1. Welcome Back! Use the manipulatives to make the following numbers (rectangles or two rows): 7 12 23 22 Are you here?

2. 7

3. 12

4. Odd, Even If you can make two rows of the same length, then your number is even. If there is one left over after making even rows, then the number is odd.

5. Use the blocks… Show why the sum of two odd numbers is an even number. Show why the sum of two even numbers is an even number. Show why the product of two odd numbers is not even.

6. Prime, Composite If you can only arrange the manipulatives into a rectangle in just one way, then the number is prime. If you can arrange the manipulatives into two or more different rectangles, then the number is composite.

7. More precise definitions: A whole number is prime if and only if it has exactly two distinct factors. A number with more than two factors is called composite.

8. Sieve of Eratosthenes Eratosthenes was born in Cyrene which is now in Libya in North Africa in 276 BC. He died in 194 BC. Eratosthenes made a surprisingly accurate measurement of the circumference of the Earth. He was also fascinated with number theory, and he developed the idea of a sieve to illustrate prime numbers.

9. Sieve of Eratosthenes You will need many different colors. Use one color for each factor. Circle the number “1”. 1 is neither prime nor composite, as we have seen earlier. Now, circle 2. Every multiple of 2 is a composite number, so put a dot of that color next to all of the multiples of 2. Use a new color. Now, circle 3. Every multiple of 3 is a composite number, so put a dot of this new color next to all multiples of 3.

10. Sieve of Eratosthenes Now, 4 has a dot next to it--it is not prime. Skip it and move on. Use a new color. Circle 5, and then put a dot of this new color next to all multiples of 5. Now, 6 has a dot next to it--it is not prime. Skip it and move on. Continue in this manner up to 11. Then, stop.

11. Sieve of Eratosthenes Questions to answer: When you circled 11, were there any multiples of 11 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?

12. Exploration 4.2 First, fill in the table on page 85, using the information on the sieve. It will help if you write them in pairs. For example, for 18: 1, 18; 2, 9; 3, 6. The order does not matter. Next, fill in the table on page 87. Use the table on page 85 to help.

13. Homework Make sure you finish tables from Exploration 4.2 by class on Wednesday Play factor game on internet 5 times (see details on assignments page) Section 4.1: p. 229: 1, 2, 4. Section 4.2: p. 239 – 241: 3beg, 7, 10, 13, 16b, 18