Grade 8Reading: grades 7-9Fractions of a numberRoundingBar modelsExponents
The Sunken Citadel Sabotage
During a midnight expedition inside the Sunken Citadel, a rogue saboteur disabled the vault defense system and stole the priceless Sun Orb. The Lead Expedition Director has secured the perimeter, but the thief is still hidden among the crew. Solve the math challenges to decipher the field notes and unmask the saboteur before they vanish into the jungle.
Suspects
Possible suspects
Cross off a row as each clue rules it out. On screen, tap a row.
21 of 21 still in play
| Name | Primary Tool | Gadget | Grip Style | Expedition Cap | Countermeasure |
|---|---|---|---|---|---|
| Sergeant Kowalski | Laser Cutter | Glider Wings | Left Handed | Silver Helmet | EMP Blast |
| Technician Cruz | Laser Cutter | Hologram Emitter | Right Handed | Golden Bandana | EMP Blast |
| Pilot Connor | Plasma Torch | Smoke Pellets | Left Handed | Crimson Cap | EMP Blast |
| Ranger Blake | Laser Cutter | Signal Jammer | Left Handed | Golden Bandana | Acoustic Shield |
| Agent Foster | Laser Cutter | Hologram Emitter | Right Handed | Crimson Cap | EMP Blast |
| Agent Ramirez | Plasma Torch | Sonic Decoy | Left Handed | Silver Helmet | Acoustic Shield |
| Professor Sterling | Laser Cutter | Glider Wings | Left Handed | Crimson Cap | EMP Blast |
| Dr Aris Thorne | Laser Cutter | Hologram Emitter | Left Handed | Silver Helmet | Flashburst Flare |
| Navigator Ross | Thermal Torch | Hologram Emitter | Right Handed | Crimson Cap | EMP Blast |
| Operative Diaz | Plasma Torch | Smoke Pellets | Left Handed | Crimson Cap | Flashburst Flare |
| Analyst Kim | Plasma Torch | Signal Jammer | Left Handed | Golden Bandana | Acoustic Shield |
| Dr Maya Lin | Sonic Drill | Hologram Emitter | Right Handed | Silver Helmet | EMP Blast |
| Specialist Mercer | Laser Cutter | Smoke Pellets | Right Handed | Golden Bandana | Acoustic Shield |
| Scout Chen | Plasma Torch | Signal Jammer | Left Handed | Silver Helmet | Acoustic Shield |
| Scholar Bennett | Sonic Drill | Smoke Pellets | Left Handed | Silver Helmet | Acoustic Shield |
| Chief Rivera | Sonic Drill | Hologram Emitter | Left Handed | Silver Helmet | Acoustic Shield |
| Captain Marcus | Plasma Torch | Hologram Emitter | Right Handed | Golden Bandana | EMP Blast |
| Surveyor Young | Laser Cutter | Glider Wings | Left Handed | Silver Helmet | Acoustic Shield |
| Tracker Hayes | Sonic Drill | Smoke Pellets | Right Handed | Silver Helmet | Acoustic Shield |
| Archivist Patel | Thermal Torch | Smoke Pellets | Left Handed | Golden Bandana | EMP Blast |
| Officer Vance | Sonic Drill | Glider Wings | Right Handed | Crimson Cap | Flashburst Flare |
Clue 1
Fractions of a number
We analyzed the energy residue left on the ruined gate to determine how much fuel the intruder used during the breach.
Solve each problem to learn its letter. Then write that letter in every box that shows the same number, and read the secret clue.
T
45
49
53
3
35
2
2
12
35
19
42
15
53
23
19
15
T
45
55
23
53
12
23
15
19
35
51
42
53
51
15
25
3/8 of 120 =T
2/10 of 95 =N
2/4 of 30 =O
1/3 of 126 =D
4/8 of 24 =A
5/8 of 88 =U
4/8 of 4 =L
1/4 of 100 =Y
5/10 of 46 =S
1/5 of 15 =V
4/8 of 106 =E
2/8 of 196 =H
1/2 of 70 =I
2/6 of 153 =C
0/14 letters found
Clue 2
Rounding
The vault sensors recorded a rough estimate of the intruder weight but the display only rounds to the nearest ten kilograms.
Solve each problem to learn its letter. Then write that letter in every box that shows the same number, and read the secret clue.
