Quandaries and Queries


Name: Keisha

Who is asking: Parent
Level: Elementary

I am helping my child with his homework. The worksheet we are trying to do ask the child to choose a number from inside of a circle and then one from inside of a triangle and use the number to build a fact family. The title of the worksheet is "Building a Fact Family House". I noticed that Silver Burdett Ginn,Inc. was the publisher of the book the worksheet came from so I was on the website trying to find an answer to my question. My question is "What is a Fact Family?"



Dear Keisha,

Thank you for your question. Let me begin by giving an example. The numbers 5,7, and 12 form a fact family. Notice that:


There are several ideas that we are trying to build when we introduce students to fact families. Here are some of them:

  1. Notice that 5+7=12 and 7+5=12, thus the first two equations
    illustrate that if we add two numbers in any order, we get the same answer.
  2. Notice that 12-7=5 and 7+5=12, so subtraction and addition are
    related. Similarly 12-5=7 and 5+7=12.
  3. Notice that 12-7=5 and 12-5=7, so if you subtract one of the
    members of the fact family from 12, you get the other.

You and your child can look for more relationships together. Fact families are really about building a conceptual understanding of how addition and subtraction work.

So, informally, you can think of a fact family as consisting of three numbers, two of which add up to the third.

If you are given two numbers, there are two possible fact families you can build. For example, if we are given 5 and 7, we can build the family 5,7, and 12 as above, or the family 2,5, and 7 since


Hopefully there will be something in the directions of your worksheet that will tell you if you should find the third member of the family using addition (ie add the two numbers (5+7=12)) or using subtraction (ie subtract the larger from the smaller (7-5=2)).

I hope this helps you with the worksheet your child was given, as well as gives you an idea of what sorts of relationships you and your child can observe as you look at fact families together. They're great for illustrating "patterns" in mathematics.

Take care,


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