Fact Families to 20 - First Grade Mathematics

Just as single-digit numbers live in fact family houses, teen numbers have their own fact families within 20! A fact family within 20 connects three numbers: a whole that is between 11 and 20, and two single-digit parts that add up to that whole. Mastering these fact families gives you complete fluency with addition and subtraction facts up to 20. In this chapter, you will build fact families for teen numbers, explore how parts and wholes interact, and see how one known fact unlocks three others.

The Structure of a Teen Fact Family

A teen fact family consists of four related equations: two addition equations and two subtraction equations.

The Fact Family House for 7, 8, and 15:

              /\
             /  \
            / 15 \       <- Whole (15)
           /------\
          / 7    8 \     <- Parts (7 and 8)
         +----------+
         | 7 + 8 = 15|
         | 8 + 7 = 15|
         | 15 - 7 = 8|
         | 15 - 8 = 7|
         +----------+

The Four Equations:

Addition Fact 1: Part + Part = Whole (7 + 8 = 15) Addition Fact 2 (Turn-Around): Switch parts! (8 + 7 = 15) Subtraction Fact 1: Whole - Part = Other Part (15 - 7 = 8) Subtraction Fact 2: Whole - Other Part = First Part (15 - 8 = 7)

Subtraction Always Starts with the Teen Number

Remember the golden rule of subtraction in a fact family: subtraction MUST begin with the whole!

Correct vs. Incorrect Subtraction:
Correct:    15 - 8 = 7   (Starts with the Whole!)
Correct:    15 - 7 = 8   (Starts with the Whole!)
INCORRECT:   7 - 8 = 15  (NEVER start subtraction with a small part!)

Why Subtraction Starts with the Whole

The whole of 15 represents the entire collection. You take away one part (8), and the other part (7) is what remains.

Teen Doubles Fact Families

When a teen number is made by doubling a number, the fact family has only two equations.

The Doubles Fact Family for 16 (8, 8, 16):
Whole = 16, Parts = 8 and 8

Addition Equation:     8 + 8 = 16
Subtraction Equation: 16 - 8 = 8

Other Teen Doubles:

Double 6: 6 + 6 = 12 and 12 - 6 = 6 Double 7: 7 + 7 = 14 and 14 - 7 = 7 Double 9: 9 + 9 = 18 and 18 - 9 = 9 Double 10: 10 + 10 = 20 and 20 - 10 = 10

Practice Exercises

Exercise 1: Write the complete four-equation fact family for the numbers 6, 8, and 14.

Exercise 2: Write the complete fact family for the numbers 9, 4, and 13.

Exercise 3: Write the two equations that belong to the fact family for 7, 7, and 14.

Exercise 4: Look at these equations: 5 + 9 = 14, 9 + 5 = 14, 14 - 5 = 9. What fourth equation is needed to complete the fact family?

Solutions and Explanations

Solution to Exercise 1: The four equations for the fact family 6, 8, 14 are: 6 + 8 = 14 8 + 6 = 14 14 - 6 = 8 14 - 8 = 6

Solution to Exercise 2: The four equations for the fact family 9, 4, 13 are: 9 + 4 = 13 4 + 9 = 13 13 - 9 = 4 13 - 4 = 9

Solution to Exercise 3: The two equations for the doubles family 7, 7, 14 are: 7 + 7 = 14 14 - 7 = 7

Solution to Exercise 4: The missing fourth equation is 14 - 9 = 5.