Fact family triangles worksheet for practicing addition and subtraction relationships.

Problem Explanation:

The task involves completing "Fact Family Triangles," which are sets of related addition and subtraction equations using three numbers. Each triangle provides a total (sum) at the top and two other numbers on the sides. Using these three numbers, you need to create four equations: two addition equations and two subtraction equations.

General Approach:

1. Identify the Numbers: The top number is the sum, and the two side numbers are the addends.
2. Write Addition Equations:
- Add the two side numbers to get the sum.
- Reverse the order of the addends for the second addition equation.
3. Write Subtraction Equations:
- Subtract one addend from the sum to get the other addend.
- Subtract the other addend from the sum to complete the set.

Solution for Each Triangle:

#### a.
- Numbers: Top = 8, Side 1 = 2, Side 2 = 6
- Equations:
- \( 2 + 6 = 8 \)
- \( 6 + 2 = 8 \)
- \( 8 - 2 = 6 \)
- \( 8 - 6 = 2 \)

#### b.
- Numbers: Top = 17, Side 1 = 12, Side 2 = 5
- Equations:
- \( 12 + 5 = 17 \)
- \( 5 + 12 = 17 \)
- \( 17 - 12 = 5 \)
- \( 17 - 5 = 12 \)

#### c.
- Numbers: Top = 20, Side 1 = 2, Side 2 = 18
- Equations:
- \( 2 + 18 = 20 \)
- \( 18 + 2 = 20 \)
- \( 20 - 2 = 18 \)
- \( 20 - 18 = 2 \)

#### d.
- Numbers: Top = 16, Side 1 = 7, Side 2 = 9
- Equations:
- \( 7 + 9 = 16 \)
- \( 9 + 7 = 16 \)
- \( 16 - 7 = 9 \)
- \( 16 - 9 = 7 \)

#### e.
- Numbers: Top = 18, Side 1 = 7, Side 2 = 11
- Equations:
- \( 7 + 11 = 18 \)
- \( 11 + 7 = 18 \)
- \( 18 - 7 = 11 \)
- \( 18 - 11 = 7 \)

#### f.
- Numbers: Top = 5, Side 1 = 1, Side 2 = 4
- Equations:
- \( 1 + 4 = 5 \)
- \( 4 + 1 = 5 \)
- \( 5 - 1 = 4 \)
- \( 5 - 4 = 1 \)

#### g.
- Numbers: Top = 11, Side 1 = 9, Side 2 = 2
- Equations:
- \( 9 + 2 = 11 \)
- \( 2 + 9 = 11 \)
- \( 11 - 9 = 2 \)
- \( 11 - 2 = 9 \)

#### h.
- Numbers: Top = 9, Side 1 = 3, Side 2 = 6
- Equations:
- \( 3 + 6 = 9 \)
- \( 6 + 3 = 9 \)
- \( 9 - 3 = 6 \)
- \( 9 - 6 = 3 \)

#### i.
- Numbers: Top = 12, Side 1 = 6, Side 2 = 6
- Equations:
- \( 6 + 6 = 12 \)
- \( 6 + 6 = 12 \) (Note: This is repeated, but it's valid as both orders are the same.)
- \( 12 - 6 = 6 \)
- \( 12 - 6 = 6 \) (Note: This is repeated, but it's valid as both subtractions are the same.)

Final Answer:

\[
\boxed{
\begin{array}{lll}
\text{a.} & 2 + 6 = 8 & 6 + 2 = 8 \\
& 8 - 2 = 6 & 8 - 6 = 2 \\
\text{b.} & 12 + 5 = 17 & 5 + 12 = 17 \\
& 17 - 12 = 5 & 17 - 5 = 12 \\
\text{c.} & 2 + 18 = 20 & 18 + 2 = 20 \\
& 20 - 2 = 18 & 20 - 18 = 2 \\
\text{d.} & 7 + 9 = 16 & 9 + 7 = 16 \\
& 16 - 7 = 9 & 16 - 9 = 7 \\
\text{e.} & 7 + 11 = 18 & 11 + 7 = 18 \\
& 18 - 7 = 11 & 18 - 11 = 7 \\
\text{f.} & 1 + 4 = 5 & 4 + 1 = 5 \\
& 5 - 1 = 4 & 5 - 4 = 1 \\
\text{g.} & 9 + 2 = 11 & 2 + 9 = 11 \\
& 11 - 9 = 2 & 11 - 2 = 9 \\
\text{h.} & 3 + 6 = 9 & 6 + 3 = 9 \\
& 9 - 3 = 6 & 9 - 6 = 3 \\
\text{i.} & 6 + 6 = 12 & 6 + 6 = 12 \\
& 12 - 6 = 6 & 12 - 6 = 6 \\
\end{array}
}
\]