rational number preview day 1
DESCRIPTION
Factor LessonTRANSCRIPT
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10/16/14- SW be able to find the prime factorization of a composite number.
What type of number is 24?What type of number is 7?
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Lesson Plan
• Rational Number Unit (includes fractions and decimals)• Journal Notes: – Prime Numbers – Composite Numbers – Prime factorization
• Two methods for prime factorization: – Division by primes – Factor Tree
• Factor Tree Race Group Activity• Writing Response Questions and scale
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What is a prime?
• Prime number - a natural number greater than 1 that has no positive divisors other than 1 and itself.
• In other words, see what you can divide thenumber by.
• If the only answers are the number itselfand one, then the number is prime.
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And if it’s not prime?If a number is not prime it is called composite.6 is divisible by 1, 2, 3, and 6. This means that 6 is a composite number. A composite number is a number with three or more factors.
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So what is prime factorization?• This is a way to break a number down into parts
where each part is a prime number. • Prime factorization is a number written as a
product of it’s prime factors.
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Let’s look at the number 6.
6 can be broken down into 3 x 2
6 3 x 2
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• For 6 we write the prime factorization as
• 6 = 3 x 2
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How do we find the prime factorization?
• Division by primes (bake a cake)
• Factor Tree (climb a tree)
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Division by Primes• The first method is called division
by primes (or the birthday cake method)• Let’s use the number 24• First we pick a prime that we can
divide 24 by. Since it is even we will try 2.
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242122632
• First we divide 24 by 2 and the result is 12
• Next we choose another prime to now divide 12 by
• We divide 12 by 2 and the result is 6
• Now we choose a prime to divide 6 by, let’s choose 3 this time
• The result is 2, which is a prime, once a prime answer is reached we stop
• Now to get our answer we look on the outside of the long division
• The prime factorization of 24 is 2 x 2 x 2 x 3
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242122632
The advantages to this method are in the ease of choosing yournumbers. You must choose a prime number to divide by eachtime, which limits your choices to a few small numbers usually.
The reason this is sometimes called the birthday cake method isbecause of the resulting shape.
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Factor Tree
• The second method is called a factor tree• Again we will use the number 24• This time we are not limited to our choice of
numbers to divide by so we will pick 8
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24
8 3
4 2
22
• First we divide 24 by 8. The result is 3. i.e. 8 x 3 = 24
• Next we look at 8. We can divide 8 by 4 to get a result of 2.
• Then we look at the 3. This is a prime so we do not touch the 3. We will circle it to indicate we are done with it.
• The 4 can turn into 2 x 2.
• The 2 is prime so we circle it.
• The last two 2’s are prime, so again we circle them.
• Now look at all of our circled numbers. This is our prime factorization. 24 = 3 x 2 x 2 x 2
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24
8 3
4 2
22
• The advantage to the factor tree method is the ability to choose from any number. (as long you can divide the original number evenly)
• This method is named for the resemblance the final results have to a pine tree.
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Journal Practice Problems: Make a factor tree for:
• 60 2836
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Group activity rules
• Talk is on task • Stay in your seats • Polite Behavior • Working quietly
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3 play1 referee/dice roller
(switch positions
each game)
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Writing Response and scale• WR: 3, 2, 1 - List 3 things that you learned this week
List 2 things that surprised you
List 1 question you still have (can be about anything)