Two Digit Subtraction

Today in my Mathematics, I learned about algorithms for subtraction. I learned that there are 2 methods and then 2 alternative methods for those students who might be a little advanced. Just like with addition, there are Visual and Expanded Notation.

With the visual for subtraction, again, you can use base-ten blocks.I'm starting to realize that with elementary students, base ten blocks are going to be my best friend when it comes to teaching to math.

So an example of visualization would be, 24
                                                            -17

 With base ten block I would write it as, 

Expanded notation is when you write the equation in words. For example,
                                           24
                                          -12

I would write that as:  2 tens and 4 ones
                               -1 ten and 2 ones
Which equals:             1 ten and 2 ones

After this step, I would write this problem:   
                                        1x10 + 2x1=
                                        10  + 2=   12

    
  http://math.about.com/od/addingsubtracting/ss/2DigitSubNR.htm      

Learning Subtraction with Story Problems

After addition, students learn to subtract. So naturally in my class, we learn addition first, and then subtraction. With subtraction, I was taught there are 3 visualizations. Take-away, Comparison, and Missing Addend. In my post this evening, I am going to give you the 3 basic steps and then give you examples using story problems. I have also created videos for each example.




Take- away, is when one set is getting smaller or reducing. For example, Joseph has 8 pens. He gives 3 pens to Larry. How many pens does Joseph have now? 8 pens -3 pens = 5 pens

Missing addend, is when you visualize one set getting bigger. I would ask my students the question "How much more..". For example, Tiffany wants to purchase a bottle of nail polish. She has 3 dollars, but the nail polish costs 5 dollars. How much more money does Tiffany need?

3+?=5

Comparison, is when you compare 2 sets and see which is larger. For example, John has 4 CD's. Peter has 1 CD. How many more CD's does John have than Peter?

The cool thing is that I tried the Take-away method, with my boyfriend's son. He is 3 years old. Last night I put 3 dollars in front of him, and said "If you have 3 dollars, and I take away 2, how many dollars do you have left?" He looked at the money, count it and said "1". Then I asked, "If you have one dollars and I give you 2, how many dollars do you have now?" Again he would look at the money, count it and said "2". Pretty cool that with visual aids, I was able to teach a 3 year old to recognize that he was either gain or losing an object.

Two Digit Addition

Last week in my Mathematics for elementary teachers, we learned about addition and story problems. We also learned about two-digit addition, using algorithms. When I hear the term "algorithm", it freaks me out, I think of this long, drawn out equation that's going to take me 15 steps to solve. But that's not it at all. I learned that an algorithm is just another word for method. The are 4 different algortihms for addition that I learned.

The first being visual.  The concept of addition, with carrying, can be shown visually by using Base Ten Blocks.

The second, is Expanded Notation. Expanded notation is basically just writing out the problem with words. For example:            
                                  13
                                +24   

I would write that as:  1 ten and 3 ones
                               +2 tens and 4 ones
Which equals:             3 tens and 7 ones

After this step, I would write this problem:     
                                        3x10 + 7x1=
                                        30  + 7=   37

Another algorithm for addition, is called Standard Algorithm, which is the long way to do the shortcut.
For example:           15
                             +46

So first, I would add 5+6, which equals 11. And write it like this:
                             15

                           +46
                             11=9+6

Then, I would take the next set of numbers and add, but since the next set of number  are in the "tens" place value, I would write it as 10+40, which equals 50, and I would write it the same way as in the last step: 
                              15

                            +46
                              11=5+6
                              50=10+40

Then, I would just add 11+50, to get my answer of 61.
                              15

                            +46
                              11=5+6
                              50=10+40
                              61

The last algorith, is called Standard Algorithm. Which is just doing addition the "easy" way, no steps just taking 14+21= 35. Plain and simple.

I have provided a link to a website that will help children in doing addition.
http://www.dositey.com/addsub/add5a.html

Learning Addition with Story Problems

In my class, Mathematics for Elementary Teachers, I have been learning about story problems for addition. I am learning there are two different ways to approach story problems with addition, the first being Unite Sets, and the second being Counting Forward.  Even though there are two different ways, the steps to getting the students to understand and answer the problems are the same. There are four steps.

