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General Lesson Information
 Lesson Plan ID: 26336 Title: Exploring Prime Numbers Overview/Annotation: Exploring Prime Numbers is a hands-on, minds-on math lesson that engages students in the discovery of prime numbers through the construction of multiplication arrays.  Students then extend on their background knowledge of multiples and their new understanding of prime and composite numbers to complete an Eratosthenes’ Sieve. This lesson plan was created by exemplary Alabama Math Teachers through the AMSTI project.

Associated Standards and Objectives
Content Standard(s):
 MA2015 (4) 3. Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. [4-OA3] MA2015 (5) 12. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally, and assess the reasonableness of answers. [5-NF2] Example: Recognize an incorrect result 2/5 + 1/2 = 3/7 by observing that 3/7 < 1/2.

Local/National Standards:

2009 Alabama Math Course of Study

4.7 Solve problems, including word problems, involving multiplication and division of whole numbers through two-digit multipliers and one-digit divisors.

* Demonstrating computational fluency in multiplication and division facts with products through 144 and quotients with dividends through 144 using horizontal and vertical forms

* Identifying prime and composite numbers through 50

NCTM National Math Standards

Number and Operations Standard for Grades 3-5

Expectations

Instructional programs from prekindergarten through grade 12 should enable all students to-

In grades 3-5 all students should-

Understand numbers, ways of representing numbers, relationships among numbers, and number systems

•describe classes of numbers according to characteristics such as the nature of their factors.

Understand meanings of operations and how they relate to one another

•understand the effects of multiplying and dividing whole numbers;

Reasoning and Proof Standard for Grades 3-5

Instructional programs from prekindergarten through grade 12 should enable all students to-

* recognize reasoning and proof as fundamental aspects of mathematics;

* make and investigate mathematical conjectures; .

Instructional programs from prekindergarten through grade 12 should enable all students to-

* communicate their mathematical thinking coherently and clearly to peers, teachers, and others;

* analyze and evaluate the mathematical thinking and strategies of others;

* use the language of mathematics to express mathematical ideas precisely.

Instructional programs from prekindergarten through grade 12 should enable all students to-

* recognize and use connections among mathematical ideas;

Instructional programs from prekindergarten through grade 12 should enable all students to-

* create and use representations to organize, record, and communicate mathematical ideas;

Primary Learning Objective(s):

The students will be able to identify prime and composite numbers through 50 by constructing multiplication arrays and determining multiples of numbers 2, 3, 5, 7, and 11.

Preparation Information
 Total Duration: 91 to 120 Minutes Materials and Resources: Teacher Materials:Chart paperMarkersSticky notes or index cardsStudent Materials:Circle counters or square tiles (1 bag of 20 for each pair of students)Student math journals or notebook paper (if journals are not used in your classroom)Pencil8 ½ by 11 inch paperScissorsMarkersGraph paper Technology Resources Needed: Computer with Internet connectionLCD Projector Background/Preparation: Teacher Background Information:  A prime number is any natural number with exactly 2 factors, 1 and itself.  Any numbers with three factors or more is a composite number. An Eratosthenes’ Sieve is a method used to filter out prime numbers by eliminating multiples of 2, 3, 5, 7, and 11 on a 100’s chart.    Student Background Information:  In order to teach this lesson successfully, students should have an understanding of the terms multiple, factor, array, and understand how to skip count as a way of multiplying.   Teacher Preparation: Prior to teaching this lesson, place each student with a working partner.  Make sure that each partner pair has at least one student with a firm understanding of the terms multiple, factor, array, and understands how to skip count as a way of multiplying. The partner pairs will be working with counters or square tiles.  Create bags of 20 counters/square tiles for each partner pair.  If possible, make all counters/square tiles the same color to keep students from being distracted by arranging the counters/square tiles by color. Write the following numbers 1-20 (excluding 12) on index cards or sticky notes to distribute during step two.  You will assign pairs of students a number between 1 and 20 by passing out the index cards or sticky notes at the beginning of step two.  Each pair should have a number or two to investigate.  Pairs receiving prime numbers with only one array arrangement will need to get an additional number that is composite.  However, DO NOT make the students aware of the reason for assigning specific numbers. Also, only assign one number to partners receiving a number that will create several arrays, such as 16, and 18.   Create a t-chart labeled “Two Factors or Less” on one side and “More than Two Factors” on the other side.   A sample t-chart is attached.   View the multimedia presentation entitled Prime Numbers Eratosthenes’ Sieve. (attached) Create a sample foldable for Step 5 (see pictures entitled Foldable 1 and Foldable 2)

Procedures/Activities: