Instructions
Welcome, Junior Math Spy! Your mission is to solve the equations below to find the value of the hidden symbol. This is called finding the Unknown Variable.
- Read the equation carefully.
- Determine which number must replace the symbol to make the equation true.
- Write the value of the symbol in the space provided.
- Use inverse operations (like subtraction to undo addition) when needed.
Section 1: Finding the Secret Number (Basic Operations)
Find the value of the shape in each equation.
-
$10 + \bigtriangleup = 18$ $\bigtriangleup$ = ____
-
$25 - \square = 15$ $\square$ = ____
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$\bigcirc + 5 = 19$ $\bigcirc$ = ____
-
$12 = 30 - \star$ $\star$ = ____
-
$5 + 6 + \zeta = 20$ $\zeta$ = ____
Section 2: Unlocking the Vault (Inverse Operations)
Use subtraction to solve the addition equations, or addition to solve the subtraction equations. Show your work or explain your thinking.
| Equation | Thinking/Work | Value of Unknown |
|---|---|---|
| $65 + P = 80$ | $80 - 65 = 15$ | P = 15 |
| $92 - D = 70$ | D = | |
| $15 + 20 + H = 50$ | H = | |
| $100 = 55 + K$ | K = | |
| $J - 10 = 42$ | J = |
Section 3: The Code Breaker Table
Complete the table by solving for the symbol and identifying the operation you used to solve it.
| Equation | Missing Symbol | Operation Used to Solve | Value of Symbol |
|---|---|---|---|
| Example: $35 - \diamondsuit = 30$ | $\diamondsuit$ | Inverse Addition (30 + 5) | 5 |
| $6 + \bigstar = 14$ | $\bigstar$ | ||
| $45 - \S = 25$ | $\S$ | ||
| $100 = 80 + \Psi$ | $\Psi$ | ||
| $2 \ imes \cup = 10$ | $\cup$ |
Challenge Mission (Spy Master Level)
These problems require basic multiplication or division thinking. Only attempt if you have completed all previous missions!
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If $5 \ imes \otimes = 30$, what is $\otimes$? (Hint: $5+5+5+5+5+5 = 30$) $\otimes$ = ____
-
If $\blacksquare + \blacksquare + \blacksquare = 27$, what is $\blacksquare$? $\blacksquare$ = ____
-
Reflection: If you were solving the problem $75 + # = 100$, why is using subtraction ($100 - 75$) faster than counting up?
Answer Key
Section 1: Finding the Secret Number
- $\bigtriangleup$ = 8
- $\square$ = 10
- $\bigcirc$ = 14
- $\star$ = 18
- $\zeta$ = 9 ($5+6=11$; $20-11=9$)
Section 2: Unlocking the Vault
| Equation | Thinking/Work | Value of Unknown |
|---|---|---|
| $65 + P = 80$ | $80 - 65 = 15$ | P = 15 |
| $92 - D = 70$ | $92 - 70 = 22$ | D = 22 |
| $15 + 20 + H = 50$ | $35 + H = 50$; $50 - 35 = 15$ | H = 15 |
| $100 = 55 + K$ | $100 - 55 = 45$ | K = 45 |
| $J - 10 = 42$ | $42 + 10 = 52$ | J = 52 |
Section 3: The Code Breaker Table
| Equation | Missing Symbol | Operation Used to Solve | Value of Symbol |
|---|---|---|---|
| Example: $35 - \diamondsuit = 30$ | $\diamondsuit$ | Inverse Addition (30 + 5) | 5 |
| $6 + \bigstar = 14$ | $\bigstar$ | Inverse Subtraction (14 - 6) | 8 |
| $45 - \S = 25$ | $\S$ | Inverse Subtraction (45 - 25) | 20 |
| $100 = 80 + \Psi$ | $\Psi$ | Inverse Subtraction (100 - 80) | 20 |
| $2 \ imes \cup = 10$ | $\cup$ | Inverse Division (10 / 2) | 5 |
Challenge Mission (Spy Master Level)
- $\otimes$ = 6
- $\blacksquare$ = 9
- Reflection: Using subtraction ($100 - 75$) uses the formal inverse operation (fact family) which is much quicker and more reliable than counting up (which could lead to errors, especially with larger numbers).