🔎 RatioGrade 7Reading: grades 7-9Fractions of a numberIntegersPercentagesOrder of operations
The Case of the Ruined Ratios
The Golden Ratio Academy is in total chaos! Someone has stolen the Master Scale, a device that keeps the city's landmarks in perfect proportion. Without it, the buildings are warping and stretching. The Chief Architect needs your help to deduce which student or staff member is the Ratio Ruiner before the city collapses!
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 | Scaling Tool | Math Specialty | Drafting Hand | Ink Stain Color | Math Error |
|---|---|---|---|---|---|
| Cartesian | proportion wheel | golden ratio | left-handed pencil grip | cyan ink smudge | dropped decimal |
| Penrose | caliper compass | vector calculus | left-handed pencil grip | magenta ink smudge | divide by zero |
| Noether | laser transit | vector calculus | right-handed pencil grip | cyan ink smudge | divide by zero |
| Mandelbrot | grid projector | prime factors | left-handed pencil grip | magenta ink smudge | swapped numerator |
| Pythagoras | laser transit | golden ratio | right-handed pencil grip | magenta ink smudge | swapped numerator |
| Lagrange | caliper compass | geometric series | right-handed pencil grip | yellow ink smudge | swapped numerator |
| Euler | caliper compass | fractal chaos | right-handed pencil grip | yellow ink smudge | divide by zero |
| Fourier | proportion wheel | golden ratio | right-handed pencil grip | cyan ink smudge | swapped numerator |
| Bernoulli | laser transit | prime factors | right-handed pencil grip | magenta ink smudge | divide by zero |
| Hypatia | laser transit | golden ratio | right-handed pencil grip | cyan ink smudge | dropped decimal |
| Ada Lovelace | laser transit | golden ratio | left-handed pencil grip | cyan ink smudge | dropped decimal |
| Da Vinci | caliper compass | geometric series | left-handed pencil grip | magenta ink smudge | dropped decimal |
| Pascal | proportion wheel | geometric series | right-handed pencil grip | cyan ink smudge | dropped decimal |
| Archimedes | proportion wheel | prime factors | left-handed pencil grip | magenta ink smudge | swapped numerator |
| Kepler | caliper compass | golden ratio | right-handed pencil grip | yellow ink smudge | dropped decimal |
| Escher | laser transit | prime factors | right-handed pencil grip | cyan ink smudge | dropped decimal |
| Le Corbusier | micrometer slide | vector calculus | right-handed pencil grip | yellow ink smudge | swapped numerator |
| Hilbert | grid projector | fractal chaos | right-handed pencil grip | cyan ink smudge | dropped decimal |
| Brunelleschi | proportion wheel | prime factors | left-handed pencil grip | yellow ink smudge | dropped decimal |
| Newton | micrometer slide | geometric series | right-handed pencil grip | cyan ink smudge | dropped decimal |
| Euclid | grid projector | golden ratio | right-handed pencil grip | cyan ink smudge | swapped numerator |
Clue 1
Fractions of a number
To unlock the drafting room blueprints, we need to analyze the fractional distribution of the blueprints stored in the vault.
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
35
59
25
10
51
60
30
25
10
34
16
25
39
30
16
T
35
39
T
35
51
34
8
11
10
57
27
T
35
57
17
27
59
57
16
39
5/8 of 56 =T
5/10 of 118 =H
5/10 of 54 =C
3/4 of 76 =A
1/2 of 16 =Y
2/6 of 51 =L
5/6 of 12 =R
1/6 of 96 =O
4/8 of 78 =S
1/2 of 102 =U
5/6 of 30 =E
2/8 of 120 =N
4/8 of 22 =F
4/6 of 51 =D
5/6 of 72 =I
0/15 letters found
Clue 2
Integers
The temperature controls on the laser transit are fluctuating wildly above and below zero, requiring a precise sum of positive and negative values.
