This week in class we learned the different methods to solve addition and subtraction problems. It is important to allow kids to do a method that works best for them when teaching because everyone has  different way of thinking.

The Traditional method is the method for addition and subtraction that used to be taught. That method consists of simply stacking the two numbers and borrowing when need be. That is a complicated way to do numbers and especially for young kis who do not fully understand the concept of numbers yet.

The Partial Sums/ Instructional Algorithm works for both addition and subtraction and consists of adding or subtracting the tens and ones to break it down and make it more manageable.
For example, to solve a problem such as 26 + 44, we could use the associative property to make easier numbers that combine with each other better, such as  (20 + 40) + (6 + 4) = 70. For subtraction, a good example would be a problem such as the following ; 66 - 44 = (60 - 40) + (6 - 2).

The Give and Take method for addition takes parts of one number to combine it with another to make it a friendly number. An example of this is ; 26 + 14 = (26 + 4) +10.

To compensate means to make up for something after you made a mistake. Therefore, the Compensation Method means to round the problem to an easier and friendlier number and then add or subtract what you rounded to make it the proper answer. An example of this would be 48 + 16. To make this an easier problem, you can add 2 to 48, to round it to 50, and subtract two at the end. So,
50 +16 = 66, and then subtracting two would be the answer to 48 + 16, so, 64.

The last method for addition, and it works for subtraction too, is Decomposition. This is breaking the number up into different "hops" on a number line to physically jump to the proper answer. The diagram below is an example of this method. This is a simple example, because there could be bigger jumps than two, but the person completing the problem felt most comfortable jumping by 2's which is okay. The problem was 0 + 10 = 10.

Something that is similar to the method above, is finding the distance between the two numbers, so instead of jumping how many is subtracted, you jump to the lower number, or the higher number, whichever is preferred. 

These are the methods for addition and subtraction that we learned in class. 

UNTIL NEXT TIME!

Week 3

Week three of class consisted of finishing up with a few rules ad complications with venn diagrams, and starting with addition and subtraction.

When we were working on venn diagrams on Tuesday, we added a third circle to the equation.

http://www.answers.com/topic/venn-diagram

The diagram above is a good example of what each section represents. And like last week, we were finding the union, intersection, and compliment of three factors. As a refresher, the union of the equation would be all of the circles. The intersection of A and B is AB, of A and C is AC and of B and C is BC. The intersection of all three factors is the place in the middle, represented by ABC. These types of problems can be tricky, and it is difficult to figure them out without shading. A good website that allows you to do a few given problems, and is also a good reference for practicing shading, is 

http://nlvm.usu.edu/en/nav/frames_asid_153_g_2_t_1.html?open=instructions&from=search.html?qt=venn

Thursday's class period was chalked full of properties and important things to remember. I will define these terms and properties below: 

Set Problem - A set problem gives distinctly different variables of the problem. 

     EX: Tyler has 2 small chocolate doughnuts and 3 small powdered doughnuts for breakfast. How

     many did Tyler eat altogether?

A problem like this is going to confuse a young student because they will not make the connection that the two different kinds of doughnuts should be added. 

Measurement/Number Line Problem - This problem is like the above problem although it does not make the distinction between the two variables being added together. 

     EX: Tyler has 2 small doughnuts for breakfast. His mom lets him have 3 more small doughnuts.    

     How many did Tyler eat total?

There are three properties of addition. These properties are very important to know, and is very important for teachers to focus on explaining why things are the way they are instead of simply making students memorize facts. 

Commutative Property - a + b = b + a, or, 6 + 4 = 4 + 6

No matter the order, things will add up to have the same answer. 

Associative Property - a + (b + c) = (a + b) + c, or, 2 + (8 + 4) = (2 + 8) + 4 

This property is grouping together the parts of the problem that will look easier in your head, such as making a 10 with the 8 and 2, instead of a 12 with the 4 and 8. It is OK to move the parentheses. 

Identity Property of 0 -  a + 0 = a, or, 8 + 0 = 8

Adding zero to a number will not change the number, Therefore, the sum will be the number that is being added to zero. 

Teaching these properties as well as relationships of numbers such as knowing which numbers are one of two more or less than any given number, what it takes to reach a 5 or a 10 from a number, or what the double of a number is, is very important for students success.

Problem Solving

The problems that we worked with in class this week were word problems. We are learning how to solve problems in the most comfortable way for ourselves. Solving word problems may be easiest for someone through making a list, drawing a picture, or even by doing some algebra.

An example of a word problem that we worked on was by finding the correct order of the cars in a race, by taking each of the clues and applying them to the cars. The clues told how far apart, in seconds, certain cars were and they did not all connect to each other. The first way that I solved it was by drawing a picture. 

This method worked, although it was time consuming. After we discussed different methods to solve this problem, I adapted a new way that I liked better and was more efficient. 

The student who used this method explained that they used hashmarks to keep track of the second in between each car. I think it was a great method to use. It was a great example of how much we can learn from each other through discussing problems and methods.

Another concept that we learned on Thursday of this week was the relationship of sets. The Union of a set (represented by a U) means to combine the two sets together as one. While the Intersection of a set (represented by an upside down U) means to only count the part that overlaps. These are shown in the pictures below.

We will learn more about this next week! That is all for this week!

Math for Everyone!

In the first week of Math 251, or Fundamentals of Elementary Math, we learned how there are many ways to approach a math problem. Everyone has different methods, and none of them can be considered to be wrong!

One way to show how everyone's brains work differently when tackling a math problem is to give the class a simple problem, such as 

66-29 = ?

and ask the class to complete the problem in their head, and then write their technique down on paper. This is how we approached this on the first day of class. After we did this, we split into different groups according to how we did it, and a representative from each group wrote on the board how the problem was completed. There were so many different ways! Eventually, we learned about many different methods, such as stacking, hopping, or finding the difference by tens and ones. 

Another thing we learned on Thursday of this past week, was that drawing pictures is a perfect way to solve math problems, and is in fact, encouraged. The problem that we were given was something of the following : 

"Lizzie collects lizards and beetles! She has 8 creatures in her collection so far, and a total of 36 legs. As you can see, below, lizards have 4 legs, and beetles have 6 legs. How many of each critter does she have?"

When I first read the problem, I was trying to think of some algebraic way of solving this word problem. Unfortunately, it has been a while since my algebra skills were in use, so that didn't work. The next thing that I thought of was to use the simplest way possible, which was to draw out the creatures and add legs to them. My work is shown below :

As it shows in my work, I added at least 4 legs to each "creature" because each of them have at least 4. That was the minimum. And then I still needed to add 4 legs to reach 36, therefore, I added them to the other creatures one at a time, to reach 6, making it a beetle. After using this method, I learned that Lizzie currently has 6 lizards, and 2 beetles in her collection!

That is all for my first blog of the unit!! I'm glad we were all able to learn so much during the first week!