# The Sieve of Eratosthenes Complete Lesson

Created ByRoom to Discover

Resource Type

Format

PDF (9 MB|15 pages)

Standards

CCSS6.NS.B.4

CCSS5.OA.B.3

CCSS4.OA.B.4

CCSS3.OA.C.7

CCSS3.OA.B.5

### Description

This activity will have your students looking at multiplication in a whole new way. It’s an “open task,” meaning that each student will learn something unique.

For some, the sieve is a way to master times tables. For others, it will help with common denominators or factoring expressions. The sieve also highlights patterns that can improve mental math with all four operations.

The lesson includes an introduction, lesson plans, two handouts with keys, and a rubric.

Total Pages

15 pages

Answer Key

Included with rubric

Teaching Duration

90 minutes

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### Standards

to see state-specific standards (only available in the US).

CCSS6.NS.B.4

Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2).

CCSS5.OA.B.3

Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.

CCSS4.OA.B.4

Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite.

CCSS3.OA.C.7

Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

CCSS3.OA.B.5

Apply properties of operations as strategies to multiply and divide. Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)