Title – Discovering Primes

By – Beth McDonough

Primary Subject – Math

Grade Level – 3-6

Objectives:

Students will list prime numbers most often used.

Students will understand why a number is prime.

Motivation:

Students will practice finding common denominators.

(Multiply two numbers together to find common denominator or use larger number as common denoninator when two numbers are multiples)

Delivery of Instruction:

• Students will write all numbers from 1-100 (10 rows with 10 columns) on a piece of paper or use a 100′s chart.
  Teacher will explain prime numbers. Students and teacher will go through numbers on the chart to determine whether they are prime.

• Students will be instructed to circle 2 and cross off 4, 6, 8 and all other multiples of 2 up to 100.
  
• Students will circle 3 and cross off all multiples of 3.
  
• Students will circle 5 and cross off all multiples of 5. Students will notice some are already crossed off, and the teacher and students will discuss how those numbers are also multiples of 2.

• 6 has been crossed off, 7 has not, so students will be instructed to circle 7 and will ask or be asked why?

• All multiples of 7 should be crossed off, discuss why some numbers are already crossed off (multiples of 5).
  
• At this point, teacher will ask the students what number has not been crossed off. They will circle 11 and check all multiples of 11. Teacher will ask why each has already been crossed off (33, multiple of 3, 22, multiple of two etc.)
  
• Teacher will ask what is the next prime number. 13. Look at multiples of 13 – all have been crossed out already.
  
• Teacher will discuss prime numbers most often used 2, 3, 5, 7, and 11.

Optional:

Teacher will tell students that in a set of 100 numbers, after 10, all numbers that have not been crossed out are either prime or are a mistake. If you had 25 numbers, you would only have to test until 5. Any guesses why? Let me give you more clues. If you had 81 numbers, you would only have to test to 9, for 49 numbers you would only have to go to 7. Any guesses now? (Answer: you only have to test to the square root.) What if you had 50 numbers. It would still be 7 because 7 is the nearest square root.

Closure:

Students will list all prime numbers from 1-100.

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Beth McDonough

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