Mathematics 7 Number Sense: Sets and Set Operations:

Mathematics 7 Number Sense: Sets and Set Operations Mr. Gerald DG Banaag Elizabeth Seton School

Essential Questions:

Essential Questions How do we know when an object is intrinsically part of a set or not? Why do we have to consider objects as such? Why do you think the study of the concept of sets important? How is the concept of sets being used in other fields of study? Which is more essential: the learning of the concept of sets or the acquisition of knowledge of the set of real numbers?

What You’ll Learn? :

What You’ll Learn? KWLH Chart Describe and illustrate well-defined sets, subsets, universal set, and null set. Define and describe the union and intersection of sets and the complement of a set. Use Venn diagram to represent sets, subsets, and set operations. Explain the concept of Venn diagram. Create a Venn diagram of elements classified in different sets. Solve problems involving sets.

Self-assessment Questions:

Self-assessment Questions Personality Development Why do we have to consider ourselves as part of a group? Is it possible for someone to be part of more than one group? Is it beneficial to be part of any group? How did you relate the lessons with your personal experiences as a teenager? How do you think these lessons will affect your personality and outlook in life? Learning Process How did you learn the lesson on sets? Which part of the lesson struck you the most? Why?

Exploration:

Exploration Group yourselves according to the photos you have. Make sure that you have a definite description of your group.

Guide Questions:

Guide Questions How many elements do you have in your group? How do you define the cardinal number of a set? Is it possible to have other sets which are smaller/larger than a given set? What do we mean when we say that two or more sets are equal or equivalent? How do you differentiate an equal sets from equivalent sets?

Definition:

Definition The cardinal number of a set A, denoted by n(A), is the number of elements in the set. ex. Given A = {a, e, i , o, u}, then n(A) = ______. Two sets that contain exactly the same number of elements are ____________________. ex. Given A = {1, 2, 3, 4} and B = {a, b, c, d}, we say that A is equivalent to B. In symbols, ___________ Two sets that contain exactly the same elements are said to be _____________________. ex. Given A = {a, b, c, d, e} and B = {e, i , o, u, a}, we say that A is equal to B. In symbols, ___________ 5 equivalent sets A ≈ B equal sets A = B

Dyad activity:

Dyad activity Equal and Equivalent Sets Are the following sets equal? 1. A = {c, a, r} and B = {a, r, c} 2. C = {1, 2, 3, 4, 5, . . . } and D = {5, 10, 15, 20, . . . } Are the following sets equivalent? 1. A = {c, a, r} and B = {a, r, c} 2. C = {m, a, t, h, e, i , c, s} and D = {e, n, g, l, i , s, h}

Exploration:

Exploration May I know what’s inside your bags? Kindly choose five objects from your bag and show them to your seatmate. Do you have the same five objects from your bag? Guide Questions: How do you identify sets contained in another set? How do you classify subsets of a given set that is not the set itself?

Definition:

Definition Set A is a subset of set B, written as A B, if and only if, every element in A is also an element in B. ex. Given A = {2, 4, 6, 8, . . . } and B = {1, 2, 3, 4, 5, . . . }, then ________. Since every element that is in Set A is also contained in Set B. Therefore, we can say that Set A is contained in Set B. A B

Here are ways of describing a set.:

Here are ways of describing a set. The Roster Notation or Listing Method This is a method of describing a set by listing each element of the set inside the symbol { }. In listing the elements of the set, each distinct elements is listed once and the order of the elements does not matter. ex. Colors of the rainbow R = { red, orange, yellow, green, blue, indigo, violet } [List the elements in Exploration # 2]

Here are ways of describing a set.:

Here are ways of describing a set. The Set Builder Notation It is a method that lists the rules that determine whether an object is an element of the set rather than the actual elements. ex. All cities in the Philippines A = {x| x is a city in the Philippines} read as: “A is the set of all x such that x is a city in the Philippines.”

Formative assessment:

Formative assessment Describe the following sets using the specified methods. A. Write a verbal description for each of the following sets: 1. D = {1, 3, 5, 7, . . . } 2. E = {a, b, c, . . . , z} 3. F = {4, 8, 12, 16, . . . , 96} Answer: The set of odd numbers. The set of small letters in the English alphabet. The set of multiples of 4 between 0 and 100.

Formative Assessment:

Formative Assessment Describe the following sets using the specified methods. B. List the elements of the following sets: 1. M = {x |x > 7, x is an odd integer} 2. A = {x |7 < x < 8, x is a counting number} 3. T = {x |x is a city in Metro Manila} 4. H = { x |x is a counting number between 7 and 10 } Answers: M = {9, 11, 13, 15, 17, . . . } A = { } or T = {Manila, Caloocan, Las Piñas , . . . Pasig} H = {8, 9}

Formative assessment:

Formative assessment Describe the following sets using the specified methods. C. Write a rule for the following: 1. S = {a, e, i , o, u} 2. E = {3, 6, 9, . . . , 30} 3. T = { Monday, Tuesday, Wednesday, . . . , Sunday } Answers: S = {x x is a vowel in the English alphabet } E = {x 3 x 30, x is a multiple of 3} T = {x x is a day in week}

Summing up:

Summing up Can you share to the class some new terms you learned today? Which definition struck you the most? If you can share a topic that you learned today to a friend, what would it be? Why?

Homework:

Homework Bring a photo of your favorite actors Define the following: 1. Equal 2. Equivalent 3. cardinality of a set 4. Universal Sets 5. Subsets

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