Writing Fact Families
Writing fact families is a Grade 4 skill in Saxon Math Intermediate 4 Chapter 2 that shows how three related numbers connect through two addition facts and two subtraction facts. For numbers like 6, 9, and 15, the four facts are: 6 plus 9 equals 15, 9 plus 6 equals 15, 15 minus 6 equals 9, and 15 minus 9 equals 6. The largest number is always the sum in addition facts and the starting number in subtraction facts. Understanding fact families builds fluency with inverse operations and helps solve for unknown values.
Key Concepts
Property Any set of three related numbers can form a "fact family" with two addition facts and two subtraction facts. For the numbers 9, 7, and 2, we have $7+2=9$ and $9 2=7$.
Examples Using 8, 5, and 3, we can write the addition facts $5 + 3 = 8$ and $3 + 5 = 8$. Using the same numbers 8, 5, and 3, we can write the subtraction facts $8 5 = 3$ and $8 3 = 5$.
Explanation Think of three numbers like members of a family—they are connected! You can arrange them in different ways to tell two true addition stories and two true subtraction stories. The largest number is always the result for addition and the starting number for subtraction.
Common Questions
What is a fact family in math?
A fact family is a group of four related equations using three numbers—two addition facts and two subtraction facts. For example, using 5, 8, and 13: 5+8=13, 8+5=13, 13-5=8, 13-8=5.
How do I write the fact family for 6, 9, and 15?
The two addition facts are 6+9=15 and 9+6=15. The two subtraction facts are 15-6=9 and 15-9=6.
Which number is always the starting point in subtraction facts within a family?
The largest number (the whole or sum) always starts the subtraction facts. You subtract one of the smaller parts to find the other part.
How do fact families relate to inverse operations?
Fact families show that addition and subtraction undo each other. Knowing 6+9=15 means you automatically know 15-9=6 and 15-6=9.
What is the most common mistake when writing fact families?
Starting a subtraction fact with a small number, like 6-15. In a fact family, subtraction always starts with the largest number.