Grade 10Reading: grades 7-9Pythagorean theoremSquare rootsExponentsOrder of operations
The Case of the Missing Star Crystal
Someone ambushed the Chief Explorer aboard the flagship Zephyr and swiped the ancient Star Crystal. Trace the flight path, analyze the evidence, and unmask the culprit.
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 Gadget | Navigation Tool | Watch Hand | Bandana Color | Weakness |
|---|---|---|---|---|---|
| Mechanic Brody | Lightning Rod | Brass Spyglass | Wears Watch On Left Wrist | Sapphire Bandana | Strong Gusts |
| Navigator Gemma | Sound Wave Cannon | Brass Spyglass | Wears Watch On Left Wrist | Sapphire Bandana | Bright Lanterns |
| Scout Tali | Glider Wings | Star Chart | Wears Watch On Left Wrist | Sapphire Bandana | Loud Whistles |
| Ranger Dax | Sound Wave Cannon | Solar Compass | Wears Watch On Left Wrist | Crimson Bandana | Strong Gusts |
| Aviator Nora | Sound Wave Cannon | Wind Gauge | Wears Watch On Left Wrist | Emerald Bandana | Bright Lanterns |
| Officer Milo | Glider Wings | Brass Spyglass | Wears Watch On Left Wrist | Crimson Bandana | Bright Lanterns |
| Commander Roy | Smoke Bomb | Star Chart | Wears Watch On Left Wrist | Sapphire Bandana | Strong Gusts |
| Deckhand Otis | Lightning Rod | Altimeter | Wears Watch On Left Wrist | Emerald Bandana | Loud Whistles |
| Tech Hugo | Lightning Rod | Brass Spyglass | Wears Watch On Left Wrist | Crimson Bandana | Strong Gusts |
| Specialist Eva | Smoke Bomb | Solar Compass | Wears Watch On Right Wrist | Sapphire Bandana | Loud Whistles |
| Engineer Jax | Grapple Hook | Wind Gauge | Wears Watch On Left Wrist | Sapphire Bandana | Strong Gusts |
| Aviator Nina | Lightning Rod | Altimeter | Wears Watch On Right Wrist | Emerald Bandana | Loud Whistles |
| Helmsman Cruz | Sound Wave Cannon | Solar Compass | Wears Watch On Left Wrist | Sapphire Bandana | Strong Gusts |
| Gunner Flint | Smoke Bomb | Brass Spyglass | Wears Watch On Right Wrist | Sapphire Bandana | Strong Gusts |
| Pilot Maya | Grapple Hook | Altimeter | Wears Watch On Left Wrist | Sapphire Bandana | Bright Lanterns |
| Explorer Seth | Glider Wings | Altimeter | Wears Watch On Right Wrist | Crimson Bandana | Strong Gusts |
| Scout Kael | Smoke Bomb | Star Chart | Wears Watch On Left Wrist | Emerald Bandana | Bright Lanterns |
| Navigator Leo | Sound Wave Cannon | Solar Compass | Wears Watch On Right Wrist | Sapphire Bandana | Bright Lanterns |
| Sailor Iris | Grapple Hook | Star Chart | Wears Watch On Left Wrist | Sapphire Bandana | Strong Gusts |
| Captain Vance | Lightning Rod | Wind Gauge | Wears Watch On Right Wrist | Crimson Bandana | Loud Whistles |
| Deckhand Zane | Sound Wave Cannon | Solar Compass | Wears Watch On Left Wrist | Sapphire Bandana | Loud Whistles |
Clue 1
Pythagorean theorem
To calculate the exact diagonal distance the thief leapt across the airship deck, you map the right triangle of the rigging.
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
30
51
17
111
82
10
74
40
25
T
30
125
25
125
52
123
T
30
82
5
17
58
100
25
52
125
34
58
82
34
17
legs 18 and 24, hypotenuse =T
legs 20 and 48, hypotenuse =N
legs 16 and 30, hypotenuse =G
legs 8 and 15, hypotenuse =E
legs 36 and 105, hypotenuse =C
legs 24 and 32, hypotenuse =R
legs 18 and 80, hypotenuse =U
legs 27 and 120, hypotenuse =O
legs 28 and 96, hypotenuse =W
legs 35 and 120, hypotenuse =D
legs 40 and 42, hypotenuse =A
legs 7 and 24, hypotenuse =I
legs 24 and 45, hypotenuse =H
legs 24 and 70, hypotenuse =P
legs 6 and 8, hypotenuse =L
legs 3 and 4, hypotenuse =S
0/16 letters found
Clue 2
Square roots
The central power grid is arranged in a square array, so finding the side length reveals which control junction was tampered with.
