TEKS Lesson Plan/Unit Plan



Focus Plan

Texarkana Independent School District

|Grading Period: |Refer to Scope and Sequence |Plan Code: | |

|Writer: |Barbara Fugitt |Course/subject: |Math |

|Grade(s): |Fifth Grade |Time allotted for instruction: |2 or 3 - 45 minute class periods |

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|Title: |Prime or Composite, That is the Question? |

|Lesson Topic: |Understanding the difference between a prime and composite number and their factorizations. |

| | |

|TAKS Objective: |Objective 2 |

| |The students will demonstrate an understanding of |

| |patterns, relationships, and algebraic reasoning. |

|FoCUS TEKS and Student Expectation: |5.5 Patterns, Relationships, and Algebraic Reasoning |

| |The student makes generalizations based on observed patterns and relationships. |

| | |

| |(B) The student is expected to identify prime and composite numbers using concrete models and |

| |patterns in factor pairs. |

| | |

|Supporting TEKS and Student Expectations: |5.3 Number, operation, and quantitative reasoning. |

| |The student adds, subtracts, multiplies, and divides to solve |

| |meaningful problems. |

| | |

| |The student is expected to identify prime factors of a |

| |whole number and common factors of a set of whole numbers. |

| | |

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|Concepts |Enduring Understandings/Generalizations/Principles |

| |The student will understand that |

|Composite |Numbers that have more than two factors. Example: 6 is a composite number since its factors are 1, 2, |

| |3, and 6. |

|Prime |Numbers that have only two factors, 1 and the number itself. Example: 2, 3, 5, 7, 11, 13, 17, 19, 23,|

| |29, 31 |

|Square Numbers |A product that can be shown in a square array or model; a product of two equal numbers. Examples: 2 x|

| |2 = 4; 3 x 3 = 9; 4 x 4 = 16 |

|Generalize |To draw a general conclusion. |

|Possible |Having a potential. |

|Reasonable |The appropriateness or good approximation in a number answer. |

|Data |Information that is displayed in a graph. |

|Array |A number of mathematical elements arranged in rows and columns. |

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[pic]I. Sequence of Activities (Instructional Strategies)

A. Focus/connections/anticipatory set

1. Start the lesson by discussing the vocabulary words. Talk about prime, composite, and square numbers. You will need overhead square tiles. Start by using 6 tiles and have students give ways that these 6 tiles could be arranged in a rectangle. Have students brainstorm the ways and write them down on the board. Once they have brainstormed, model their solutions to see if they work. (You should come up with a 1 by 6, a 6 by 1, a 2 by 3, and a 3 by 2 rectangle.) Explain to students that this is one way to find all the factors of a given number. Next have students brainstorm how many rectangles could be done with only 5 tiles. (They should only come up with two, a 1 by 5 and a 5 by 1.) With this activity, explain to students that the 5 is a prime number because it only has two factors, 1 and 5 and that 6 is a composite number because it has more than two factors.

B. Instructional activities

1. Objectives: The student will determine if factors of numbers are prime or composites.

2. Procedures: The teacher will explain the difference in prime and composite and students will complete activities in order to determine which numbers are prime and composite.

3. Modeling: The teacher will use square tiles, computers, and may use the overhead or chart paper for recording answers to demonstrate prime and composite numbers.

C. Guided activity or strategy

Day 1

1. Divide students into small groups. Give each group a set of square tiles (give each group 7 tiles) and have them practice arranging tiles. Students will also need a sheet of paper to record their answers. Have students find solutions to the following questions: In how many ways can you arrange 4 tiles to form a rectangle? 3 ways: 1x4; 4x1; and 2x2. How many ways can you arrange 7 tiles to form a rectangle? 2 ways: 1x7 and 7x1. Ask students if there are any other ways to arrange the 7 tiles? There aren’t any other ways. Ask students why they can not arrange 7 tiles any other way? Because 7 is a prime number. Have students arrange other sets of tiles to show different arrays of numbers. (This comes from Math Advantage p. 286).

