Activity 4.2: Prime Sieve

A Prime Number Sieve

Purpose: Explore the ideas of prime, composite, and factorizations.

Materials: 10 by 10 grid, 5 colors

We will systematically strike out numbers in the grid below. To do so, we will need 4 different colors. See question 1 for details.

1. We will strike out multiples of a number from the grid above by drawing a colored lines through them.
   Complete the instructions below, filling in each blank with the color of your choice, with a different color for each prime.
   
   
   1. Circle the number 2, then draw a _______ line through every number that is divisible by 2.
   2. Circle the number 3, then draw a _______ line through every number that is divisible by 3.
   3. Circle the number 5, then draw a _______ line through every number that is divisible by 5.
   4. Circle the number 7, then draw a _______ line through every number that is divisible by 7.
2. What was the first number colored by the given prime?
   1. The first number colored by 2 was ________.
      
      
   2. The first number colored by 3 was ________.
      That is, the number wasn't already colored by 2.
      
      
   3. The first number colored by 5 was ________.
      That is, the number wasn't already colored by 2 or 3.
      
      
   4. The first number colored by 7 was ________.
      That is, the number wasn't already colored by 2, 3, or 5.
      
      
3. Are there any numbers that are not struck out, that are divisible by 11? Why?
   
   

Looking Beyond this Grid

4. If the list of numbers continued beyond 100, what would the first number be that 11 got to strike out on it's own?
   That is, the number wasn't already struck out by 2, 3, 5, or 7.
   
   
5. If the list went to 400, what is the last prime number needed to strike out composite numbers? For example, 7 was the last prime number needed to strike out composite numbers less than 100.
   
   
6. What is the last prime number before 400? Guess and check. Show your work.
   
   
7. What is the last prime number before 1200? Guess and check. Show your work.
   
   
8. Make at least three observations about the grid after it is completed.
   1. _
      
      
   2. _
      
      
   3. _