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)

Patterns and Problem Solving

Fibonacci Numbers
In the first chapter we covered in Math for Elementary Teachers, included Patterns and Problem Solving.  Something that was a reoccurring theme that the teacher Amy DelMedico went over was the patterns in our daily life or living things in nature.  When when we saw a picture of a  a Nautilis shell, or a sunflower, I would have never thought math.. or even patterns.  These patterns that occur naturally in nature are interrelated to Fibonacci numbers. Fibonacci numbers traditionally start with 1 and 1, each successive number can be obtained by adding the two previous numbers. 1,1,2,3,5,8,13,21..and so on. Amy Del Medico showed us a very cool video on Fibonacci numbers in class, the link will be listed below.

http://www.etereaestudios.com/movies/nbyn_movies/nbyn_mov_youtube.htm
(This movie was made by Cristobal Vila)

Some examples of the Fibonacci sequence in nature is a sunflower or a pine cone 

Example of Fibonacci Numbers in nature (Below)

Image: Brewbrooks Found At: http://www.google.com/imgres?imgurl=http://amazingdata.com


>A good Blog About Fibonacci Numbers is: Geometry and Nature
>Fun Game for Fibonacci Numbers (its a little tricky at first) http://www.yourdiscovery.com/games/play/fibonacci/




Pascal's Triangle
Another topic we reviewed in Math for Elementary Teachers is Pascal's Triangle. Pascals Triangle is very interesting and has a lot of different patterns. Pascal's Triangle is a triangular pattern of numbers that starts with 1 (in Row 0) and continues to row 1 with 1 and 1 (example below)

1

1              1

1              2              1

1              3              3              1

1              4              6              4              1

The top Row is 0

The second row is 1 

The third row is 2

and so on

the yellow highlight shows 1+1=2 and that is how that line is formed

the second line has 1 and two listed in blue and in the fourth line 3 listen in blue because 1+2=3.

I have highlighted a few just to show how the numbers in in the next line down are developed.

I never really looked at math in patterns, but when I do it seems to come a lot easier.  If you would have told me to try to figure out the next line in Pascals triangle in the beginning I would never have been able to.  But when breaking a big problem down into a smaller one it is much easier to understand it. It is crazy to think that nature and math is related at all.  

>A couple games to help finding patterns are :
Pattern Cracker
Preschool- Crazy Patterns
What Comes Next

I have found on YouTube a video to help finding sequences


I have learned that making connections with math and the real world make it a lot easier to understand and when you break big problems down in to smaller ones it is much simpler. With Fibonacci numbers and Pascals triangle when broken down you can find the next numbers  or sequence with simple addition.

Problem Solving

Something that we have just recently learned in Math for Elementary Teachers is a technique for problem solving. 

Polya's Four Steps to problem solving. (This can apply to more then just math)

Step One - Understanding the Problem

Ask yourself do you understand what is being asked?

If you do not know what a word means look it up, or ask your teacher to clarify further.

Step Two- Devise a Plan

In step two this is where you choose your strategy to solve the problem.

Step Three- Carry Out the Plan

This is the step in what you are doing.

Step Four- Looking Back

In this step of the process you review or evaluate your outcome.  This part involves more then just finding the answer, and this may take more then one time.

I have found that this process is very important in some problems I have encountered in math.  By making sure I understand what is being asked then I know that I am going to answer correctly (or I am at least on track).  When devising a plan I found it important to break the problem down into smaller parts and working from there (carrying out the plan). By looking back on what I have done I can see what I have and have not done correctly and what little mistakes I have made.  

Another important thing I learned from our teacher Amy Del Medico is, Never erase your work.  For example if you have a very long math problem with many steps and you get to the end of it and you do not get the right answer, if you do not erase your work you can look back at your work and see if you made a simple mistake. If you erase your work and you made a simple mistake you may be doing a lot more work then you need.

Me

Hi, My name is Brianna Harvey and I am taking Math for Elementary Teachers at Waubonsee Community College.  I am taking this course because it is a required course to both transfer and to get my associates degree in Special Education.  I love working with children and can not wait to start teaching.

To be completely honest I was really worried about taking this course because I am not the best at math.  As it turns out I am enjoying class so far, it is very hands on, which is different from any math class I have ever taken. When learning new concepts each step is broken down in the problem, and you are told why you are doing it- which helps me better understand a problem and better explain to others what should be done.

One of the assignments for this course is to make a blog, and another is a Inquiry Based Learning Project.

(I have never done a blog before this is my first one, so this is going to be an adventure on its own.)