Lesson 4:  Basic Addition (Part 1 of 2)

Many students, including older ones, have trouble understanding how basic addition works.  Sometimes this is because they learned the procedure, but never really learned why it worked.  Other times it's because they became used to doing every computation on the calculator.  It's very important to have a very clear understanding of how addition works.

Don't forget to watch the embedded YouTube video clip for this lesson at the bottom of the page.

To add two numbers together, all we really have to do is count.  If we want to add 3 + 8, we should start with the bigger number, 8, and then count up three more....9...10...11, and that is our answer.  It's important that you able to add small numbers quickly and easily.  The best way to practice this is with flashcards, either store-bought, or home-made.   

Many older students are permitted to use calculators on every exam, but if you have trouble doing very basic math in your head, you'll have a hard time figuring out if you made a mistake with your calculator, which is very easy to do. 

There is a trick that you can use to add two numbers such as 9 + 7.  You can increase the 9 to 10, and decrease the 7 to 6.  Make sure you can see why this does not actually change the problem, and why it is OK to do this.  Once you have 10 + 6, it's very easy to see that the answer is 16.  This trick works with adding, but not with other operations such as subtraction and multiplication, so be careful.  Try experimenting using objects as counters, to convince yourself that it's ok to move an items from one pile to another, and you'll still be adding up the same total quantity of items.

Adding two-digit numbers can be hard to do in your head.  There is a procedure for adding them, and it's important to understand how the procedure works, in addition to actually knowing how to use it.

Look at problem 1 below.  To add two, two-digit numbers, line them up one on top of the other.  Remember to line up the ones places and the tens places right on top of each other.  Always start on the right, which is the ones place.  In problem 1, we'll add 2 + 5, to get 7, and we'll write it below the line in the ones place.  Then we'll move left to the tens place.  We'll add 1 + 2 to get 3, and we'll write it in the tens place below the line.  The final answer is 37.  Make sure you understand what is happening.  We're adding two 1s and five 1s to get seven 1s.  Then we're adding one 10 and two 10s to get three 10s, which is 30.  Then we're adding our three 10s (30), to our seven 1s (7) to get 37. 

Take a look at problem 2.  First we will add the ones column, 8 + 5, but not we have a problem.  That equals 13, but we can fit two digits into one column.  We know that 13 has three 1s, so we can write a 3 in the ones column below the line.  But then we have one 10 left over.  To represent that, we write a small 1 at the top of the 10s column.  We call that "carrying the 1."  Now we'll add up the values in our 10s column, including the 1 that we carried.  Remember, the one that we carried is really 10.  It's the 10 part of the 13 that we got when we added the ones column.  We add 1 + 1 + 2, and we get 4 in our tens column.  The final answer then becomes 43. 

Continued in Lesson 4a

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