly
3	Write a real-life example of disjoint sets (e.g., types of animals vs. types of vehicles) and represent it with a labeled Venn diagram	Apply understanding to real-world context

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✍️ Summary / Exit Ticket (Wrap-up)

• Ask: “What does it mean if two sets are disjoint?”

• Students write their own sentence using the word disjoint and draw a quick Venn diagram of disjoint sets.

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📚 Materials & Resources:

• Venn diagram chart

• Cut-out set items (images or words)

• Markers, chart paper, or interactive whiteboard

• Tablets/laptops (if available) for online Venn simulation

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