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The Sieve of Eratosthenes

Jenn Bohler
5th Grade
Dearing Elementary School
McDuffie County Schools

Contents

Task
Overview
In this task, students will identify prime numbers up to 100 using the Sieve of Eratosthenes.

Illustrative Task
Use a hundreds board to complete the following:
  1. Cross out the number 1, because it is not a prime number.
  2. Circle the number 2 with yellow, because it is the smallest prime number. Cross out every multiple of 2 with yellow.
    How do you know which numbers to cross out? Write an algebraic expression for the numbers you crossed out with yellow.
  3. Circle the number 3 with blue. This is the next prime number. Now, cross out every multiple of 3 with blue.
    What do you notice about the number 6? What do you think it means when a number is crossed out with two colors – in this case yellow and blue?
  4. Circle the next open number, 5 with red. Cross out all multiples of 5 with red.
    Write an algebraic expression for the numbers you crossed out in red.
  5. Circle the next open number with orange. Cross out all multiples of 7 with orange.
  6. Continue doing this until all the numbers through 100 have either been circled or crossed out.
  7. Which numbers are circled? What do you notice about these numbers?
  8. Write a short paragraph about your findings and conclusions.

GPS Addressed
M5N1. Students will further develop their understanding of whole numbers.

M5N4. Students will continue to develop their understanding of the meaning of common fractions and will compute with them.

M5A1. Students will represent and interpret the relationships between quantities algebraically.

Video Information
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Use these questions to guide your thinking about some of the important teacher ideas in the lesson featured in the video clip.
  1. What kinds of questions does the teacher ask to promote students’ problem solving?
  2. How is the teacher gauging students’ current understandings and building from those understandings?
  3. Consider the GPS standards listed with this video.
  4. What makes this lesson different from lessons you have taught on this topic?

Classroom Materials

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