Fact family
Fact Family in Grade 4 Saxon Math Intermediate 4 Chapter 1 shows students that three numbers can generate four related math facts — two addition and two subtraction. For the numbers 4, 7, and 11, the family is: 4 + 7 = 11, 7 + 4 = 11, 11 - 4 = 7, and 11 - 7 = 4. The two smaller numbers are the parts; the largest is always the whole. Students find the third member of a family when given two numbers (e.g., 6 and 15: subtract to find 15 - 6 = 9). Subtraction facts always start with the largest number. This reveals how addition and subtraction are inverse operations.
Key Concepts
Property A fact family is a group of three numbers that can be arranged to form four facts.
Example The numbers 3, 5, and 8 form a fact family: $3+5=8$, $5+3=8$, $8 5=3$, and $8 3=5$. For the numbers 5, 6, and 11, the fact family is: $5+6=11$, $6+5=11$, $11 6=5$, and $11 5=6$.
Explanation Think of a fact family like a little gang of numbers that always hang out together. Using just three numbers, you can write two addition and two subtraction problems that are all related. It is a great way to see how addition and subtraction are just reverse versions of each other!
Common Questions
What is a fact family in math?
A fact family is a set of three numbers that produce four related addition and subtraction equations. For 3, 5, and 8: 3+5=8, 5+3=8, 8-5=3, 8-3=5.
Write the four facts for the numbers 7, 9, and 16.
7+9=16, 9+7=16, 16-7=9, 16-9=7.
If two members of a fact family are 6 and 15, what is the third?
Subtract: 15 - 6 = 9. The three members are 6, 9, and 15.
Which number is always the starting number in subtraction facts?
The largest number (the whole) always goes first in subtraction: 11 - 4 = 7 and 11 - 7 = 4.
Why are fact families useful?
Knowing a fact family means knowing all four related facts automatically. If you know 4 + 7 = 11, you also know 7 + 4, 11 - 4, and 11 - 7.