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.