Greatest Common Factor

Greatest Common Factor: For any two non-zero whole numbers a and b, the greatest common factor, usually written GCF(a,b). There are several methods to find the GCF of two numbers such as 1) List the Factors, 2) Prime Factorization, and 3) Linear ( Cuisenaire rods).

Listing Factor
To use this method you list the multiples that equal each number a and b. For this example it is 36 and 54

Linear ( Rods)

Prime Factorization

When dealing with the prime factorization of a number you start with the number and you break it down into all the multiples the number has using the prime numbers that are left and comparing and seeing what the other side has.

( for this example we are using 240 and 28 for example.) 

Since they only share 2x2 when u multiply those you get 4 as the GCF, so it will be written like GCF(240,28) is 4.

( Here is a Fun and interesting video to look for more help with Prime Factorization) 

http://www.math.com/school/subject1/lessons/S1U3L2GL.html 

(Above is a link to a great site to help you step by step to finding GCF!)

Fractions

We touched base in class about fractions and three models of fractions; which are Part to whole, Division, and Ratio. Fractions is pretty much a part of a portion of a WHOLE. When there are many examples to show fractions and how they are represented.

Typically Fractions are represented in a fway like this (1/2) making the number 1 a numerator, and the bottom number 2 the denominator. The Part to whole concept is one that we are all used to seeing 

Division Concept

Sharing concept

Ratio Concept

Extra Practice :

http://www.mathsisfun.com/fractions.html

Dealing with Ratios

In class 3/8/11, the class did not have much notes to take. We actually did more hands on and actual practicing with ratios. Ratio is a pair of numbers that are used to compare two sets. Ratio can be written in various forms such as a fraction or using a colon. For example we used to number of males to females in the class and the results ended up as following. We have a total of 20 people in class today, 6 are male and 14 and female; the way to properly write this as a ratio is either 6/14 or 6:14 number of males to females. Ratios are used in alot of everyday things from your T.V ratio to Miles per gallon. Anytime given a question on percent; key rule of thumb is that it is any number over 100, and it is written like 4% , meaning 4/100.Below is a link to a site to seek for more practice with ratios.
http://www.math.com/school/subject1/lessons/S1U2L1GL.html

(Ratios of widescreen to regular spectrum)

( This picture illustrates 23miles:1 gallon)

We also touched base on Proportions which ties in with Ratios; for any two ratios a/b and c/d, the equation is called a proportion. Proportions are typically used in  trying to solve a problem, such as you are given a,b,d and you have to figure out what c is? The easiest way to figure out that number is my using cross multiplication  once you have your proportion set up with the (X) to be solved. you can check your answer then by just simply plugging into the original problem and justifying if it is a positive fit. 

working with fractions

When working with fractions you are pretty much dealing with a WHOLE . A fraction is an ordered pair of integer a&b, with b=/= 0, written a/b , the integer a is known as the numerator and the integer b is known as the denominator.

There are several models in which we can use to teach students how to find the answer to a problem dealing with integers. Such as Part to whole concept using the circle on the bottom as an example, whats the fraction of the figure shaded? 2/4 are shaded, that can be worked down to 1/2 of the circle being shaded. Below is a link for more additional information

http://www.helpwithfractions.com/math-homework-helper.html

In Class on Tues. 3/1 Amy introduced Decimals and Rational Numbers.When dealing with Decimals and Rational numbers you are to always keep in mind the place value of where the digits are located. A little tip to keep in mind is that any numbers to the right of the decimal point ALL have (ths) at the end of the place value.  Versus to the left having (ands,ed.etc)

Decimals: Any number written in base ten positional numeration can be called and considered a decimal
Rational Number:Any number that can be written in the form a/b, where b=/=0 and a and b are intergers, is what is called and considered rational numbers.Below is a link to a site to look into if you need additional help
http://cstl.syr.edu/fipse/decunit/opdec/opdec.htm

We learned how to write numbers in Expanded Notation for example
123.45= 1(100)+2(10)+3(1)+4(1/10)+5(1/100)
also in Exponential Notation
123.45= 1(10^2)+2(10^1)+3(10^0)+4(10^-1)+5(10^-2)

We also learned about place values.
Example 123.456
3 is in the ones place
4 is tenths place
5 is hundredths place
6 is in the thousandths place