1. Thinking about the problem.
2. Representing the Problem.
3. Solving the problem. 
4. Write the numeric (addition) problem.  

Uniting sets, is used to add two different sets together. For example, Joseph has 4 pennies that he got from the bank. Kelly has 3 pennies that she got from her mother. They both put their pennies in a bowl. How many pennies are in the bowl?

Another way to use addition with a story problem, is to Count Forward. For example, Amanda has 2 pennies. While cleaning, she found 3 more pennies. How many pennies does Amanda have now?

I've also included a link to a poster that can help children with solving story problems.


http://www.abcteach.com/free/p/poster_strategiesforwordproblems.pdf

Service Learning

In my class, I was asked to participate in 15 hours of service learning in a classroom at a school. Most of our time must be spent inside a math classroom or a math setting like tutoring. My objective is to be able to make a connection  between what I am taught in class, and what I will doing in my own classroom once I become a certified teacher.  I was given this assignment on the first day of class.

This has been a hard assignment for me because in order to do service learning in classroom, you have to have a fingerprint clearance card. No problem. Well, the problem is that the card is $80 for Education students and that it takes 6-8 weeks to be processed and sent back. Well, a person such as myself I don't really have time to sit around and wait for a clearance card when I'm on a time crunch.

The past few weeks I have been a little stressed out, trying to find a school that doesn't require fingerprinting. I emailed about nine different principles in the Gilbert Public Schools district. I thought "OK, since I have emailed nine different schools, I have hear something." My Education teacher told me that Gilbert does not require fingerprinting, so I thought I was going to be a shoe-in and that I would be doing service learning by last week. The following day, my teacher then again told me that an "incident" had happened and now Gilbert requires all persons to be fingerprinted. Great!!

I was back to square one. I decided I was going to do the same thing but with Mesa School District. I decided I was going to email, again, at least nine principles. And I did. Within the hour I had received a few emails back but all of them stated that I needed to bring in my fingerprint clearance card. I thought to myself that I was going to be fail both of my courses that required service learning because I couldn't get place. Then the clouds opened up, and a Ms. Carey, from Adams Elementary in Mesa, called me on the phone and told me that she would love to have me in her classroom and that she couldn't wait to have an extra pair of hands!! I was ecstatic! I am so very happy that was persistent and didn't give up. I start this Wednesday I and I cannot wait to put my skills to work, and help her classroom full of 5th graders!! Wish me luck!!

Base-Ten What Now?

Last week, my teacher introduced my fellow classmates and me to classmates a little something called "bases". She told us that we have been doing base ten our entire lives and to not worry. What did I do? I worried. I had no idea what she was talking about, I was thinking "OK, so we are going to multiply numbers by 10". Nope. Wrong. Let me explain. First, you have to start out by understanding number systems. Our number system relies on 10 digits-0,1,2,3,4,5,6,7,8,9. The written symbols for these digits, like 3 or 4, are numerals. A numeration system, is a collection of properties and symbols agreed upon to represent numbers systematically. The numeration system that we use today, relies on two properties: All numerals are constructed from the 10 digits;  Place values are based on powers of ten, the number of digits in the number base of the system. Confused yet? Ya I was too, but let me break it down.

Place value assigns a value to the digit depending on its placement in a numeral. For example: 

So, to find the value of a digit in a whole number,we multiply the place value of the digit by its face value. For example in the numeral 3647, the 3 has place value"thousands", the 6 has a place value"hundreds", the 4 has a place value "tens" and the 7 has a place value "units". The easiest way I've come to figure this out, is to use base-ten blocks. With base-ten blocks, a student can get a better understanding of place value and adding and subtracting multi-digit numbers. A set of base-ten blocks, consists of units(one), longs(tens), flats(hundreds), and so on and so forth.

Once I figured out what place value and digits were, it was really pretty simple to work out the rest. we are still working on bases in class. I understand whats going on, and I hope that after this you do too!