unit 1 crime scene decoders geometry: shapes, lines & angles
TRANSCRIPT
© 21st Century Math Projects
Unit 1: Crime Scene Decoders Geometry: Shapes, Lines & Angles
Standard Focus: Geometry and Spatial Sense Time Range : 1-3 Days
Supplies : Pencil and Paper
Topics of Focus :
- Distance and Midpoints, Segment Addition, Polygons , Writing Equations of Lines, Parallel
Lines
This particular was mapped to the introductory curriculum of most geometry textbooks and
can be used as an enrichment or review activity.
Geometry 8.G 1b. Angles are taken to angles of the same measure.
Geometry 8.G 8. Apply the Pythagorean Theorem to find the distance between two
points in a coordinate system.
Congruence G-
CO
1. Know precise definitions of angle, circle, perpendicular line, parallel
line, and line segment, based on the undefined notions of point, line,
distance along a line, and distance around a circular arc.
Congruence G-
CO
9. Prove theorems about lines and angles. Theorems include: vertical
angles are congruent; when a transversal crosses parallel lines, alternate
interior angles are congruent and corresponding angles are congruent;
Expressing
Geometric Properties
with Equations
G-
GPE
6. Find the point on a directed line segment between two given points
that partitions the segment in a given ratio.
Expressing
Geometric Properties
with Equations
G-
GPE
7. Use coordinates to compute perimeters of polygons and areas of
triangles and rectangles, e.g., using the distance formula.★
Procedures:
A.) Student will be given the letter from Chief Harris, the possible suspects, and crime scene puzzles.
B.) Students will work in pairs or individually to solve the crime.
C.) Students will determine which suspect should be arrested.
D.) Students will create a portfolio of evidence proving that they have arrested the right person and will
demonstrate their understanding of their mathematical content present in the problem.
*E.) Students can present their evidence to the class as an oral presentation.
*Extensions
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CSD: The eviDenCe
name:_______________________________
1.
Clue
___________ 2.
Clue
___________ 3.
Clue
___________
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4.
Clue
___________ 5.
Clue
___________ 6.
Clue
___________ CrypTiC TexT meSSage
SuSpeCT
___________
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Crime Scene Decoders Geometry: Shapes, Lines & Angles
Detectives,
Once again the world has been rocked by a string of high profile robberies. This time it seems that
South Africa has been victimized by the evil genius group, the Mathemagicians. We believe the
Mathemagicians have been successfully piecing together a world conquering device – to conquer the
world. Notes signed “Euclid Swaggster” have been discovered at each crime scene. As is the calling
card of the Mathemagicians, these notes are laden with mathematical puzzles. A cryptic text message
was sent to police, but it requires the puzzles to be cracked. We’ve been told the result of the cryptic
text message will calculate to Swaggster’s favorite number.
Thus far there are six suspects that police have questioned. It is
hoped that someone with relatively strong geometry skills can crack
the codes that have puzzled the detectives on the case so far.
You need to be prepared to state your case and demonstrate your
understanding of the following skills that Swaggster is known to use
in his notes.
- Distance and Midpoints
- Segment Addition
- Polygons
- Writing Equations of Lines
- Parallel Lines
Be sure to include:
- Other examples of the concepts
- Definitions
- Any other relevant information.
Keep in mind, the slightest miscalculation or illegible footnote could result in a not guilty verdict. Oh,
did I mention that use of a calculator might prematurely set off his world conquering device?
Good luck to you, gumshoe.
Chief Harris
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Who is Euclid Swaggster?
Name: Kofi
Occupation: Musician
Favorite Number: -230
Name: Safiya
Occupation: Librarian
Favorite Number: 0
Name: Andy
Occupation: Writer
Favorite Number: 105,300
Name: Chloe
Occupation: High
School Teacher
Favorite Number:
970
Name: Ting Fen
Occupation: Speech
Pathologist
Favorite Number: 37,120
Name: Hank
Occupation: Engineer
Favorite Number:
21,016
© 21st Century Math Projects
Scene #1 King Shaka Int’l Airport –- Durban, South Africa Euclid Swaggster apparently smuggled mystic Zulu powders through airport security. To
celebrate, Swaggster left this note in a bathroom stall.
Hello Lads,
I, the great Euclid Swaggster, have been
racking up some frequent flier miles while
swagging in first class. I’ve traveled the great
golden triangle of airports in South Africa for a
total of 3026 kilometers! Isn’t that exciting?
If you can figure out the f, then you can figure
out the clue to my first puzzle.
f = ____
Scene #2 The Big Hole –- Kimberely, North Cape
Posing as an ordinary tourist, Swaggster broke into the Big Hole Diamond Mine Museum and made off
with their 19 largest diamonds. Investigators are unsure how the diamonds will be used for the World
Conquering Device at this time.
Let’s play everyone’s favorite game! Who
Can Guess Which One is My Diamond
Fragment?
1. My fragment is a polygon
2. My polygon is not a diamond
3. My polygon has an even
number of vertices.
4. My polygon is convex.
5. My polygon is irregular
The number on the fragment that
meets these requirements is equal to s.
s =______
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Scene #3 Capetown Stadium -- Capetown, South Africa
A security guard reported a break-in this morning and discovered the theft of 42 game-used vuvuzelas.
Made famous at the 2010 World Cup, the vuvuzela is the most annoying sound maker in the world.
BZZZZ. Go, South Africa Go! With these two passes, the home team is going to spring a counter!
