Week Four.

Tuesday January 29th

Today in math class we did an activity out of our activity booklet. In this activity we were doing three diget addition and subtraction problems, at first with base ten blocks, then place value holders, then finally with paper and pencil. By using these three different ways to solve a problem, we were able to manipulate the ways that children go through the process of learning math problems.

First they need to have base ten blocks, where they can clearly see that 10 ones blocks, are equal to 1 tens block, and so on. The picture below illustrates the blocks that we used in the first activity.
 


In the first activity we rolled three dice to determine how many 'hundreds' we will have, then rolled two dice to find out how many 'tens' we would have, and so on. We had to do this for two three diget numbers.

Once we found out what numbers we were going to illustrate, we had to copy both numbers exactly with the base ten blocks. Making sure to not change 13 'tens' blocks into a 1 hundred block, and 3 tens blocks, that part comes later.

 

After you had both numbers laid out on the table, then you can manipulate the numbers to have the correct amount of numbers in each section, by not exceeding 10 blocks in one column.

Then it is a simple addition or subtraction problem from here, where you either add or subtract the needed manipulative. Doing addition or subtraction this way makes it easier for children to see what is actually happening with the numbers, instead of just having numbers written on a piece of paper.

 This is the final answer to the addition problem above, 571


The second activity that we did in class was the same type of activity only a step above the method of using the base ten blocks. In this activity instead of being able to see the relationship that 10 ones is the same as 1 ten, the manipulative that you are using are the exact same size for every place value in the problem.



Similar to the problem before, you pick two numbers then add or subtract them from one another. Only this time it is easier to lose track of your place values because you cant clearly see their relationship. You have three sections labeled ones, tens and hundreds, then place the two numbers that you are adding together in those slots by using the place value holder chips.

In this problem, the answer is 595.

The last activity that we did in class was one more step above using the place value holders. It is all done on paper with pencil, it is the traditional way of doing an addition or subtraction problem...

  634                        634
+120                      +120
  754                         700---- 600+100
                                   50----30+20
                                     4----4+0
                                 754


Thursday January 31st

Thursday in class we spent all class period going over the different ways that you can solve both addition and subtraction problems.

We learned that there are 5 ways to solve an addition problem. Those ways are illustrated as follows:

Traditional:

The traditional way of doing a subtraction problem is just what you would think, you stack the numbers and add them together up and down.

  59
+83
142

Decomposing:

The decomposing method is illustrated on a number line, where you 'hop' your way from one number to the other, using friendly numbers to figure out the answer.




Instructional/Partial Sums:

The instructional or partial sums method is a way of doing an addition problem by breaking up the numbers into ones and tens, and even hundreds if needed. By doing this the problem seems much smaller, and its easier to see how you got your answer.

  59
+83
  130---50+80
    12---9+3
  142

Compensating:

The compensating method is a way of solving a problem by rounding a single number in the problem to make it more friendly, then at the end, adding or taking away the amount that made it a friendly number to get your answer.

59+83= --------60+83= 143      143-1= 142

since we added one more then the problem asked to the number 59 to make it 60, we had to take one away from the answer that we got to set the problem back into balance.

Give and Take:

This method is giving part of one number to another to make it a more friendly number to work with.

59+83=

59+(1+82)=

(59+1)+82= (60) + 82= 142

We also learned that there are 6 ways of solving a subtraction problem:

Traditional:

 75
-42
 33

Partial Differences:

 75
-42
 30---70-40
   3----5-2
 33

 Decomposing:




Difference/Distance:

The difference between the decomposing method and the difference method is that the difference method can be seen as an addition problem that is done on the number line, where you start with the smaller number, and add up to your larger number finding the difference of the two which ends us being your answer.



Compensating:

75-42=?            75-45=30        30+3=33

Holy Shift:

This method is similar to the give and take method for addition.

75-42=

(75-2)-40=

73-40=33

In this method we are just shifting the problem to make it easier to solve. the numbers are different, but since we are trying to find the difference between the two numbers, we can move the numbers up or down and ultimately get the same answer.