A) WHOLE NUMBERS
OBJECTIVES: know and use the concept of factor,
multiple, common factor, lowest common
multiple, prime and composite numbers
A number may be made by multiplying two or more other numbers together. The numbers that are multiplied together are called factors of the final number. All numbers have a factor of one since one multiplied by any number equals that number. All numbers can be divided by themselves to produce the number one. Therefore, we normally ignore one and the number itself as useful factors.There are several clues to help determine factors.
The number fifteen can be divided into two factors which are three and five.
The number twelve could be divided into two factors which are 6 and 2. Six could be divided into two further factors of 2 and 3. Therefore the factors of twelve are 2, 2, and 3.
If twelve was first divided into the factors 3 and 4, the four could be divided into factors of 2 and 2. Therefore the factors of twelve are still 2, 2, and 3.
Any even number has a factor of two
Any number ending in 5 has a factor of five
Any number above 0 that ends with 0 (such as 10, 30, 1200) has factors of two and five.
To determine factors see if one of the above rules apply (ends in 5, 0 or an even number). If none of the rules apply, there still may be factors of 3 or 7 or some other number.
Divisibility RulesEasily test if one number can be evenly divided by another
"Divisible By" means "when you divide one number by another the result is a whole number"
14 is divisible by 7, because 14÷7 = 2 exactly
But 15 is not divisible by 7, because 15÷7 = 2 1/7 (i.e., the result is not a whole number)
"Divisible by" and "can be evenly divided by" mean the same thing
Multiply and Divide Whole Numbers
The Distributive Property states that when you multiply the sum of two or more addends by a factor, the product is the same as if you multiplied each addend by the factor and then added the partial products. The Distributive Property is illustrated below graphically, arithmetically, and algebraically. At this time, students do not need to know the algebraic explanation of the Distributive Property.
This lesson is foundation for the topic of properties of integer exponents. For the first time in this lesson, students are seeing the use of exponents with negative valued bases. It is important that students explore and understand the importance of parentheses in such cases, just as with rational base values. It may also be the first time that students are seeing the notation (dots and braces) used in this lesson. If students have already mastered the skills in this lesson, it is optional to move forward and begin with Lesson 2 or provide opportunities for students to explore how to rewrite expressions in a different base, 4 2 as 2 4 , for example.
Generate common whole number sequences, including oddand even numbers, prime numbers, multiples, square numbersand cube numbers.
Assessments1.Whole Numbers questions
2.This is worksheet on whole numbers.
4.Paper from columbus high school, (Scientific Notation)