W
5000
500
3000
90
1300
130
130
1300
130
130
70
W
5000
70
2900
1300
1700
3000
300
70
90
30
1300
30
430
20
1300
50
70
3000
500
200
1300
Round 4,509 to the nearest thousandW
Round 20 to the nearest tenP
Round 241 to the nearest hundredV
Round 1,289 to the nearest hundredE
Round 471 to the nearest hundredI
Round 29 to the nearest tenD
Round 3,436 to the nearest thousandT
Round 93 to the nearest tenN
Round 130 to the nearest tenS
Round 2,916 to the nearest hundredL
Round 434 to the nearest tenO
Round 1,684 to the nearest hundredF
Round 66 to the nearest tenA
Round 49 to the nearest tenR
Round 336 to the nearest hundredH
0/15 letters found
Clue 3
Bar model word problems
To compare the power output logs across the different security sectors our team sketched out comparative bar diagrams.
Draw a bar model to solve each word problem. Its answer reveals a letter — write the letters in the boxes to fill in the missing word.
Someonescaredthevillainoffwith .
A
20
112
21
62
83
11
72
112
83
H
72
E
L
D
One group collected 13 relic and another group collected 7 relic. How many relic in all?
draw a bar model
Answer:→A
Expedition Quartermaster has 9 times as many relic as a teammate. The teammate has 8 relic. How many relic does Expedition Quartermaster have?
draw a bar model
Answer:→I
One group collected 6 solar battery and another group collected 5 solar battery. How many solar battery in all?
draw a bar model
Answer:→T
Expedition Quartermaster has 84 map cylinder, packed 4 to a bag. How many bags can be filled?
draw a bar model
Answer:→O
One group collected 40 scanner and another group collected 72 scanner. How many scanner in all?
draw a bar model
Answer:→C
The red team has 101 scanner and the blue team has 39 scanner. How many more scanner does the red team have?
draw a bar model
Answer:→U
There were 120 map cylinder in all. 37 map cylinder were used. How many map cylinder are left?
draw a bar model
Answer:→S
0/7 letters found
Clue 4
Exponents
The security mainframe logged the exponential growth rate of the corrupted code injected into the defense grid.
Solve each problem to learn its letter. Then write that letter in every box that shows the same number, and read the secret clue.
A
729
625
243
225
256
125
400
64
125
225
289
125
144
361
A
729
625
196
400
216
81
81
125
196
A
729
144
144
64
125
625
32
125
8
125
3^6 =A
9^2 =P
19^2 =W
14^2 =D
2^5 =C
5^4 =S
4^4 =V
4^3 =H
2^3 =N
20^2 =R
3^5 =I
17^2 =M
6^3 =O
12^2 =T
5^3 =E
15^2 =L
0/16 letters found
Clue 5
Fractions of a number — the last clue
By calculating the exact fraction of encrypted data packets recovered from the comm tower we unlocked another clue.
First solve each problem. Then find each answer in the list below and cross that sentence out. One sentence will be left — that's exactly what the villain did!
Step 1 — solve these
1/8 of 40 = ?
1/2 of 22 = ?
2/10 of 35 = ?
4/8 of 12 = ?
6/10 of 15 = ?
3/6 of 4 = ?
2/10 of 5 = ?
6/8 of 4 = ?
2/8 of 32 = ?
1/8 of 80 = ?
8/10 of 5 = ?
Step 2 — cross out the sentence with each answer
1.The villain breached the outer wall using a grapple launcher, then soared over the canopy with glider wings.
2.The villain shattered the stone seal using a sonic drill, then soared over the canopy with glider wings.
3.The villain melted the security door using a thermal torch, then disrupted the guard comms with a signal jammer.
4.The villain disintegrated the locks using a plasma torch, then escaped under cover of smoke pellets.
5.The villain shattered the stone seal using a sonic drill, then escaped under cover of smoke pellets.
6.The villain breached the outer wall using a grapple launcher, then distracted the patrol with a sonic decoy.
7.The villain shattered the stone seal using a sonic drill, then confused the pursuers using a hologram emitter.
8.The villain breached the outer wall using a grapple launcher, then disrupted the guard comms with a signal jammer.
9.The villain melted the security door using a thermal torch, then escaped under cover of smoke pellets.
10.The villain breached the outer wall using a grapple launcher, then confused the pursuers using a hologram emitter.
