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Math Foundations

You will discover prime numbers by drawing rectangles with different side lengths but same area.

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After completing this tutorial, you will be able to complete the following:

- Find factor pairs of numbers through 30.
- Discover prime numbers by drawing rectangles with different side lengths but same area.
- Identify prime numbers from a given list of whole numbers.
- Describe prime numbers and composite numbers.
- Use the Sieve of Eratosthenes to identify prime numbers.

Prime numbers are whole numbers which have exactly two factors: one and itself, such as 2, 3, 5, 7, and 11.

In this Activity Object, students will discover prime numbers by drawing rectangles with different side lengths but same area. In Section 1, students will draw rectangles to determine the factor pairs of numbers through 30. Special Numbers are identified when only one rectangle can be formed.

Students will have repeated practice during this Activity Object to reinforce multiples and factors. Beginning with a prime number, such as two, students are reminded of their two's multiplication facts and learn quickly that any even number can be factored by two. Likewise, any number multiplied by two is not a prime number. Because only one and two divide the number two, two is defined as prime. This definition is reinforced throughout the Activity Object as students quickly learn by trial and error that the factors of a prime number are one and itself.

Eratosthenes was a famous Greek mathematician.

Eratosthenes was a famous Greek mathematician who was specifically well-known for his work determining prime numbers. The tool he created, the Sieve of Eratosthenes, is particularly useful in number theory still today.

The Sieve of Eratosthenes can be used to determine prime numbers.

In Section 3, the Sieve of Eratosthenes is introduced as a method for finding all prime numbers up to a specified integer. The Sieve of Eratosthenes is a simple, ancient algorithm for finding all prime numbers up to a specified integer, in which composite numbers are "drained out" and leaves prime numbers behind. To use the Sieve, circle the first number, 2. Then, cross off all multiples of 2. Then, circle the next number, 3, and cross off all the multiples of 3. This process is repeated until all multiples and been crossed off and the remaining circled numbers are left as the prime numbers.

The following key vocabulary terms will be used throughout this Activity Object:

algorithm - a step-by-step method for computing or carrying out mathematical procedures

area - The number of square units that cover a surface enclosed by a geometric figure.

composite number - a whole number which has more than two factors; all composite numbers are the product of prime numbers

factor - a factor of a number will divide that number exactly, without any remainder

factor pair - two factors, which result in a given product; for example, 2 × 3 is a factor pair of 6

multiple - a multiple of a number is the product of that number and another number

· prime number - a whole number which has exactly two factors: one and itself (1 is neither prime nor composite).

· rectangle - a quadrilateral with two pairs of congruent, parallel sides and four 90 degree angles

· Sieve of Eratosthenes - a simple, ancient algorithm for finding all prime numbers up to a specified integer, in which composite numbers are "drained out" and leaves prime numbers behind

· whole number - any of the numbers 0, 1, 2, 3, etc.

Approximate Time | 25 Minutes |

Pre-requisite Concepts | Students should be familiar with factors, multiples, and prime numbers. |

Course | Math Foundations |

Type of Tutorial | Concept Development |

Key Vocabulary | special number, prime number, rectangle |