Day 3

1. Review with students about Prime and Composite numbers. Put students into small groups. Give each group a different amount of sugar free gummy bears or gum drops and toothpicks. Put some different numbers in a container and have each group draw two numbers. Demonstrate to students how to build a factor tree. On the board put the number 21. Ask students what two factors equal 27. They should say 9 and 3. See the diagram below to demonstrate how to create a factor tree. Keep going until all the numbers at the bottom of the tree are prime numbers. Tell students that this is the prime factorization of the number 27.

Diagram: 27

9 3

3 3 The prime factorization of 27 is 3x3x3.

D. Accommodations/modifications

See student IEP for modifications.

E. Enrichment

Students can create a number pyramid by finding the missing numbers in that pyramid. Enrichment from Math Advantage p. E93 (Activity sheet 4).

II. STUDENT PERFORMANCE

A. Description

The students should be able to recognize a prime or composite number and be able to decipher a prime factorization of a number.

Day 1

1. Students will continue to work in small groups. Give each group more tiles, about 20 for each group and have students find the arrays for the following numbers: 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20. Have students draw the arrays on graph paper (Activity Sheet 1), write their factors for those numbers, and determine whether they are prime or composite.

Day 2

1. Students will use the following website from the school adoption to find prime and composite numbers. . Go to The Learning Site, Math, Math Advantage (at the very bottom), E-Lab, 5th grade, and scroll down to Prime and Composite numbers. (Students will use Activity Sheet 2 with this activity or you can print it from the website.)

2. Guide students through just questions 1-4 and 9-10 of the computer experiment. Have students complete the rest of the questions on their own.

Day 3

1. After showing students the prime factorization tree, instruct them to create prime factorization trees with their gummy bears and tooth picks. Have them write the prime factorization for their number and their factor tree on a sheet of paper. Monitor to make sure students are doing this right. (You may be wondering how they are to do this factor tree. Students need to brainstorm how to get the 3 gummy bears needed for that factor on the toothpick. Not every factor tree will look the same because of the fact that students will come up with different ways to show their factor tree. Just make sure they are on the right track.) After students have completed their factor bears and turned in their papers to you, have students complete Activity sheet 3, On My Own p. P93 from Math Advantage.

B. Accommodations/modifications

See student’s IEP for specific modifications.

C. Enrichment

III. Assessment of Activities

A. Description

The teacher will know the students have mastered prime and composite numbers when they:

• Complete the Day 2 activity with a 70% or higher.

• Complete the Prime and Composite Assessment with 70% or higher.

• One other Assessment that can be done is having students write the first 20 prime numbers from memory with a 70% success or higher. (2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71)

B. Rubrics/grading criteria

• Complete all Activities with a 70% or higher.

C. Accommodations/modifications

All accommodations/modifications need to align with the student’s IEP.

D. Enrichment

E. Sample discussion questions

1. Name the first 10 prime numbers? 2,3,5,7,11,13,17,19,23,29

2. What is the difference between a prime number and a composite number? A prime number only has two factors, 1 and itself, where a composite number has more than two factors.

3. What is a prime factorization? It is the all the prime factors that make up the whole number.

4. How do you find the prime factorization of a composite number? Create a factor tree.

IV. TAKS Preparation

A. Transition to TAKS context

1. Students will complete a TAKS formatted Assessment.

B. Sample TAKS questions

The teacher needs to take sample questions from the 2003 and 2004 TAKS released tests to emphasis how probability is tested on the TAKS test.

(Use TAKS Transparency)

V. Key Vocabulary

Prime numbers, composite numbers, square numbers, prime factorization, factors, reasonableness, data, array, possible, generalize

VI. Resources

A. Textbook

Math Advantage Harcourt Brace

Step Up to TAKS

B. Supplementary materials/equipment

• Transparency: Sample TAKS questions from 2003 and 2004 Released TAKS test.

• Students will complete activity sheets from Step Up to TAKS Step 1A-1B and Step 2.

• Toothpicks

• Sugar free Gummy Bears or Gumdrops.

C. Technology

1. Overhead projector: Modeling prime and composite arrays and prime factorization trees.

VII. Follow up activities

The next lesson in this sequence would move into finding common factors and greatest common factors.

VIII. Teacher Notes

The teacher should make sure that students have a complete understanding of prime and composite numbers. The teacher can make other accommodations as they see fit for their students.

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This is a prime number so underline it.

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