11.The villain sliced through the reinforced vault using a laser cutter, then soared over the canopy with glider wings.
12.The villain disintegrated the locks using a plasma torch, then disrupted the guard comms with a signal jammer.
Solve it
Name the culprit
Choose the one suspect left standing.
Answer Key — The Sunken Citadel Sabotage
Culprit: Scout Chen (Plasma Torch · Signal Jammer · Left Handed · Silver Helmet · Acoustic Shield)
- Clue 1 (Fractions of a number): "THE VILLAIN DOES NOT USE A SONIC DECOY"3/8 of 120 = 45 (T) · 2/10 of 95 = 19 (N) · 2/4 of 30 = 15 (O) · 1/3 of 126 = 42 (D) · 4/8 of 24 = 12 (A) · 5/8 of 88 = 55 (U) · 4/8 of 4 = 2 (L) · 1/4 of 100 = 25 (Y) · 5/10 of 46 = 23 (S) · 1/5 of 15 = 3 (V) · 4/8 of 106 = 53 (E) · 2/8 of 196 = 49 (H) · 1/2 of 70 = 35 (I) · 2/6 of 153 = 51 (C)
- Clue 2 (Rounding): "WITNESSES SAW A LEFT HANDED OPERATIVE"Round 4,509 to the nearest thousand = 5000 (W) · Round 20 to the nearest ten = 20 (P) · Round 241 to the nearest hundred = 200 (V) · Round 1,289 to the nearest hundred = 1300 (E) · Round 471 to the nearest hundred = 500 (I) · Round 29 to the nearest ten = 30 (D) · Round 3,436 to the nearest thousand = 3000 (T) · Round 93 to the nearest ten = 90 (N) · Round 130 to the nearest ten = 130 (S) · Round 2,916 to the nearest hundred = 2900 (L) · Round 434 to the nearest ten = 430 (O) · Round 1,684 to the nearest hundred = 1700 (F) · Round 66 to the nearest ten = 70 (A) · Round 49 to the nearest ten = 50 (R) · Round 336 to the nearest hundred = 300 (H)
- Clue 3 (Bar model word problems): "ACOUSTIC SHIELD"One group collected 13 relic and another group collected 7 relic. How many relic in all? = 20 (A) · Expedition Quartermaster has 9 times as many relic as a teammate. The teammate has 8 relic. How many relic does Expedition Quartermaster have? = 72 (I) · One group collected 6 solar battery and another group collected 5 solar battery. How many solar battery in all? = 11 (T) · Expedition Quartermaster has 84 map cylinder, packed 4 to a bag. How many bags can be filled? = 21 (O) · One group collected 40 scanner and another group collected 72 scanner. How many scanner in all? = 112 (C) · The red team has 101 scanner and the blue team has 39 scanner. How many more scanner does the red team have? = 62 (U) · There were 120 map cylinder in all. 37 map cylinder were used. How many map cylinder are left? = 83 (S)
- Clue 4 (Exponents): "A SILVER HELMET WAS DROPPED AT THE SCENE"3^6 = 729 (A) · 9^2 = 81 (P) · 19^2 = 361 (W) · 14^2 = 196 (D) · 2^5 = 32 (C) · 5^4 = 625 (S) · 4^4 = 256 (V) · 4^3 = 64 (H) · 2^3 = 8 (N) · 20^2 = 400 (R) · 3^5 = 243 (I) · 17^2 = 289 (M) · 6^3 = 216 (O) · 12^2 = 144 (T) · 5^3 = 125 (E) · 15^2 = 225 (L)
- Clue 5 (Fractions of a number): surviving statement (box 12) → Scout Chen1/8 of 40 = 5 · 1/2 of 22 = 11 · 2/10 of 35 = 7 · 4/8 of 12 = 6 · 6/10 of 15 = 9 · 3/6 of 4 = 2 · 2/10 of 5 = 1 · 6/8 of 4 = 3 · 2/8 of 32 = 8 · 1/8 of 80 = 10 · 8/10 of 5 = 4
About this mystery
- Grade level
- Grade 8 math
- Math topics
- Fractions of a number, Rounding, Bar models, Exponents
- Reading level
- grades 7-9
- Theme
- The Sunken Citadel Sabotage — set in Sunken Citadel in the Amazon basin
- Format
- Interactive online & printable worksheet with answer key
- Solution
- One unique, verified culprit among 21 suspects