November 17, 2010

Sieve of Eratosthenes (located at the National Library of Virtual Manipulatives)

This virtual manipulative displays a grid containing numbers from 2 to 200. You can use it to explore patterns and relationships involving multiples.

Using this virtual manipulative you may:

• Remove multiples of a number
• Show multiples of numbers
• Reset the workspace
• Choose how many rows to display

Prime Factorization - Using the Cake Method

You can use the cake method and prime factorization to find the GCF and LCM

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• The cake method allows you to find the GCF and the LCM at the same time.

Finding the LCM

If there are no common factors then multiply the numbers together (For example: 10 and 3)

November 10, 2010

The Cake Method is a way to find the prime factorization and even least common multiple

It's called the cake method because it looks like an upside down layered cake.

Even numbers are divisible by 2

Is zero divisible by 2? Yes

What are odd numbers?  Numbers that are not divisible by 2.

Divisibility Rules

• 2 - if the number is an even number, then that number is divisible by 2
• 3 - the sum of the digits of a number is a multiple of 3, then the number is divisible by 3.  Example:  7491 = 7+4+9+1 = 21, 21 is a multiple of 3, so 7291 is divisible by 3
• 4 - if the last two digits of a number are divisible by 4, then that number is divisible by 4. or  Half half rule.  If you can half those last two number twice, then the number is divisible by 4. Example; 48 divided in half is 24, 24 divided in half is 12.  48 is divisible by 4. (up to 100)
• 5 - if the number ends with a zero of 5, then the number is divisible by 5
• 6 - If the number is divisible by 2 and 3, then the number is divisible by 6
• 8 - look at the last 3 digits of the number, cute them in half.....cut in half again.....cut in half again...if you can cut that number in half 3 times, the number is divisible by 8. (up to 100)
• 9 - add all of the digits, if the sum is divisible by 9 then the number is divisible by 9
• 10 - if the number ends in a zero, then that number is divisible by 10
• 11 - if the last two digits of a number are a double number for example; 44, 55 or even 66....then the number is divisible by 11.

Forehead Multiplication Game (Name is still in progress, input is welcome) 

• Needed:  one deck of cards, but take out the aces and face cards
• students get in groups of 3
• one person is the captain
• the captain draws two cards, and multiplies the two together (without showing the two cards to the other students)
• captain hands the cards to the other two players face down
• captain the says the product as the two players hold their card on the forehead.  (the two players don't see what their card is.  They can only see what the other player has.)
• Students then have to figure out what their card is.  
• The student who says their number first and accurately gets to keep the cards,
• The player with the most cards at the end wins and gets to be the captain.

October 27th Reflection

I really liked the cauldron activity.  What a great activity to help demonstrate the addition and subtraction of integers.  For example, -7 - 5 is n -7 subtract +5.  Doing this problem using the cauldron can help me demonstrate what this means.  It also helps demonstrate "zero pairs".  So when I have -7 (which is the yellow pieces in my cauldron) I can't take out 5 positives (the green pieces) so that is why I add my zero pairs and I can now take out 5 positives and when I take those out, I am left with the answer.  My question about this is, when do teachers teach about adding and subtracting integers.  As they are teaching addition and subtraction?  I guess, since I am not in the classroom, I can't picture when I would do this type of activity.

Ahhhh....teaching addition and subtraction of integers using the number bond.  I totally get the addition of integers, but for some reason I struggle with the subtraction of integers. The more I worked with the problems, I was starting to get it.  I was never taught to look at addition and subtraction problems as part part whole.  This class is challenging me to remember that, but this is good for me.