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
16
4
22
14
5
14
20
22
3
T
16
11
10
18
22
25
11
25
T
16
3
4
10
12
T
16
4
22
2
22
19
T
16
11
18
7
14
T
16
sqrt(256) =T
sqrt(324) =R
sqrt(49) =I
sqrt(100) =O
sqrt(16) =H
sqrt(361) =F
sqrt(196) =S
sqrt(4) =L
sqrt(25) =U
sqrt(625) =A
sqrt(400) =P
sqrt(121) =W
sqrt(9) =C
sqrt(144) =N
sqrt(484) =E
0/15 letters found
Clue 3
Exponents
Signals from the stolen crystal double in intensity with each cloud layer crossed, letting you calculate its total broadcast range.
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
8
125
243
81
25
324
324
49
25
225
32
49
36
289
225
27
256
289
243
400
625
49
256
289
625
441
36
T
8
100
27
225
196
196
729
36
T
8
36
2^3 =T
2^5 =W
6^2 =S
5^3 =H
21^2 =Y
14^2 =G
10^2 =R
5^4 =B
5^2 =I
17^2 =K
4^4 =C
3^3 =O
15^2 =N
20^2 =D
7^2 =A
3^4 =V
18^2 =L
9^3 =U
3^5 =E
0/19 letters found
Clue 4
Order of operations
Deciphering the airship captain's locked logbook requires solving the priority sequence of security bypass codes.
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
119
41
55
111
95
55
24
55
41
26
109
T
119
41
53
55
26
109
111
77
97
26
111
26
110
110
41
8
53
55
7
26
24
109
26
24
26
92 + 9 × 3 =T
79 + 6 × 5 =D
87 + 6 × 4 =S
83 + 2 × 7 =F
9 × 9 - 4 =O
9 × 6 - 30 =N
10 × 4 - 14 =A
10 × 5 - 9 =H
11 × 11 - 26 =C
47 + 9 × 7 =P
2 × 12 - 17 =B
4 + 2 × 2 =I
39 + 2 × 7 =R
15 + 5 × 8 =E
0/14 letters found
Clue 5
Square roots — the last clue
Measuring the area of the storm field surrounding the vault gives the exact root radius needed to track the escape vessel.
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
sqrt(121) = ?
sqrt(16) = ?
sqrt(64) = ?
sqrt(81) = ?
sqrt(100) = ?
sqrt(144) = ?
sqrt(1) = ?
sqrt(4) = ?
sqrt(9) = ?
sqrt(25) = ?
sqrt(36) = ?
Step 2 — cross out the sentence with each answer
1.The villain vanished into thin air using a smoke bomb, then checked coordinates on a solar compass.
2.The villain disrupted the sensors with a sound wave cannon, then monitored elevation using an altimeter.
3.The villain channeled power using a lightning rod, then monitored elevation using an altimeter.
4.The villain disrupted the sensors with a sound wave cannon, then checked coordinates on a solar compass.
5.The villain disrupted the sensors with a sound wave cannon, then plotted a course across a star chart.
6.The villain soared over the railings with glider wings, then measured airflow with a wind gauge.
7.The villain channeled power using a lightning rod, then scouted the horizon with a brass spyglass.
8.The villain vanished into thin air using a smoke bomb, then plotted a course across a star chart.
9.The villain soared over the railings with glider wings, then scouted the horizon with a brass spyglass.
10.The villain swung across the deck with a grapple hook, then checked coordinates on a solar compass.
11.The villain swung across the deck with a grapple hook, then plotted a course across a star chart.
12.The villain disrupted the sensors with a sound wave cannon, then scouted the horizon with a brass spyglass.
Solve it
Name the culprit
Choose the one suspect left standing.
