Fact Families

​Hi friends,

     How are you today?  I think of math as a cool puzzle.  In most puzzles, there are only a right way and a wrong way to put the puzzle together. Yet, with math, the puzzle pieces can go together in a variety of ways and still be right.  Teaching fact families once students know how to count and start learning to add is a great way to show them that math can be a cool puzzle.

     There are fact families for addition and subtraction as well as multiplication and division.  However, right now, I am only addressing the fact families for addition and subtraction. I believe the skill should be taught in addition and subtraction.  Yet, I think it should be reinforced in multiplication and division.  

     Fact families are four closely related math statements.  To me, it shows that numbers can be manipulated to make them easier to solve or explain.  This may not make much difference in the early years of simple addition and subtraction. However, in later years during more difficult problems and algebraic equations, this skill will come in handy.
 
     Let’s look at a sample fact family: 2+3=5, 3+2=5, 5-2=3, 5-3=2
 
These four equations use the same three numbers. There are two addition equations and two subtraction equations.  The first two equations shows that it doesn’t matter which order you add two numbers the answer is still the same.  This is also known as the commutative property.

     Fact families help you to know more than you think you know.  For example, if you know that 2+3=5, you also know that 3+2=5. If you know that 2+3=5, you also know that you can “undo it” by saying that 5-3=2.  And, if you know that 5-3=2, you can also switch the order of the numbers you “take away” to make 5-2=3.

     Attitude can make a difference as to whether students find this information to be “more that they HAVE to remember” or “more that they GET to know.”

     Sometimes adding silly parts to a lesson make it more enjoyable to students. Maybe start off by asking, if I put two purple and pink polka-dotted pigs and Johnny puts three purple and pink polka-dotted pigs in a pile and we add them up, how many purple and pink polka-dotted pigs do we have all together?  (Yes, five. That is right.) If we take them back and then Johnny puts his three purple and pink polka-dotted pigs in the pile first and then I put my purple and pink polka-dotted pigs in the pile second, then how much will we have all together? (Yes, five.  That is right.) So, does it matter who puts their purple and pink polka-dotted pigs in the pile first?  Does the number of purple and pink polka-dotted pigs that we have all together change in any way by which order we put them down?  (No, that is right.)  It is the same with adding numbers.  It doesn’t matter if we add 2+3 or 3+2 because the answer is still 5. Then, you can go through the same process, showing that it doesn’t matter in which order you pick up your purple and pink polka-dotted pigs, because the same three numbers are being used.  You are just “undoing” what you did when you put them down.  You can then relate the picking up of the purple and pink polka-dotted pigs to subtraction.

     Make it a game.  Have students come up with the objects that are being put in the pile and picked up again. Ask them to choose silly objects, fun objects, dull objects, sharp objects, etc.  Relate them all back to numbers.  Have the students to choose the numbers, count them, and add them too. Ask the students to write and/or draw the math equations that make up their fact families.

     The idea is to not only teach the important skill of fact families, but to also show students that math doesn’t have to be difficult and boring.  The idea is to show students math can be helpful and exciting as well.  It also gives you as a teacher to role model to students that the right attitude matters.

Now, it is your turn.
     Do you teach fact families?  How do you introduce fact families?  I would be interested in your thoughts.  Please, leave a comment.
     Also, if you find value in the Education Blog by DUO Inspirations, please consider signing up below.  Thank you.

---

...