Dungeon Escape Slides Dungeon Denominators
The ancient gates have sealed shut. Only those who can find common ground—and common denominators—will find their way out.
Groups of 3-4
45 Minutes
The Curse
For centuries, the Fraction Fortress has guarded the secrets of the ancients.
You have entered the Chamber of Disparity, where every fraction stands alone, separated by their denominators.
To unlock the final exit, you must unite them by finding their shared identity.
Mission Objectives
Master the LCM (Lowest Common Multiple)
Forge Equivalent Fractions
Calculate the Sums & Differences
Rules of Engagement
Complete in Order
You cannot enter the next chamber until the current lock is broken.
Unite Your Party
Every member of your group must agree on the answer before checking with the DM.
The Torch Limit
You have 3 "Hint Torches." Use them wisely when your group is truly stuck.
Room One
The Echoing Hall
"To walk these floors, you must match the beat of the drums. Find the smallest number where both rhythms meet."
Find the Lowest Common Multiple of the denominator pairs given on your scroll.
The numbers you find will reveal the first Code Word.
Freedom Awaits
The exit portal opens in 45 minutes.
??:??
Remaining Time
4
Chambers
Prepare your party. Pick up your scrolls. Begin!
Dungeon Escape Pack Chamber 1: The Echoing Hall
Status: Locked
Party Members: _________________________
"The floor tiles hum with two different frequencies. To cross safely, you must find the first number where both rhythms sync up. Find the Lowest Common Multiple (LCM) for each pair of denominators."
Tile A
\(\frac{1}{4}\) and \(\frac{2}{6}\)
Multiples of 4: _____________________
Multiples of 6: _____________________
LCM:
Tile B
\(\frac{3}{8}\) and \(\frac{1}{12}\)
Multiples of 8: _____________________
Multiples of 12: ____________________
LCM:
Tile C
\(\frac{2}{9}\) and \(\frac{5}{6}\)
Multiples of 9: _____________________
Multiples of 6: _____________________
LCM:
Tile D
\(\frac{5}{6}\) and \(\frac{3}{10}\)
Multiples of 6: _____________________
Multiples of 10: ____________________
LCM:
CHAMBER 1 DECRYPTION KEY
9 = STONE
12 = PATH
18 = GATE
20 = WALL
24 = DOOR
30 = OPEN
36 = KEYS
48 = LOCK
The Secret Phrase to Proceed:
Chamber 2: The Hall of Mirrors
"Distorted fractions must find their true forms. Rewrite each pair using the Lowest Common Denominator (LCD)."
1
\(\frac{1}{4}\) , \(\frac{2}{6}\)
12
,
12
2
\(\frac{3}{8}\) , \(\frac{1}{12}\)
24
,
24
3
\(\frac{2}{9}\) , \(\frac{5}{6}\)
18
,
18
4
\(\frac{5}{6}\) , \(\frac{3}{10}\)
30
,
30
The Mirror Code
Sum of all 8 NEW numerators above:
Chamber 3: The Scales of Truth
Scale A: Sum
\(\frac{1}{4} + \frac{2}{6} =\)
12
Scale B: Difference
\(\frac{3}{8} - \frac{1}{12} =\)
24
Scale C: Sum
\(\frac{2}{9} + \frac{5}{6} =\)
18
Scale D: Difference
\(\frac{5}{6} - \frac{3}{10} =\)
30
Show Your Work Area:
Chamber 3 Sum
Numerators Sum: + + + = ?
The Final Gate
"All efforts culminate here. To break the seal, perform the ritual."
The Master Algorithm
Take the Secret Phrase from Chamber 1.
Take the Mirror Sum from Chamber 2.
Take the Chamber 3 Sum from Chamber 3.
Final Code = Mirror Sum + Chamber 3 Sum.
Final Calculation Area
Notes / Scratchpad
The Escape Code
Call the Dungeon Master once you have the code and the phrase.
Secret Scroll Key Secret Scroll Key
Dungeon Denominators Facilitator Answer Key
Chamber 1: LCM & Phrase
Tile A (4, 6): 12 (PATH)
Tile B (8, 12): 24 (DOOR)
Tile C (9, 6): 18 (GATE)
Tile D (6, 10): 30 (OPEN)
Phrase:
PATH DOOR GATE OPEN
Chamber 2: Equivalents
P1: \(\frac{3}{12}, \frac{4}{12}\) (Nums: 3, 4)
P2: \(\frac{9}{24}, \frac{2}{24}\) (Nums: 9, 2)
P3: \(\frac{4}{18}, \frac{15}{18}\) (Nums: 4, 15)
P4: \(\frac{25}{30}, \frac{9}{30}\) (Nums: 25, 9)
Mirror Sum: 71
Chamber 3: Sums
Scale A (+): 7 / 12
Scale B (-): 7 / 24
Scale C (+): 19 / 18
Scale D (-): 16 / 30
Chamber 3 Sum: 49
"The final code is the combination of the work in the second and third chambers. Mirror Sum (71) + Result Sum (49)."
The Final Escape Code
Verification Code for Final Seal
71 + 49 =
120
Dungeon Master Guide Dungeon Master Guide
Facilitator Instructions • Dungeon Denominators
Duration
45-60 min
Group Size
3-4 Students
Focus
Unlike Denom.
Quest Setup
Materials: Print one 4-page Dungeon Escape Pack per group.Hint Torches: Give groups 3 markers. These are "Hint Torches" for clues.
The Quest Path
1
Chamber 1: The Echoing Hall
LCM calculation. Verify Phrase: "PATH DOOR GATE OPEN" .
2
Chamber 2: The Hall of Mirrors
Equivalent fractions. Sum all 8 new numerators. Mirror Sum: 71.
3
Chamber 3: Scales of Truth
Addition/Subtraction. Sum the 4 result numerators. Chamber Sum: 49.
4
The Final Gate
Synthesis. Final Code = Mirror Sum (71) + Chamber 3 Sum (49) = 120 .
Facilitator Clues
Chamber 1: Finding Multiples
"Try listing the multiples of the larger number first. Then check if the smaller number can 'multiply' into any of those values. It saves time!"
Chamber 2: Keep it Balanced
"A fraction is like a see-saw. If you triple the bottom (denominator) to get to the LCM, you must triple the top (numerator) to keep it balanced."
Chamber 3: The Label Rule
"The denominator is just the label for the size. When you add 3 twelfths and 4 twelfths, you still have twelfths—just 7 of them!"
The Final Portal
"Look back at your previous totals. The Mirror Sum was the sum of all intermediate numerators. The Chamber 3 sum is the sum of your four final answers."
End of Facilitator Guide
