Lesson+B



Individual Work 1-2 Days  Content Standard: M6N1. Students will understand the meaning of the four arithmetic operations as related to positive rational numbers and will use these concepts to solve problems. a. Apply factors and multiples. b. Decompose numbers into their prime factorization. c. Determine the greatest common factor and the least common multiple for a set of numbers. Objectives: Students should be able to find all the factors of a number by constructing or drawing arrays. Students should be able to list all the factors of any given number and discuss how they know that the number is prime, composite, or neither. Students should be able to determine the greatest common factor of two or more numbers and offer situations in which it would be useful to know common and greatest common factors of two or more numbers. Activity 2:

Part I: Arrays, Factors, and Number Theory

Create, draw or shade all possible arrays for the numbers 1-20.Label all of the dimensions of the arrays, which are the factors of each number. Look for patterns in the arrangements, factors, or drawings. Describe the patterns or observations that help you "see" the factors, prime numbers, composite numbers and square numbers. In the numbers 1-20, label the prime, composite, and square numbers. Describe all the things you notice about the arrays and patterns, but especially discuss what you notice about the number 1.
 * Part II: **

1. Using your previous work from **Arrays, Factors and Number Theory, **list all the factors in order from least to greatest, for each number 1-20. 2. Choose any two numbers from your list of 1-20. What factors are in both lists? 3. What is the largest factor that they have in common? 4. Try this on several other pairs of numbers from 1-20. 5. Can you do it for 3 of the numbers? Try it for 3 numbers. 6. When would it be useful to know the common factors or the greatest common factor of two or more numbers? 7. What advice would you offer to a friend who was having trouble finding all the factors of any number?

Resources: Blank Paper