# 2 Turn Around Fact Rule for Addition

The students have learned that in an addition equation, the two addends can be turned around and the sum will remain the same.

For example,  5 + 8 = 13   and   8 + 5 = 13

The students are very good at being able to demonstrate this rule; however, when they are shown variations, it becomes apparent that they do not internally understand the rule.  Don’t be fooled by how simple some of these might be.  Students who think they know this well, find out that they make simple errors.

Variation  I

(If I weren’t using a computer, I’d be able to use more interesting pictures than what you’ll see in the equations below , and in class, we have more fun with the symbols.)

I will put this on the board and ask for the turn around fact:

∆ + 7 = 23

Some students stare at me with a blank look on their faces.  Some try to solve for the triangle.  After I keep saying, “All I want is the turn around fact.”  Sometimes someone gets it; sometimes I have to show them the answer:

7 + ∆ = 23

They need to understand that in addition, the rule means:  switch the two items in the addend spots, NO MATTER WHAT’S THERE!

They pick up on it rather quickly and see it as a fun game.  Then I give them problems like this and ask them to tell me the turn around fact (answers are underneath):

√ + \$ = !          G + M = R          333 + 444 = 777       etc.

(\$ + √ = !)     (M + G = R)       (444 + 333 = 777)

Variation II

After they get really good at understanding that the turn around fact means to switch addends regardless of whether they are numbers or symbols, I throw this at them and suddenly we are sometimes back at square one:

What’s the turn around fact for: 8 + ____ = 10.

Some get it but others again think they are supposed to solve for the blank and tell me two.  Then I tell them, “The turn around fact is ____+ 8 = 10.  I didn’t want to know what goes on the blank.  I wanted the turn around fact.”

(Note to parents:  This might seem redundant, but it is getting them ready to manipulate equations when it is time to solve for the blank.  Later, when they see this:  _____ – 7 = 8, they will have learned to move the numbers around like this:  7 + 8 = _____ and then solve the blank.  But we’re getting ahead of ourselves.)

So then we practice the turn around facts for equations that simply have a blank in them.

_____ + 13 = 26              88 + _____ = 100             35 + _____ = 1,000

(13 + _____ = 26)         ( _____ + 88 = 100)        (_____ + 35 = 1,000)

Variation III

I will then put these on the board and ask for the turn around fact:

15 = 6 + 9               17 = _____ + 8               12 = 5 + _____

(15 = 9 + 6)           ( 17 = 8 + ____)            ( 12 = ____ + 5)

Yep, the students need to know what to do when they see the equal sign on the left.  This is also the time I begin to tell them that if they don’t like looking at an equation with the equal sign on the left, they may cross it out and put in on the right:

17 = _____ + 8    I tell them to do this:  17 = _____ + 8 = 17