Addition without the Confusing Rules

How to Teach Addition without the Confusing Rules

In this article, I’ll discuss how to teach addition with and without regrouping or renaming. Second grade math usually involves two digit as well as three digit addition. I clearly remember that this is where my daughter had to apply her understanding of the ones place and tens place. It quickly became clear that that she didn’t really get it. We fixed this by going back and playing a lot of place value games. In the mean time, we worked on a math hack I discovered on Mental Math Secrets (see below). This is something I wish I had learned earlier in school.

How to Teach Addition Without Regrouping or Renaming

Traditionally, when teachers teach two digit addition, they have you add the numbers in the ones column first.  If the result is 9 or less write it in the ones column. Then, add the numbers in tens column.  If the result is  nine or less write it in the tens column.

However, the strategy of the math hack is to add the numbers in the tens column first. Second, we added the numbers in the ones column. The reason this works so well is this uses a concept students already know.  Using the numbers above, 52 is equal to 50 plus 2.  Also, 23 is equal to 20 plus 3. Therefore, the addition follows 50 plus 20 which is 70. Then 70 plus 2 which is 72. Finally, 72 plus 3 which is 75.

My daughter tends to take a short cut.  She adds 52 plus 20 which is 72.  Then, she adds 72 plus 3 which is 75.  The advantage of this is she can do this in her head and she’s pretty fast at it.

How to Teach Addition With Regrouping or Renaming

Traditionally, when teachers teach two digit addition, they have you add the numbers in the ones column. If the result is 10 or more, the result is split into two columns. Part of the result goes into the ones place. The second part is carried over to the tens column. My daughter really did not get this!

When we switched to Mental Math Secrets, it completely opened up a new world for her. Now, she didn’t need to understand why sometimes you carry and sometimes you don’t.  She could add numbers that she already understood. The second advantage of mental math secrets is that it does not necessarily depended on a pencil and paper.

In the problem above, the addition is 40 plus 20 which is 60. 60 plus 3 is 63, 63 plus 9 is 72. So, how did my daughter know that 63 plus 9 is 72? We spent a lot of time playing games about numbers that add to 10. First she goes up to the nearest 10 which would be 70.  She explains that 63 plus 7 is 70.  Then she knows she has 2 left over.  Then, she adds 2 more.  Understanding numbers that complement each other to sum to 10 is key to understanding this simple math hack.

My daughter tends to make a short cut out of this math.  She adds 43 plus 20 which is 63.  Then she adds 63 plus 9.  First, she goes up to the nearest 10 which would be 70.  Therefore, 63 plus 7 is 70.  She still has 2 more left.  So, she adds 70 plus 2 which is 72.  Even though I think I’m explaining how to teach addition, she teaches me something all the time.

Addition Game

At our house, we use a game similar to Chutes and Ladders, but we call it the Addition and Subtraction Treasure Trail. In this game, I lay out a number of flash cards (usually 10) in a snake like pattern on the floor. I make the flash cards so that I’m sure she can answer the math question. The answer is on the back of the card, and she can check herself. Every few cards I put a treat on the card. These treats can be toys or snacks. Needless to say, I never have to motivate her to do this game. I try to use it toward the end of the week when she’s starting to get a little tired. She does the math using the method above, and she doesn’t need to write anything down to get to the right answer.

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