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
22
25
30
24
6
24
3
30
16
T
22
21
12
1
T
22
30
24
21
1
T
22
25
T
22
25
30
1
12
12
1
4
25
T
22
25
15
20
2
(-4) + 26 =T
(-8) + 14 =U
(-6) + 8 =D
(-13) + 16 =P
4 - (-12) =C
(-9) + 13 =G
(-2) + 22 =N
(-1) + 2 =I
7 - (-14) =W
19 - (-11) =E
(-11) + 26 =A
(-9) + 21 =R
16 - (-9) =H
10 - (-14) =S
0/14 letters found
Clue 3
Percentages
The academy's scale models are only partially complete, and we must calculate the exact percentage of the remaining marble blocks.
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
15
3
34
17
35
42
21
34
17
38
7
42
22
34
59
T
15
36
7
22
42
43
21
T
15
3
34
59
34
33
42
18
7
22
32
36
42
21
T
15
5% of 300 =T
50% of 86 =G
5% of 660 =C
20% of 160 =P
20% of 110 =L
5% of 340 =R
50% of 68 =E
60% of 5 =H
60% of 60 =O
20% of 295 =D
40% of 105 =I
10% of 380 =F
25% of 28 =A
10% of 350 =U
60% of 35 =N
75% of 24 =M
0/16 letters found
Clue 4
Order of operations
The security system requires a complex mathematical expression to override, following the strict sequence of operations.
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
80
20
19
115
42
19
35
19
20
75
56
115
87
33
T
80
115
33
48
42
86
75
35
56
46
75
48
T
80
23
35
55
23
35
68
12 × 8 - 16 =T
8 × 12 - 28 =K
9 × 10 - 3 =P
68 + 3 × 6 =Y
4 + 8 × 2 =H
12 + 4 × 9 =F
3 × 12 - 1 =N
8 × 6 - 2 =R
12 × 10 - 5 =S
12 × 5 - 4 =D
61 + 7 × 2 =A
7 × 8 - 23 =O
10 × 3 - 7 =I
35 + 5 × 4 =G
11 × 4 - 2 =C
3 + 4 × 4 =E
0/16 letters found
Clue 5
Fractions of a number — the last clue
We recovered a damaged ledger from the suspect's desk showing a fraction of the total stolen design files.
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
1/4 of 44 = ?
1/2 of 24 = ?
3/10 of 10 = ?
1/10 of 70 = ?
2/8 of 20 = ?
4/8 of 16 = ?
1/5 of 30 = ?
2/6 of 27 = ?
1/10 of 100 = ?
2/3 of 3 = ?
2/10 of 5 = ?
Step 2 — cross out the sentence with each answer
1.The villain stretched the clock tower with a grid projector, then mapped the escape path using vector calculus.
2.The villain skewed the library columns with a laser transit, then scrambled the school database with fractal chaos.
3.The villain skewed the library columns with a laser transit, then calculated a perfect golden ratio spiral.
4.The villain skewed the library columns with a laser transit, then factored the security code into prime factors.
5.The villain recalibrated the city arch with a caliper compass, then factored the security code into prime factors.
6.The villain warped the museum dome with a proportion wheel, then calculated a perfect golden ratio spiral.
7.The villain recalibrated the city arch with a caliper compass, then calculated a perfect golden ratio spiral.
8.The villain recalibrated the city arch with a caliper compass, then mapped the escape path using vector calculus.
9.The villain recalibrated the city arch with a caliper compass, then scrambled the school database with fractal chaos.
10.The villain shrank the main bridge with a micrometer slide, then calculated a perfect golden ratio spiral.
11.The villain shrank the main bridge with a micrometer slide, then plotted a shrinking geometric series.
12.The villain warped the museum dome with a proportion wheel, then plotted a shrinking geometric series.
Solve it
Name the culprit
Choose the one suspect left standing.
