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

• 
  
  
• 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.

October 27

Real numbers are all numbers, the number system. Both rational and irrational
Rational numbers are numbers that can be written as fractions and decimals
Irrational numbers - numbers that you cannot find a perfect square of. "pie" is an irrational number, numbers that keep repeating
Natural numbers - the counting number not including zero,
Whole numbers - counting numbers including zero, don't include negative numbers
Integers - negative numbers, positive numbers and zero.  NOT including fractions and decimals.

3 - real, rational, integer, natural

-3 - integer, rational, real

3.33 - rational, real

1/2 - rational, real

√7 - irrational, real

pie - irrational and real

√25 - natural, whole, integer, rational, real

9/3 - natural, whole, integer, rational, real

√16/4 - natural, whole, integer, rational, real

4^{3 - natural, whole, integer, rational, real}

^{e - irrational, real}

^{Number Bonds}

^{Addition is always part plus part equals whole}

Subtraction is whole minus part to find the other part

Multiplying Integers

negative x negative = positive

positive x positive = positive

positive x negative = negative

negative x positive = negative

The first statement is the who  The second is the action (what happened)  and the = is the result.

example:

1. Mother Teresa wins the lottery = a good thing ( + x + = +)
2. Mother Teresa gets mugged = a bad thing  (+ x -- = --)
3. The Devil wins the lottery = a bad thing (-- x + = --)
4. The Devil gets mugged = a good thing (-- x -- = +)

positive - Eric Bana

action - wins an oscar

negative - Lindsay Lohan

negative action - bad accident and gets deformed

1. Eric Bana wins an oscar = a good thing - he gets more movie opportunities  (+ x + = +)
2. Eric Bana gets in a horrible car crash and gets deformed =  a bad thing no more acting career for Eric Bana  (+ x -- = -)
3. Lindsay Lohan wins an oscar = a bad thing - Why on earth would she win an oscar?  She's a horrible actress (-- x + = --)
4. Lindsay Lohan gets in a horrible car crash and gets deformed = a good thing - she can get out of the spotlight and rebuild her life. (-- x -- = +)

Distributive Property

Trichotomy - there are three relationship 2 integers can have and only three.  

1. negative < 
2. less than > 
3. equal to =

This is a transitivity statement;  a = b  b = c => a = c  

                                                6 < 8,  8 < 10 =>  6 <10

October 20 Reflection

I really liked the explanation for why a negative times a negative is a positive.  I remember getting this question from students and not being able to give them a good answer/explanation.  I like the explanation that Steve gave about positives and negatives using the example of money.  That is a great way to share w/students because money is an example they can relate to.   I like the idea of using the example, "If you take something bad away from you its "good".

October 20, 2010

What have we learned?  Things to make sure I am familiar with for the content test at the end of this class....

• Part Part Whole -
• Commutative Propery
• Associative Property
• Distributive Property
• Identity Property
• Zero Property
• Concrete - Representational - Abstract
• Set/Measurement Models
• Base Ten
• Standard
• Expanded
• Word
• Shortened
• One to one correspondent
• Terminology
• "Nice" numbers
• Regrouping
• Inverse operation
• Operations
• +
• -
• x
• divide
• Hops, jumps, skip counting
• Array
• Area
• Compensation Method
• Algorithm
• Minuend
• Addened
• Difference
• Factor
• Sum
• Product
• Compatable numbers
• Rounding
• Estimating
• Shortened form
• Partitive
• Quotative

Integers

• We started with counting, then there is zero, and then progressed to Integers which includes negative numbers. 
• 

• The number line is a tool kids should be familiar with.
• Where do the negative integers start?  With -1, don't include the fractions that fall between zero and 1. 

• Less than - numbers to the left of that number on number line

• Greater than - numbers to the right of that number on the number line

• Absolute Value - how far a number is from Zero 

• The point of absolute value is distance, and is used in physics
• Opposites - relationship between numbers that make the whole number Zero.

Addition = Part + Part = Whole
Subtraction = Whole - Part = Part

Readings for Next Week
Van de Wall pgs 479 - 481 - Integers 481 - 486 (problems - look at them)
Parker - pgs 185 - 189

October 12th Reflection

I feel like I didn't get very much from last weeks class.  Part of the is my fault, since I was late coming to class.  I feel like each week I leave with different strategies for teaching that particular different, and this week I left knowing about the scaffolding method for divison and the lattice mathod for multiplication.  I really liked learning the scaffolding method, I have never seen that before and can see how that could help some students with the whole division process.  I thought it was funny how long we spent talking about the different ways to remember the steps to division, Multiply, Divide, Subtract, Bring Down.  Some teachers are very creative, I was boring when I taught this to my students.  I just had a poster I created that was on my whiteboard and as we solved the division problem we would put a check mark next to each step as we finished it. 

Was there more I should have gotten from last week's class?