Algorithm's for Addition

Different Algorithm's for Addition

>Left to Right
>Partial Sums
>Right to Left (the traditional way of doing addition)

Left to Right

-Advantages to doing addition left to right: you also read left to right and do division left to right.
  Example:

In this problem you would start with 4+9 and then got to 7 +6, which equals 13. You would list the 3 under 7 +6 and the 1 under the 3 from 4 +9. after completing the problem from left to right, you will have another addition problem and after adding those numbers you will come to the total from the original problem.  I like this way because I have found when tutoring the little boys I nanny they for get to add the 1 from the carried number and they always try to start from the left and go right.  I feel they tend to try to start from the left and go right because that is the way they were taught to read, so it would make sense to do math that way as well.
Still having problems? Here is a video that might be helpful:

 

Partial Sums

Another Algorithm for addition is the Partial Sums Method. I personally really like this method because you get to see what each product of the two numbers you are adding and what the true place value is.   This is something that a lot of us adults just do, we don't really think about the place value of each digit when adding.  when we say we have $740, we ( or at least I ) think of the entire amount of the money, we don't really think about I have 4 ten dollar bills and 7 one hundred dollar bills.  With this method of addition it really breaks down each addition process.

 When adding you start in the tens place and then go hundreds, thousands, and so on.  Since 6+7 is 13 you put it in the tens place. Then you go to 7+6 is 11, so you put it in the hundreds place making it 110 in the second line, and so on. 

This video does a great job of explaining the traditional method and the partial sums method.

Math Tube

Right to Left 

This is the kind of addition we are use to. This is went you add from right to left and carry the number above to the next place value.

Functions with arrow diagrams

After doing homework and reviewing for our test this past week I have found a few easy ways of remembering what functions are or are not.

A function  is two sets and a rule that assigns each element of the first set to exactly one element in the second set.

Domain is is the input and the Range is the output.

Function (picture below):

When it is not a function, is when the domain has two outputs. (Picture below is not a function)

Since 5 people have red shits and 5 people have white shirts, it is not a function because the Domain of 5 has to out puts.
Another example of a non function is a father to his children
A father can have 2 or more children, so the father being the domain, would make it a non function. However if the father was in the range and the fathers children what in the domain, it could be a function since each child would only have one output.

Awesome Function Game: Cyberchase-What Is My Function

Venn Diagrams

Venn Diagrams are used to represent sets, and what the do or do not have in common. There are several ways in which sets can be related to one another.  Sets may have no common elements (which are called disjoint) or all elements in common (which are equal sets); or one set may be contained in another (which are subsets.)
 (Bennett, Burton, Nelson)

The U in the picture of the Venn Diagram above stands for universal; which mean everything that is contained in that diagram.

A and B are the two sets that are contained in the universal set.

The yellow part in this picture stands for what elements A and B share. The blue in the picture is where all the elements that do not fit into A or B go, since the are still part of the Universal Set.

-Example:

U = {0,1,2,3,4,5,6,7,8,9,}

A = {1,2,3}

B = {3,4,5,6}

In the picture above  the numbers 1 and 2 will be in the red section of the Venn diagram. The numbers 4,5,6, will be listed in the orange section of the Venn Diagram, and the number 3 will be listed in the yellow section of the Venn Diagram since both sets A and B share this number.

all the other numbers ( 0, 7, 8, 9) will be listed in the blue portion since they do not belong to either set A or B but are part of the Universal Set. 

When trying to find what numbers go where I find it easiest to draw out the problem. Making a picture makes you able to see what visually goes where.  

Citation:

Bennett, Albert B., Laurie J. Burton, and Leonard T. Nelson. Mathematics for Elementary Teachers: a Conceptual Approach. Dubuque, IA: McGraw-Hill, 2010. Print.


GAMES FOR VENN DIAGRAMS:
Interactive: Venn Diagram
Venn Diagrams
Illuminations: Shape Sorter
Video for Venn Diagrams ( A little more complex, this is very similar to what we were actually learning in my math class)