Answer Key — The Case of the Ruined Ratios
Culprit: Escher (laser transit · prime factors · right-handed pencil grip · cyan ink smudge · dropped decimal)
- Clue 1 (Fractions of a number): "THE RUINER DOES NOT STUDY FRACTAL CHAOS"5/8 of 56 = 35 (T) · 5/10 of 118 = 59 (H) · 5/10 of 54 = 27 (C) · 3/4 of 76 = 57 (A) · 1/2 of 16 = 8 (Y) · 2/6 of 51 = 17 (L) · 5/6 of 12 = 10 (R) · 1/6 of 96 = 16 (O) · 4/8 of 78 = 39 (S) · 1/2 of 102 = 51 (U) · 5/6 of 30 = 25 (E) · 2/8 of 120 = 30 (N) · 4/8 of 22 = 11 (F) · 4/6 of 51 = 34 (D) · 5/6 of 72 = 60 (I)
- Clue 2 (Integers): "THE SUSPECT WRITES WITH THEIR RIGHT HAND"(-4) + 26 = 22 (T) · (-8) + 14 = 6 (U) · (-6) + 8 = 2 (D) · (-13) + 16 = 3 (P) · 4 - (-12) = 16 (C) · (-9) + 13 = 4 (G) · (-2) + 22 = 20 (N) · (-1) + 2 = 1 (I) · 7 - (-14) = 21 (W) · 19 - (-11) = 30 (E) · (-11) + 26 = 15 (A) · (-9) + 21 = 12 (R) · 16 - (-9) = 25 (H) · 10 - (-14) = 24 (S)
- Clue 3 (Percentages): "THE RUINER FAILED TO ALIGN THE DECIMAL POINT"5% of 300 = 15 (T) · 50% of 86 = 43 (G) · 5% of 660 = 33 (C) · 20% of 160 = 32 (P) · 20% of 110 = 22 (L) · 5% of 340 = 17 (R) · 50% of 68 = 34 (E) · 60% of 5 = 3 (H) · 60% of 60 = 36 (O) · 20% of 295 = 59 (D) · 40% of 105 = 42 (I) · 10% of 380 = 38 (F) · 25% of 28 = 7 (A) · 10% of 350 = 35 (U) · 60% of 35 = 21 (N) · 75% of 24 = 18 (M)
- Clue 4 (Order of operations): "THE SCENE HAD SPOTS OF CYAN DRAFTING INK"12 × 8 - 16 = 80 (T) · 8 × 12 - 28 = 68 (K) · 9 × 10 - 3 = 87 (P) · 68 + 3 × 6 = 86 (Y) · 4 + 8 × 2 = 20 (H) · 12 + 4 × 9 = 48 (F) · 3 × 12 - 1 = 35 (N) · 8 × 6 - 2 = 46 (R) · 12 × 10 - 5 = 115 (S) · 12 × 5 - 4 = 56 (D) · 61 + 7 × 2 = 75 (A) · 7 × 8 - 23 = 33 (O) · 10 × 3 - 7 = 23 (I) · 35 + 5 × 4 = 55 (G) · 11 × 4 - 2 = 42 (C) · 3 + 4 × 4 = 19 (E)
- Clue 5 (Fractions of a number): surviving statement (box 4) → Escher1/4 of 44 = 11 · 1/2 of 24 = 12 · 3/10 of 10 = 3 · 1/10 of 70 = 7 · 2/8 of 20 = 5 · 4/8 of 16 = 8 · 1/5 of 30 = 6 · 2/6 of 27 = 9 · 1/10 of 100 = 10 · 2/3 of 3 = 2 · 2/10 of 5 = 1
About this mystery
- Grade level
- Grade 7 math
- Math topics
- Fractions of a number, Integers, Percentages, Order of operations
- Reading level
- grades 7-9
- Theme
- The Case of the Ruined Ratios — set in The Golden Ratio Academy
- Format
- Interactive online & printable worksheet with answer key
- Solution
- One unique, verified culprit among 21 suspects