302A pp section 4.1 and 4.2a-2

# 302A pp section 4.1 and 4.2a-2 - Warm-Up Problem If 16 2 =...

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Warm -Up Problem If 16 ÷ 2 = 8, and 160 ÷ 2 = 80, and 1600 ÷ 20 = 80, what is 160,000,000 ÷ 200? Explain how you know!!! You may not say “move the decimal” or “count the zeros.”

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Agenda Discuss Exams. Difference between odd and even Difference between prime and composite Difference between factor and multiple After SB, 23 March Sieve of Eratosthenes Begin Exploration 4.2.
Odd, Even, Prime, Composite Use the manipulatives to make arrays for the following numbers: 7 12 23 22 Can you make an array for each? Can you make more than one array for any?

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Odd, Even, Prime, Composite If you can make two rows of the same length, then your number is even . If there is one left over after making even rows, then the number is odd . If you can only arrange the manipulatives into a rectangle in just one way, then the number is prime . If you can arrange the manipulatives into two or more different rectangles, then the number is composite .
Use the blocks… Show why the sum of two odd numbers is an even number. Show why the sum of two even numbers is an even number. Show why the product of two odd numbers is not even.

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Make a list with your group How can I remember??? Factor Multiple
Factors and Multiples--using manipulatives One way to visualize factors and multiples is to make rectangles or rectangular arrays. In a rectangle, the length times the width is equal to the area. So, the sides are the factors and the area is a multiple. Use these chips. How many different rectangles can you make using 24 chips? Be systematic.

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Factors of 24--How do we know when we have them all? 1 • 24 2 • 12 3 • 8 4 • 6
You try: 36 1 • 36 2 • 18 3 • 12 4 • 9 6 • 6

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Sieve of Eratosthenes Eratosthenes was born in Cyrene which is now in Libya in North Africa in 276 BC. He died in 194 BC. Eratosthenes made a surprisingly accurate measurement of the circumference of the Earth. He was also fascinated with number theory, and he developed the idea of a sieve to illustrate prime numbers.
Sieve of Eratosthenes You will need many different colors. Use one color for each factor. Circle the number “1”.

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## This note was uploaded on 11/29/2009 for the course HIST 110 taught by Professor Staff during the Spring '08 term at Arizona.

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302A pp section 4.1 and 4.2a-2 - Warm-Up Problem If 16 2 =...

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