Prime and Composite — Sieve of Eratosthenes

Primes are the atoms of multiplication. Eratosthenes, 3rd century BCE, found the primes by sieving. The sieve is the control — every composite gets crossed. Indirect aim: number theory, prime factorization, preparation for algebra.

• Framework: Montessori
• Unit: Sensorial
• Learning area: Algebraic Sensorial
• Level: Ages 8-10

Objectives

• Distinguish prime from composite numbers
• Execute the Sieve of Eratosthenes for primes up to 100
• Factor composite numbers
• Recognize 1 as neither prime nor composite

Materials

• Hundred chart grid
• Colored pencils
• Multiplication chart for verification
• Eratosthenes story card

Instructions

1. Tell Eratosthenes's story. 2. Lay hundred chart 1-100. 3. Cross out 1 (not prime). 4. Circle 2; cross all multiples of 2. 5. Circle 3; cross all multiples of 3. 6. Continue: 5, 7, 11. 7. Remaining circled = primes. 8. List the 25 primes ≤ 100.

Educator tip

The sieve is visual and beautiful. Let children see the pattern.

Assessment

Observe correct sieve execution and prime identification.

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