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. Associate the members of a set with the
properties of that set.
2. Name and list members in the intersection or
union of two sets.3. Draw Venn Diagram to show the intersection or union of two sets.
CONTENT
A set is a group of things that have something in common. Members of a set should be written in curly braces. An empty set contains no members or elements. It is also called a null set. The cardinality of a set refers to the number of elements or members in the set. The ordinality of a set refers to the position or place a certain element/member holds in a set. A Venn diagram is a pictorial representation of sets. We can also see the relationship between different sets in a Venn diagram.
NB The rectangle represents the universal set.
ENGAGE:
Students, you would have remembered the topic Sets from grades 4 and 5. What exactly is a set?
Well you should have the following answer:
It is a group of things that have something in common. We could also say a group of things that are related.
Let's try to create some sets. Remember now that the members of a set should always be written in curly braces. Let's go!
Set P = {mangoes, pineapples, melons, cherries}
1. How could this set be described?
2. How are the elements/members common?
3. How many elements/members are in the set P?
4. What other way could question 3 be asked?
Well if you have answered the questions above correctly, then you deserve a 👍.
Let's see.
1. Set of fruits
2. They are all fruits
3. 4
4. What is the cardinality of the set P?
EXPLORE:
Ok students, I want you to read the scenario below. You are going to need two rubber bands and 6 very small pieces of paper with the following numbers written on them 2,3,4,5,6,8 (one number on each paper) for this activity. Please have them ready.
Romario was given the numbers (2, 3, 4, 5, 6, 8) to place in sets labelled as prime numbers and even numbers. He was given two rubber bands by his teacher, and asked to ensure that all the numbers were used up.
Imagine that you are Romario and use the rubber bands to show the sets.
Well by this time you should have inserted your numbers in the rubber bands as shown below.
(Now students, the section where the 2 is found is called the intersection. The common members of the two sets are placed in this region that overlaps. Therefore, it says that the 2 belongs to both sides/sets). There is a special symbol used for this. ( Ո) It means intersection.
Watch this video clip which explains more about intersection of
sets.
EXPLAIN:
Can you now tell me what a set is?
What is the Venn diagram?
Can you now explain to someone why the numbers were placed in the rubber bands as shown above?
Beautiful! 2 is a prime number and it is also an even number so it was placed where the two rubber bands overlapped. Looking at the rubber bands now you will notice that 4, 6, and 8 are also even numbers but not prime numbers so they are found in the green section. The 3 and 5 are prime numbers but not even numbers so they would be found in the purple section.
EXTEND/ELABORATE:
Read pages 16-17 of Prime Mathematics Book 6 to get more information for note taking.
EVALUATE:
Answer the following questions.
1.
2.
3. Use the diagram below to answer the questions that follow.
4.
(a) What are the members of Set A?
(b) What are the elements of Set B?
(c) 7 forms part of the __________________________ set.
(d) What is A Ո B?
(e) What is A Ս B?
(f) What is the cardinality of Set A?
5.
Consider the two sets below.
Set C = { a, b, d, g, k, y}
Set N = { c, d, k, w}
Draw a Venn diagram to represent the information.
6. Represent the given information on the Venn Diagram below, then answer the questions that follow.
26 Students students study French
18 students study Spanish
28 students study Science
7 students study both French and Spanish
3 students study both Spanish and Science
8 students study both French and Science
2 students study all three subjects
(a) How many students study Science only?
(b) How many students study French only?
(c) How many students study Spanish only?
(d) How many students are in the class altogether?
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