Answer Key — The Case of the Missing Star Crystal
Culprit: Mechanic Brody (Lightning Rod · Brass Spyglass · Wears Watch On Left Wrist · Sapphire Bandana · Strong Gusts)
- Clue 1 (Pythagorean theorem): "THE CULPRIT DID NOT USE A WIND GAUGE"legs 18 and 24, hypotenuse = 30 (T) · legs 20 and 48, hypotenuse = 52 (N) · legs 16 and 30, hypotenuse = 34 (G) · legs 8 and 15, hypotenuse = 17 (E) · legs 36 and 105, hypotenuse = 111 (C) · legs 24 and 32, hypotenuse = 40 (R) · legs 18 and 80, hypotenuse = 82 (U) · legs 27 and 120, hypotenuse = 123 (O) · legs 28 and 96, hypotenuse = 100 (W) · legs 35 and 120, hypotenuse = 125 (D) · legs 40 and 42, hypotenuse = 58 (A) · legs 7 and 24, hypotenuse = 25 (I) · legs 24 and 45, hypotenuse = 51 (H) · legs 24 and 70, hypotenuse = 74 (P) · legs 6 and 8, hypotenuse = 10 (L) · legs 3 and 4, hypotenuse = 5 (S)
- Clue 2 (Square roots): "THE SUSPECT WORE A WATCH ON THE LEFT WRIST"sqrt(256) = 16 (T) · sqrt(324) = 18 (R) · sqrt(49) = 7 (I) · sqrt(100) = 10 (O) · sqrt(16) = 4 (H) · sqrt(361) = 19 (F) · sqrt(196) = 14 (S) · sqrt(4) = 2 (L) · sqrt(25) = 5 (U) · sqrt(625) = 25 (A) · sqrt(400) = 20 (P) · sqrt(121) = 11 (W) · sqrt(9) = 3 (C) · sqrt(144) = 12 (N) · sqrt(484) = 22 (E)
- Clue 3 (Exponents): "THE VILLAIN WAS KNOCKED BACK BY STRONG GUSTS"2^3 = 8 (T) · 2^5 = 32 (W) · 6^2 = 36 (S) · 5^3 = 125 (H) · 21^2 = 441 (Y) · 14^2 = 196 (G) · 10^2 = 100 (R) · 5^4 = 625 (B) · 5^2 = 25 (I) · 17^2 = 289 (K) · 4^4 = 256 (C) · 3^3 = 27 (O) · 15^2 = 225 (N) · 20^2 = 400 (D) · 7^2 = 49 (A) · 3^4 = 81 (V) · 18^2 = 324 (L) · 9^3 = 729 (U) · 3^5 = 243 (E)
- Clue 4 (Order of operations): "THE SCENE HAD THREADS OF A SAPPHIRE BANDANA"92 + 9 × 3 = 119 (T) · 79 + 6 × 5 = 109 (D) · 87 + 6 × 4 = 111 (S) · 83 + 2 × 7 = 97 (F) · 9 × 9 - 4 = 77 (O) · 9 × 6 - 30 = 24 (N) · 10 × 4 - 14 = 26 (A) · 10 × 5 - 9 = 41 (H) · 11 × 11 - 26 = 95 (C) · 47 + 9 × 7 = 110 (P) · 2 × 12 - 17 = 7 (B) · 4 + 2 × 2 = 8 (I) · 39 + 2 × 7 = 53 (R) · 15 + 5 × 8 = 55 (E)
- Clue 5 (Square roots): surviving statement (box 7) → Mechanic Brodysqrt(121) = 11 · sqrt(16) = 4 · sqrt(64) = 8 · sqrt(81) = 9 · sqrt(100) = 10 · sqrt(144) = 12 · sqrt(1) = 1 · sqrt(4) = 2 · sqrt(9) = 3 · sqrt(25) = 5 · sqrt(36) = 6
About this mystery
- Grade level
- Grade 10 math
- Math topics
- Pythagorean theorem, Square roots, Exponents, Order of operations
- Reading level
- grades 7-9
- Theme
- The Case of the Missing Star Crystal — set in The Cloud Spire Archipelago
- Format
- Interactive online & printable worksheet with answer key
- Solution
- One unique, verified culprit among 21 suspects