Make a list with your group How can I remember??? Factor Multiple Are you here?

Factors and Multiples--using manipulatives One way to visualize factors and multiples is to make rectangles or rectangular arrays. In a rectangle, the length times the width is equal to the area. So, the sides are the factors and the area is a multiple. How many different rectangles can you make using 24 chips? Be systematic.

Factors of 24--How do we know when we have them all? 1 • 24 2 • 12 3 • 8 4 • 6

You try: 36 1 • 36 2 • 18 3 • 12 4 • 9 6 • 6

Sieve of Eratosthenes In pairs answer the following questions: When you circled 11, were there any multiples of 11 smaller than 100 that did not already have dots next to them? Can you explain to a child why this was true? What does this have to do with factors and multiples? What are the prime numbers that are between 1 and 100? Is 1 a prime number?

Exploration 4.2 How was the sieve helpful for filling in the table on page 85? How did you use your table on page 85 to fill in the table on page 87?

Exploration 4.2 In pairs, examine your work from the Sieve of Eratothsenes, and from the table on pages 85 and 87. In pairs, complete 3a, 3c, 3d, 3e, and 3f. This will be turned in next Wednesday (include the two tables and sieve – including your answers to the questions about the sieve.)

Factor Game Let’s play the factor game. Player 1 picks a number from 1 - 30, and gets that many points. However, there must be an available factor for that number. So no primes. If you pick a number with no available factors, you lose your turn, and get no points. Player 2 then selects as many factors as possible for that number, and scores the sum of those factors. Roles switch, and play continues.

More on Factors Question: If 5 is a factor of 35, what are all of the factors of 35? If 7 is a factor of 105, what are all of the factors of 105? What is the smallest factor that 35 and 105 share? What is the largest?

Exploration 4.3 Let’s list all the factors of 36. Use the beans to help you. Make sure you don’t miss any! Let’s list all the factors of 72. Can you use the work you did for 36 to help you? True or false? 72 is a factor of 36. Explain your answer.

Let’s write the prime factorization of 36: 22 • 32 There’s more than one way! 36 36 36 2 • 18 3 • 12 4 • 9 2 • 9 2 • 6 2 • 2 3 • 3 3 • 3 2 • 3

22 • 32 = 2 • 2 • 3 • 3 Use this to make an organized list of factors: 1 • 36; 2 • ____ 3 • ____ 4 (2•2) • ____ 6 (2•3) • ____ 9 (3•3) • ____ 12 (2•2•3) • ____ 18 (2•3•3) • ____ Notice the duplication.

Prime factorization for 72 = 23 • 32 How can you make sure you get every factor? 1, 2, 4, 8, 3, 9, 6, 12, 24, 18, 36, 72 Try this one: 60 = 22 • 3 • 5 1, 2, 4, 3, 5, 6, 10, 15, 12, 20, 60 Try this one: 48 = 24 • 3 1, 2, 4, 8, 16, 3, 6, 12, 24, 48