Chapter 3:  Factoring and Prime Numbers  (pg. 184 from teacher resource book)

Big Idea:  Develop an understanding of factors, multiples, divisibility, and other number relationships.

Factors, Multiples, and Divisibility:

Factors, multiples, and divisibility are different points of view on the same relationship.  “Is the number a multiple of 2?”, “Is 2 a factor of the number?”, and  “Is the number divisible by 2?” are all asking the same question in different ways.  In finding factors and multiples students begin to “see” sets of related numbers (such as all the numbers that are divisible by 2) and to recognize relationships among numbers (such as numbers divisible by 2 that are also divisible by 6).  Identifying common multiples of two numbers also sets the stage for later work in computation with factors. 

Students generate lists of the multiples of 2, 5, 10, 3, 6, and 9, and look for patterns in each list.  From these patterns, students determine divisibility rules based on the digits and digit sums.  These rules provide an efficient way to know some of the factors of greater numbers.

Prime and Composite Numbers:

By observing factor pairs, students identify prime and composite numbers.  They discover that every composite number can be written as the product of prime factors.  Whether we factor the number 18 first into 2 X 3 X 3.  Students begin to work with the fundamental idea that all of the non-prime factors of a number result from multiplying some of these “building blocks” together.           

Important Vocabulary:

digit, even, odd, factor, multiple, product, square number, factoring, common factors, common multiples, prime, composite, prime factorization, divisibility, divisible by,