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? 

October 12, 2010

Division

Help students remember the division process - D, M, S, B - Divide Multiply Subtract, Bring Down

Ideas to show students how to divide by zero and why it doesn't work

• show an equation
• give students a word problem

Scaffolding Method

The Lattice Multiplication Method

The answer is 64,470

October 6 Reflection - Better Late than Never Right?

So, I didn't do my reflection until just now but to be honest I didn't really know what to write after that class.  I feel better about the break it up strategy.  I think as a teacher I would present these different math strategies and let the students decide what works best for them.  I am not satisfied with students just getting the right answer, I like to know that students know HOW to get to the right answer.  I think it is important to show students that there are multiple ways to get to an answer.  I was always taught to solve problems using one method, and I think I would have done better in math had I been shown different strategies.

October 6, 2010

Grid Multiplication Model:

Multiplication Facts

• As math gets more challenging, kids need to make sure they know their math facts or they won't be able to move on.
• Kids can't go back in mathematics
• There is forced progression in math, THEY NEED TO KNOW THEIR MULTIPLICATION FACTS

Multiplication Fact Strategies

• 9 = 10 take away 1 
• 9 x 4 = 10 x 4 = 40 then take away one group of 4 40 - 4 = 36
• 2 = double
• 4 x 2 = (4 + 4 = 8)
• 3 = skip counting
• 4 = double, double
• 4 x4 = (4 +4 +4 +4 = 8 + 8 = 16)
• 5 = skip counting, there is a pattern
• 6 = 5 plus 1
• 6 x 5 = (5 x5 = 25 + 5 = 30)
• 7 = skip counting
• 8 = double, double, double
• 12 = ten plus 2s 
• 12 x 2 = (10 x 2 = 20 +2 + 2 = 24)

Lesson Study

• Launch - how are you going to prep those kids for the lesson
• What are the guiding questions?  Get the students talking.
• Anticipatory set - where students may make mistakes
• Interventions - how can you respond to the student errors
• Exploration
• What are the guided questions
• Anticipatory set
• Interventions
• Wrap Up/Classroom Discussion
• What are the guided questions
• Anticipatory set
• Interventions
• Assessment Piece

Readings for Next Week:

• Beckman p 115 Activity 6B #1-2
• Beckman reading 234 - 235
• Van de Wall pg 155
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