Puzzle Box Math Worksheet
The Multiplication Puzzle Box
NY-4.OA.5
Crack the factor locks, open the vault matrix, and power the gear tracks!
Agent:
Date:
Code:
Puzzle Box Rule: Each lock chamber contains a missing factor. Solved factors unlock the central vault and power the gear tracks below.
LEVEL 4
1
Chamber I • The Four Dial Locks
Find the missing factor in each dial
Dial A
\( 4 \times \Box = 36 \)
Factor A:
Dial B
\( \Box \times 7 = 56 \)
Factor B:
Dial C
\( 6 \times \Box = 42 \)
Factor C:
Dial D
\( \Box \times 9 = 45 \)
Factor D:
2
Chamber II • The Interlocking Vault Matrix
Inside cells = Row Factor \( \times \) Column Factor
| \( \mathbf{\times} \) |
Col 1
6
|
Col 2
[ Factor \( Y \) ]
|
| --- | --- | --- |
|
Row 1
[ Factor \( X \) ]
|
Chamber 1-1
18
|
Chamber 1-2
24
|
|
Row 2
[ Factor \( Z \) ]
|
Chamber 2-1
24
|
Master Vault
\( ? \)
|
Deduce the unknown factors:
Factor \( X \):
\( X \times 6 = 18 \)
Factor \( Y \):
\( X \times Y = 24 \)
Factor \( Z \):
\( Z \times 6 = 24 \)
Master Vault Key:
Product of \( Z \times Y \)
3
Chamber III • The Pattern Gear Tracks
Multiply by each unlocked factor to extend the gears
Track 1 (Uses Factor \( X \) as multiplier) Rule: Multiply by
2
6
18
Track 2 (Uses Factor \( Z \) as multiplier) Rule: Multiply by
3
12
48
Track 3 (Uses Factor D from Chamber I as multiplier) Rule: Multiply by
2
10
50
PUZZLE BOX SCHEMATIC #4-OA-5 Turn to Page 2: Inside the Mechanism →
Inside the Box Mechanisms
Analysis
Analyze unstated mathematical features that make the puzzle box work!
NY-4.OA.5 CORE
Mechanic's Note: A pattern rule states what to do (e.g., multiply by 4). An unstated feature is a pattern behavior that happens automatically (e.g., all outputs are even, or ones digits repeat) even though the rule never stated it!
A
Mechanism A • The Parity Tumbler (Track 2)
Terms: 3, 12, 48, 192, 768...
Observation: The starting number \( 3 \) is ODD. The rule is to multiply by the even factor \( 4 \).
1. Look at all the numbers after the first term: \( 12, 48, 192, 768 \). Are they EVEN or ODD?
2. Informally explain why: Why does multiplying any whole number by an EVEN factor always produce an even number?
B
Mechanism B • The Perpetual Ones-Digit Cycle
Terms: 6, 36, 216, 1,296, 7,776...
Observation: Start at \( 6 \). The rule is "Multiply by \( 6 \)".
1. What hidden pattern feature do you notice in the ones place of every single number in this sequence?
2. Explain the mechanism: If a number ends in \( 6 \) and is multiplied by \( 6 \), why does the new product always end in \( 6 \)? (Hint: Think about \( 6 \times 6 = 36 \).)
C
Mechanism C • Build Your Own Puzzle Box Lock
Master Challenge
Your 2x2 Mini-Vault
| \( \times \) | 2 | 5 |
|---|
| \( \Box \) | 14 | \( ? \) |
1. Unknown Factor (\( \Box \times 2 = 14 \)):
2. Vault Output (\( \text{Factor} \times 5 \)):
3. Generate 4 terms multiplying by your factor:
4. One unstated feature you notice:
NY-4.OA.5 • PATTERNS & UNKNOWN NUMBER INVESTIGATION Master Puzzle Box Complete ✓
