3rd Grade Math Puzzles Worksheets - Free Printable

Problem Explanation:

The task involves solving a series of puzzles where you need to fill in missing numbers based on the relationship between the TOTAL, DIFFERENCE, and two numbers. The formula provided is:

\[
\text{TOTAL} = \text{Number 1} + \text{Number 2}
\]
\[
\text{DIFFERENCE} = \text{Number 1} - \text{Number 2}
\]

Using these formulas, we can solve for any missing values.

---

Step-by-Step Solution:

#### Puzzle 1:
\[
\begin{aligned}
&\text{Number 1} = 13, \quad \text{Number 2} = 15, \quad \text{DIFFERENCE} = ? \\
&\text{TOTAL} = 13 + 15 = 28 \\
&\text{DIFFERENCE} = 13 - 15 = -2
\end{aligned}
\]

#### Puzzle 2:
\[
\begin{aligned}
&\text{Number 1} = 8, \quad \text{Number 2} = 17, \quad \text{DIFFERENCE} = ? \\
&\text{TOTAL} = 8 + 17 = 25 \\
&\text{DIFFERENCE} = 8 - 17 = -9
\end{aligned}
\]

#### Puzzle 3:
\[
\begin{aligned}
&\text{Number 1} = 14, \quad \text{Number 2} = 6, \quad \text{DIFFERENCE} = ? \\
&\text{TOTAL} = 14 + 6 = 20 \\
&\text{DIFFERENCE} = 14 - 6 = 8
\end{aligned}
\]

#### Puzzle 4:
\[
\begin{aligned}
&\text{TOTAL} = 24, \quad \text{Number 1} = 13, \quad \text{DIFFERENCE} = ? \\
&\text{Number 2} = \text{TOTAL} - \text{Number 1} = 24 - 13 = 11 \\
&\text{DIFFERENCE} = \text{Number 1} - \text{Number 2} = 13 - 11 = 2
\end{aligned}
\]

#### Puzzle 5:
\[
\begin{aligned}
&\text{TOTAL} = 25, \quad \text{Number 2} = 18, \quad \text{DIFFERENCE} = ? \\
&\text{Number 1} = \text{TOTAL} - \text{Number 2} = 25 - 18 = 7 \\
&\text{DIFFERENCE} = \text{Number 1} - \text{Number 2} = 7 - 18 = -11
\end{aligned}
\]

#### Puzzle 6:
\[
\begin{aligned}
&\text{TOTAL} = 31, \quad \text{Number 1} = 14, \quad \text{DIFFERENCE} = ? \\
&\text{Number 2} = \text{TOTAL} - \text{Number 1} = 31 - 14 = 17 \\
&\text{DIFFERENCE} = \text{Number 1} - \text{Number 2} = 14 - 17 = -3
\end{aligned}
\]

#### Puzzle 7:
\[
\begin{aligned}
&\text{TOTAL} = ?, \quad \text{Number 1} = 12, \quad \text{DIFFERENCE} = 2 \\
&\text{Let Number 2 be } x. \quad \text{Then:} \\
&\text{DIFFERENCE} = \text{Number 1} - \text{Number 2} \implies 2 = 12 - x \implies x = 10 \\
&\text{TOTAL} = \text{Number 1} + \text{Number 2} = 12 + 10 = 22
\end{aligned}
\]

#### Puzzle 8:
\[
\begin{aligned}
&\text{TOTAL} = ?, \quad \text{Number 1} = 15, \quad \text{DIFFERENCE} = 3 \\
&\text{Let Number 2 be } x. \quad \text{Then:} \\
&\text{DIFFERENCE} = \text{Number 1} - \text{Number 2} \implies 3 = 15 - x \implies x = 12 \\
&\text{TOTAL} = \text{Number 1} + \text{Number 2} = 15 + 12 = 27
\end{aligned}
\]

#### Puzzle 9:
\[
\begin{aligned}
&\text{TOTAL} = ?, \quad \text{Number 1} = 26, \quad \text{DIFFERENCE} = 6 \\
&\text{Let Number 2 be } x. \quad \text{Then:} \\
&\text{DIFFERENCE} = \text{Number 1} - \text{Number 2} \implies 6 = 26 - x \implies x = 20 \\
&\text{TOTAL} = \text{Number 1} + \text{Number 2} = 26 + 20 = 46
\end{aligned}
\]

---

Final Answers:

\[
\boxed{
\begin{array}{ccc}
\text{Puzzle 1:} & \text{TOTAL} = 28, \text{DIFFERENCE} = -2 \\
\text{Puzzle 2:} & \text{TOTAL} = 25, \text{DIFFERENCE} = -9 \\
\text{Puzzle 3:} & \text{TOTAL} = 20, \text{DIFFERENCE} = 8 \\
\text{Puzzle 4:} & \text{DIFFERENCE} = 2 \\
\text{Puzzle 5:} & \text{DIFFERENCE} = -11 \\
\text{Puzzle 6:} & \text{DIFFERENCE} = -3 \\
\text{Puzzle 7:} & \text{TOTAL} = 22 \\
\text{Puzzle 8:} & \text{TOTAL} = 27 \\
\text{Puzzle 9:} & \text{TOTAL} = 46 \\
\end{array}
}
\]