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Algebra Prime and Composite numbers 7th grade – Mrs. DeGraaf
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Focus attention/motivation: 5 minutes Instructional input and modeling: 20 minutes Student engagement/practice: 15 minutes Closure: 5 minutes
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The overall goal of this lesson is to learn how to use divisibility rules to find all factors of a given number and to identify a number as prime or composite. These skills will help them in the next lesson which is factoring.
 * Overall Goal/ Purpose **

**6.B.3b ** Apply primes, factors, divisors, multiples, common factors and common multiples in solving problems.
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The student will be able to use the divisibility rules to find all the factors of a given number and to identify a number as prime or composite. Students will discover that these rules are helpful in everyday life when they need to split a bill 2 ways, 3 ways, 4 ways, etc. 1. Smartboard 2. Individual white boards and expo markers
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**<span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Focus Attention/Motivation: **<span style="font-family: 'Times New Roman','serif'; font-size: 12pt;"> On the board will be various numbers. I will ask the students to tell me what numbers can divide into these various numbers. As they share the correct answers, I will ask them how did they know or how did they DISCOVER the right numbers. I will share with them that today we are going to learn the divisibility rules which are so helpful when they need to split a restaurant bill or the cost of a gift 2 ways, 3 ways. 4 ways, etc. I will review vocabulary with the students. The following words will be reviewed: 1. Factor 2. Divisible 3. Prime number 4. Composite number I will have the following rules on the smart board, and the students will write these notes in their algebra notebook: <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">1. A number is divisible by 2 if the last digit ends in 0, 2, 4, or 8. 2. A number is divisible by 3 if the sum of the digits is divisible by 3. 3. A number is divisible by 4 if the last two digits form a number divisible by 4. 4. A number is divisible by 5 if the last digit ends in 0, or 5. 5. A number is divisible by 6 if it divisible by both 2 and 3. 6. A number is divisible by 9 if the sum of the digits is divisible by 9. 7. A number is divisible by 10 if the last digit ends in 0.
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 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Instructional Input & Modeling: **<span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Divisibility Rules **

Then I will have the students write the following problem from the smart board in their notes as I go over it orally:

Determine whether 516 is divisible by 2,3,4,5,6,9, or 10. 2 yes The last digit is 6. 3 yes 5+1+6=12; 12 is divisible by 6. 4 yes The last two digits are 16. 16 is divisible by 4. 5 no The last digit is not 0 or 5. 6 yes 2 and 3 are factors. 9 no 5+1+6=12. 12 is not divisible by 9. So 516 is divisible by 2,3,4, and 6.

With this information, the students can then be taught the difference between prime and composite numbers. A prime number is a number that has only two factors: 1 and itself. For example, 29 is prime because it only has two factors, 1 and 29. A composite number has more than two factors. For example, 12 is a composite number because it has the factors of 1,2,3,4,6, and 12. By definition, the number 1 is neither prime nor composite.

We will do these problems together: Determine 1,000 is divisible by 2, 3, 4, 5, 6, 9, or 10. Is 1,000 prime or composite? (cross-curricular with science)
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Volume: **<span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">1L=1,000ml and **Mass:** 1kg=1,000g.

Table salt has a melting of 801 degrees, and a boiling point of 1,465 degrees. Determine whether 801 and 1,465 are each divisible by 2, 3, 4, 5, 6, 9, or 10. Is 801 prime or composite? Is 1,465 prime or composite? (cross-curricular with science)

1. After the notes and teaching time, I will pass out individual white boards and have the students do some sample problems on their white boards. They will hold up each of their boards as they complete each problem. 2. Then, their assignment will be to list 7 numbers that have either three or four digits. Examples: 406, 6000. 3. On separate piece of paper each student must determine whether each number is divisible by 2,3,4,5,6,9, and 10. 4. They also must list whether each number is prime or composite. 5. Next, each student will trade the first sheet or the list of 7 numbers with another student. 6. Each student will determine whether the 7 numbers are divisible by 2,3,4,5,6,9, and 10 and label each number prime or composite. 7. When they complete this task, students will trade back. 8. The original owner will check his or her partner’s answers with his or her own. 9. All papers will be turned in.
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Student Engagement/Practice: **<span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">

Closure: Students will be instructed to finish the work at home if needed. I will them that knowing these divisibility rules will help them accurately divide any number that needs to be split 2 ways, 3 ways, 4 ways, etc. The Discovery will be reviewed: divisibility rules and prime and composite numbers. <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">I will be using 3 different assessments in this lesson. I will use the motivation time to determine if the students have any prior knowledge regarding factorization as my pre-assessment in the beginning of the lesson to see where the students are at. I will use observations and examples on the smart board to see where students are at during the lesson. My final assessment will be when the students work in partners to figure out whether the list of numbers are each divisible by 2,3,4,5,6,9, and 10 and to determine whether each number in the list is prime or composite.
 * <span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">Assessment **

<span style="font-family: 'Times New Roman','serif'; font-size: 12pt;">The students who are having trouble will be grouped with me at the back table. I will work with them on the rules for factoring.
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The successful students will have the opportunity to create another list of five or six digit numbers and determine whether each number in the list is divisible by 2,3,4,5,6,9,and 10.