Module-2-Math-2nd-Sem.docx - PBEED008 TEACHING MATH IN THE...

PBEED008
TEACHING MATH IN
THE INTERMEDIATE
GRADE
MODULE 2
NUMBER THEORY
Prepared by:
Lilia D. Antonio, Ph. D.

Instructor
MODULE 2
NUMBER THEORY
Prepared by: Lilia D. Antonio, Ph. D
Introduction
This module introduces the foundation in which the “house of numbers”
called the number theory is built. In times you need to divide or multiply numbers
quickly you can use the divisibility rules. This process can help you easily
identify whether the numbers are exactly divisible by a certain number without
doing the actual division process.
In this module you will study prime and composite numbers, divisibility
rules, greatest common factor and least common multiple as contents of teaching
Mathematics in the intermediate grade which you need to master as a future
elementary school teacher.
You are expected to finish studying this module within two weeks.
Learning Outcomes
At the end of this module, the students are expected to:
1. Differentiate prime and composite numbers;
2. Write a given numbers as a product of its prime factors;
3. Identify the divisibility rules for one- digit numbers and selected two digit
numbers;
4. Find the common factors and the greatest common factor(GCF) of two to
three numbers using the following methods: listing, prime factorization and
continuous division;
5. Find the common multiples and the least common multiple(LCM) of two or
more numbers using the following methods: listing, prime factorization and
continuous division;
6. Solve word problem involving prime and composite numbers;
7. Solve routine and non routine problems involving divisibility rules;
8. Solve real – life problems involving the greatest common factors and least
common multiple of 2-3 given numbers.

TOPIC OUTLINE
1. Prime and composite number
2. Divisibility rules
3. Greatest common factors
4. Least common multiple
A. PRIME AND COMPOSITE NUMBERS
Samuel writes the following numbers on a piece of paper: 48, 57, 37, 91 and 76.
He then asks Dave to identify the number which does not belong to the group. Dave
gives the correct answer. What is his answer?
What do you think is the basis of Dave in identifying the number which is different
from the rest? You consider some possible ways:
1. All five numbers have two digits so it cannot be used as basis.
2. Two of the numbers are even while three are odd, so again, this classification
does not make any one number different.
How about finding all the factors of each number?
48 – 1,2,3,4,6,8,12,16,24,48
57 – 1,3,19,57
37 – 1,37
91 – 1,7,13,91
76 – 1,2,4,19,38,76
Observe that the number 37 has only two factors, 1 and 37 (the number itself)
while each of the rest has other factors aside from 1 and itself.
A number is called Prime if it has only two factors. A few examples of prime
numbers are 2, 13, 29 and 83.
On the other hand, numbers with more than two factors are called Composite.