Presentation on theme: "Musical Chairs No more than 2 people at one table who have been at the same table before. I suggest that one person remain at the table you have been at."— Presentation transcript:
1Musical ChairsNo more than 2 people at one table who have been at the same table before.I suggest that one person remain at the table you have been at for the past few weeks and the rest move, making sure that there is no more than one person at your new table with whom you have previously shared a table.
2Even and odd numbersWhat can you say about two numbers if their sum is even and their product is odd?Why?
3Even and odd numbersThe sum of three numbers is an even number. Does the product have to be an even number or an odd number or can it be either one?
4Finding factors of a number Use the beans to find factors of 24Count out 24 beansWe know that products can be illustrated using a rectangular modelMake a rectangle using the beansWhat are the numbers you multiply to get 24?Can you arrange the beans into a different rectangle?What product does this represent?
5How many different rectangles can you make? Count out 11 beans.How many rectangles can you make with 11 beans?
6Sieve of EratosthenesEratosthenes 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.
7The Sieve of Eratosthenes Prime NumberDivisible only by 1 and itselfFinding prime numbers using the sieve
8Sieve of EratosthenesYou will need many different colors. Use one color for each factor.Circle the number “1”. 1 is neither prime nor composite, as we have seen earlier.Now, circle 2. Every multiple of 2 is a composite number, so put a dot of that color next to all of the multiples of 2.Use a new color. Now, circle 3. Every multiple of 3 is a composite number, so put a dot of this new color next to all multiples of 3.
9Sieve of EratosthenesNow, 4 has a dot next to it--it is not prime. Skip it and move on.Use a new color. Circle 5, and then put a dot of this new color next to all multiples of 5.Now, 6 has a dot next to it--it is not prime. Skip it and move on.Continue until you know that only prime numbers are left. When can you stop? How do you know?
10Sieve of Eratosthenes Questions to answer: When you circled 11, were there any multiples of 11 that did not already have dots next to them?Can you explain to a child why this was true?What does this have to do with factors and multiples?What are the prime numbers that are between 1 and 100?Is 1 a prime number?
11Sieve of Eratosthenes123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100
13Names for these numbers 11 is an example of a24 is an example of a
14Factors of 24 List How should they be ordered? How do you know you have them all?
15Factors of 24--How do we know when we have them all? 1 • 122 • 243 • 84 • 6
16Exploration 4.2First, fill in the table on page 85, using the information on the sieve. It will help if you write them in pairs. For example, for 18: 1, 18; 2, 9; 3, 6. The order does not matter.Next, fill in the table on page 87. Use the table on page 85 to help.
17Exploration 4.3Do #1 yourself, compare answer with the others in your group.Do #2 with the following numbers6072
18FactorizationFactorization is writing a number as a product of factors.2460
19Prime FactorizationA factorization of the number in which all of the factors are prime numbers.1012