Factoring Quadratics in My Own Words March 8, 2012

Factoring Quadratics in Your  Own Words

 

The factoring of quadratics is done to simplify the equation. You are taking a trinomial and changing it to a binomial.  The formula for a Quadratic is ax² +bx +c.

1^st look at c and determine its’ factors. Choose the two factors whose sum equals b (7).

Example: x² + 7x+ 12       factors of 12 (1*12) (2*6) (3*4). 3+4 =7 so this is the one.)

2^nd Look at the first term in the equation, (ax²)and divide by 2.

Example x² = x * x

Now put the parts together in a binomial (x+3) (x+4).

It did make me internalize the concept because I had to explain it. It is like teaching to one’s self. This activity could be incorporated in the journal, having them paraphrase a definition, a process or simply what they learn that day will help them learn and remember the concept because it is a form of teaching only to oneself.

Evalutating My Definition Functions and Equations February 18, 2012

After reading everyone’s definitions of functions and equations they all have the basic definition or revised it to such. My own definition for functions could be elaborated to include that the functions are  what  (the numbers) are plotted on a coordinate plane graph. And possibly give more examples of equations.

In the classroom to ensure the students understand the difference I would use visuals when explaining the two, pointing out likes and differences using a Vin diagram. Then conduct a scavenger hunt, that encompass all 4 team members classroom. I would us index cards and write functions on half and equations on the other half. Each student would have to find 2 of each within  the next 24 hours. In class the next day have then present their finding to class and determine their accuracy.

Equations and Functions in Your Own Words February 15, 2012

Equations and Functions in Your Own Words.

 

Function is when you take a variable for x and plugged it into the equation and get I result. The function machine takes a number in, knows the equation, and puts out a new number out (y). Or simply what is done to a number to make it another number.

If f(x) =2   then in 4x-4          If f(x) = 3   then 4x-4                 If f(x) = 4   then 4(x)-4

4(2)-4                                                                    4(3)-4                                                    4 (4) -4

8-4 =4                                                                    12-4=8                                                  16-4=12

F(x) =4                                                                 F(x) =8                                                  F(x) =12

                                                                                                                                                                                                                                                                                                

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07s104.jpg

raider.mountunion.edu

Equation in the algebraic problem, 4x-4=y. It is similar to the expression but must equal something.

Supplemental Activities

Journal blog assignment

Complete in journal. Show all work equation table function. Try to graph results.

At school you are in a jump rope -athon to raise money for the Heart Association.  Your sponsors have pledged to give you $3.00 for every 30 minute session of jumping you complete, plus a $.25 bonus if you don’t miss during the session. Assume you never miss, how much will each sponsor owe if you jump 3 sessions?  4 session? 5 session?

5 sessions?

Web based tutorial activities and games.

http://www.ixl.com/math/grade-8

http://www.mathwarehouse.com/algebra/relation/math-function.php

http://www.coolmath.com/algebra/15-functions/01-whats-a-function-domain-range-01.htm

http://www.math-play.com/Algebra-Math-Games.html

Translating Pattern Narrative into Formal Math language February 10, 2012

 

 

 

 

Pascal’s Triangle

Pascal’s triangle is an equilateral triangle consisting of positive integers. The perimeter of the two legs and the vertex angle are all 1’s.  The size can go small and as great as infinite by adding 1 to the outer legs at the base. The base is made up of the sum of the pattern rule. The integers in the entire perimeter are highlighted. All the integers form a straight line on the diagonal, but not vertically or horizontally. Not all rows have an integer on the altitude line.

The integers on each horizontal row are symmetrical from center to edge.

Along with the base line being highlighted, other integers are highlighted.  The highlighted  integers that encompass the bottom rows running parallel with the base form two small triangles with a larger inverted triangle in the center.  This triangle consists of odd numbers. Two smaller triangles highlighted in the top section consist of prime numbers.

The pattern is as follows:

Starting at the top right of the vertex is row 0 consisting of ones. It runs diagonally to the lower left.  Row 1 consist of counting numbers 1-15, representing the sum of 1 plus it diagonal to form the next number. 1 + 1= 2 .The numbers in the following rows  arethe sum of the two numbers on the diagonal line above the sum.

 

                

 

 

 

 

 

 

 

The formula is a invert triangular shape. Therefore the sums are triangular numbers. The formula works in any direction and any combination of the inverted triangle.

Math Vocabulary January 23, 2012

Graphic organizer to use with math vocabulary

Frayer Diagram

1. Integers- all whole numbers and their opposites.

Integers- any of the natural numbers, the negatives of these number or zero.

Merriam Webster The Free Dctionary\

2. Number sense  Ones awareness and understanding about what Numbers are,   the relationships, the magnitude, the related effect of operating on numbers, including the use of mental math and estimation.

Number sense In mathematics education, number sense can refer to “an intuitive understanding of numbers, their magnitude, relationships, and how they are affected by operations.”^[

There are also some differences in how number sense is defined in the field of mathematical cognition. For example, Gersten and Chard say number sense “refers to a child’s fluidity and flexibility with numbers, the sense of what numbers mean and an ability to perform mental mathematics and to look at the world and make comparisons.”

http://en.wikipedia.org/wiki/Number_sens…

Posted 1 year ago

3. algebraic Numbers variables that represent rational numbers.

The sub set of the real algebraic numbers: the real roots of polynomials, Real algebraic numbers may be rational or irrational.

Http://thinkzone.wlonk.com/Numbers/NumberSets.htm.

An algebraic number is any real number that is a solution of some single-variable polynomial equation whose coefficient s are all integer s.

http://whatis.techtarget.com/definition/0,,sid9_gci283964,00.html

4. Real numbers all numbers, rational or irrational.

Real numbers are all the numbers on the continuous number line with no gaps. Every decimal expansion is a real number. Real numbers may be rational or irrational, and algebraic or non-algebraic (transcendental). pi = 3.14159… and e = 2.71828… are transcendental. A transcendental  numbers can be defined by an infinite series.

Http://thinkzone.wlonk.com/Numbers/NumberSets.htm

 5. Whole numbers counting numbers and their factions, 6/1 including 0.

Whole numbers counting numbers, positive integers. can be refered to as natural numbers
http://thinkzone.wlonk.com/Numbers/NumberSets.htm

6. Rational Numbers Any number that can be expressed as a/b with b not equal to 0.

Rational numbers are the ratios of integers, also called fractions, such as 1/2 =0.5 and 1/3 = 0.333… Rational decimal expansions end or repeat.

http://thinkzone.wlonk.com/Numbers/NumberSets.htm

 7. Irrational Numbers- any number that cannot be expressed as a/b. In decimals never ending.

8. Commutative properties –

For adding

The order in which you add a series of numbers doesn’t change the sum. Simple  for any numbers a and b,  a + b = b + a.

For multiplying

The order in which you multiply a series of numbers doesn’t change the product.

Simply for any numbers a and b ab = ba,

9. Addends-  numbers being added.

10. Inverse refers to the relationship to the opposite  of a number. It can mean to reverse something, turn it upside down. Or it can mean the opposite.

When adding, add the opposite:

a+ -a = o     3 + -3= 0

Used in matrix.

When multiplying, find the reciprocal

a * 1/a = 1

for whole numbers

1. Convert to fraction: 3= 3/1

2. To inverse turn upside down   1/3 known as reciprocal.

sS the inverse of 3/1=1/3   so 3/1 * 1/3=1           (a/1=1/a)

Used in dividing rational numbers and in a Matrix