Practice fact families with this educational math worksheet designed for elementary students.

Problem Overview:

The task involves completing "fact families" for given groups of numbers. A fact family is a set of related addition and subtraction (or multiplication and division) equations that use the same three numbers. The goal is to fill in the missing equations for each group of numbers.

Steps to Solve:

1. Understand the Structure of a Fact Family:
- For addition and subtraction, if you have three numbers \(a\), \(b\), and \(c\) such that \(a + b = c\), then the fact family includes:
- \(a + b = c\)
- \(b + a = c\)
- \(c - a = b\)
- \(c - b = a\)
- Similarly, for multiplication and division, if \(a \times b = c\), then the fact family includes:
- \(a \times b = c\)
- \(b \times a = c\)
- \(c \div a = b\)
- \(c \div b = a\)

2. Complete Each Group:
- For each group of numbers, identify the relationships and fill in the missing equations.

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Solution:

#### Group 1: Numbers 9, 4, 5
- Fact Family:
- \(9 - 4 = 5\)
- \(9 - 5 = 4\)
- \(4 + 5 = 9\)
- \(5 + 4 = 9\)

#### Group 2: Numbers 6, 7, 13
- Fact Family:
- \(6 + 7 = 13\)
- \(7 + 6 = 13\)
- \(13 - 6 = 7\)
- \(13 - 7 = 6\)

#### Group 3: Numbers 3, 8, 11
- Fact Family:
- \(3 + 8 = 11\)
- \(8 + 3 = 11\)
- \(11 - 3 = 8\)
- \(11 - 8 = 3\)

#### Group 4: Numbers 6, 7, 1
- Fact Family:
- \(6 - 7 = -1\) (This is not a typical fact family scenario since it involves negative numbers. Assuming positive integers only, this might be an error or special case.)
- \(7 - 6 = 1\)
- \(6 + 1 = 7\)
- \(1 + 6 = 7\)

#### Group 5: Numbers 2, 9, 11
- Fact Family:
- \(2 + 9 = 11\)
- \(9 + 2 = 11\)
- \(11 - 2 = 9\)
- \(11 - 9 = 2\)

#### Group 6: Numbers 2, 3, 5
- Fact Family:
- \(2 + 3 = 5\)
- \(3 + 2 = 5\)
- \(5 - 2 = 3\)
- \(5 - 3 = 2\)

#### Group 7: Numbers 1, 3, 4
- Fact Family:
- \(1 + 3 = 4\)
- \(3 + 1 = 4\)
- \(4 - 1 = 3\)
- \(4 - 3 = 1\)

#### Group 8: Numbers 12, 2, 10
- Fact Family:
- \(12 - 2 = 10\)
- \(12 - 10 = 2\)
- \(2 + 10 = 12\)
- \(10 + 2 = 12\)

#### Group 9: Numbers 10, 5, 5
- Fact Family:
- \(10 - 5 = 5\)
- \(5 + 5 = 10\)
- \(5 + 5 = 10\)
- \(10 - 5 = 5\)

#### Group 10: Numbers 6, 3, 9
- Fact Family:
- \(6 + 3 = 9\)
- \(3 + 6 = 9\)
- \(9 - 6 = 3\)
- \(9 - 3 = 6\)

#### Group 11: Numbers 4, 2, 6
- Fact Family:
- \(4 + 2 = 6\)
- \(2 + 4 = 6\)
- \(6 - 4 = 2\)
- \(6 - 2 = 4\)

#### Group 12: Numbers 5, 7, 12
- Fact Family:
- \(5 + 7 = 12\)
- \(7 + 5 = 12\)
- \(12 - 5 = 7\)
- \(12 - 7 = 5\)

---

Final Answer:

\[
\boxed{
\begin{array}{l}
\text{Group 1: } 9 - 4 = 5, 9 - 5 = 4, 4 + 5 = 9, 5 + 4 = 9 \\
\text{Group 2: } 6 + 7 = 13, 7 + 6 = 13, 13 - 6 = 7, 13 - 7 = 6 \\
\text{Group 3: } 3 + 8 = 11, 8 + 3 = 11, 11 - 3 = 8, 11 - 8 = 3 \\
\text{Group 4: } 6 + 1 = 7, 1 + 6 = 7, 7 - 6 = 1, 7 - 1 = 6 \\
\text{Group 5: } 2 + 9 = 11, 9 + 2 = 11, 11 - 2 = 9, 11 - 9 = 2 \\
\text{Group 6: } 2 + 3 = 5, 3 + 2 = 5, 5 - 2 = 3, 5 - 3 = 2 \\
\text{Group 7: } 1 + 3 = 4, 3 + 1 = 4, 4 - 1 = 3, 4 - 3 = 1 \\
\text{Group 8: } 12 - 2 = 10, 12 - 10 = 2, 2 + 10 = 12, 10 + 2 = 12 \\
\text{Group 9: } 10 - 5 = 5, 5 + 5 = 10, 5 + 5 = 10, 10 - 5 = 5 \\
\text{Group 10: } 6 + 3 = 9, 3 + 6 = 9, 9 - 6 = 3, 9 - 3 = 6 \\
\text{Group 11: } 4 + 2 = 6, 2 + 4 = 6, 6 - 4 = 2, 6 - 2 = 4 \\
\text{Group 12: } 5 + 7 = 12, 7 + 5 = 12, 12 - 5 = 7, 12 - 7 = 5 \\
\end{array}
}
\]