How far will the soccer ball travel after both passes?
Round your answer to the nearest whole number. This answer and its
corresponding letter is the clue.
______=______
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Scene #4 Highgate Ostrich Show Farm –- Oudtshoorn, South Africa
After abusing riding privileges, Euclid Swaggster ostrichnapped the current world champion
and a jockey uniform.
These ostriches go crazy fast. Since I’m trying to conquer the world quickly, I need the fastest
ostrich. After doing some riding I calculated some linear models.
Which one is the fastest? (x = seconds, y = feet). (Hint: Which ostrich has the highest slope?)
(letter of ostrich)=(ft/s speed of ostrich)
______=______
Scene #5 Kruger National Park –- South Africa
Although the details are sketchy, a park ranger believes that tails were shaved from an entire rhino
family. Investigators are unsure of the value of rhino tail hair, but they later found this note.
My friends and I are a little mathematically anal and they’ve stopped in to
visit me in the middle of my rhino tail hair heist! Let’s meet in the middle!
R =____
highgate Invitational
A i r s -5x + y = -2
Travels through points (0, -5) and (6, -2)
Travels through the point (-2, -1) and is perpendicular to the
line y = -¼ x + 2
x9
20-2y
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Scene #6 MuseuMAfricA -- Johannesburg, South Africa
Last night, Euclid Swaggster repelled into the heavily alarmed MuseuMAfricA. Swaggster
most definitely has soft feet and great swagg. He left with hundreds of tokens and headrests
from African history.
I’ll be eBaying these headrests later. You can check out my listings @SwaggfromtheSwaggster14.
Before I’m out, I’ll be taking a trip on the luxury Blue Line train.
Wonderboom Street and President Steyn Street are parallel to each other. If you can figure out
angles A and E, you might have a chance to stop me. LOL!
C =_______
CRYPTIC PUZZLE SOLVER TEXT MESSAGE
Good luck. Lol. Stay Swaggin.
S • A + (F • R)I – C + A
Euclid Swaggster
© 21st Century Math Projects
Who is Euclid Swaggster?
Name: Kofi
Occupation: Musician
Favorite Number: -230
Name: Safiya
Occupation: Librarian
Favorite Number: 0
Name: Andy
Occupation: Writer
Favorite Number: 105,300
Name: Chloe
Occupation: High School Teacher
Favorite Number: 970
Name: Ting Fen
Occupation: Speech Pathologist
Favorite Number: 37,120
Name: Hank
Occupation: Engineer
Favorite Number: 21,016
© 21st Century Math Projects
Scene #1 King Shaka Int’l Airport –- Durban, South Africa Euclid Swaggster apparently smuggled mystic Zulu powders through airport security. To celebrate, Swaggster left this note in a bathroom stall.
Hello Lads,
I, the great Euclid Swaggster have been racking up some frequent flier miles while swagging in first class. I’ve traveled the great golden triangle of airports in South Africa for a total of 3026 kilometers! Isn’t that exciting?
If you can figure out the f, then you can figure out the clue to my first puzzle.
14f + 926 = 3026
f = ____150
Scene #2 The Big Hole –- Kimberely, North Cape
Posing as an ordinary tourist, Swaggster broke into the Big Hole Diamond Mine Museum and made off with their 19 largest diamonds. Investigators are unsure how the diamonds will be used for the World Conquering Device at this time.
Let’s play everyone’s favorite game! Who Can Guess Which One is My Diamond Fragment?
1. My fragment is a polygon 2. My polygon is not a diamond 3. My polygon has an even
number of vertices. 4. My polygon is convex. 5. My polygon is irregular
The number on the fragment that meets these requirements is equal to s.
s =_______ 6
© 21st Century Math Projects
Scene #3 Capetown Stadium -- Captone, South Africa
A security guard reported a break-in this morning and discovered the theft of 42 game-used vuvuzelas. Made famous at the 2010 World Cup, the vuvuzela is the most annoying soundmaker in the world.
BZZZZZZZZZZ. Go, South Africa Go! With these two passes, the home team is going to spring a counter!
How far will the soccer ball travel after both passes? First pass: 302 + 102= SQRT (900 +100) = 31.63, Second Pass 252 + 252 = SQRT(625+625) = 35.36 so ~ 66.99
Round your answer to the nearest whole number. This answer and its corresponding letter is the clue.
______=______ i=67
A i r s 65 units 67 units 69 units 71 units
© 21st Century Math Projects
Scene #4 Highgate Ostrich Show Farm –- Oudtshoorn, South Africa
After abusing riding privileges, Euclid Swaggster ostrichnapped the current world champion and a jockey uniform.
These ostriches go crazy fast. Since I’m trying to conquer the world quickly, I need the fastest ostrich. After doing some riding I calculated some linear models.
Which one is the fastest? (x = seconds, y = feet). (Hint: Which ostrich has the highest slope?)
(letter of ostrich)=(ft/s speed of ostrich)
______=______ A = 5
Scene #5 Kruger National Park –- South Africa
Although the details are sketchy, a park ranger believes that tails were shaved from an entire rhino family. Investigators are unsure of the value of rhino tail hair, but they later found this note.
My friends and I are a little mathematically anal and they’ve stopped in to visit me in the middle of my rhino tail hair heist! Let’s meet in the middle!
I am at the Kruger National Park in Skukuza with the latitude and longitude coordinates (-24.98, 31.58). my friends are exploring the Nelson Mandela Museum in Mpumalanga at (-29.82, 30.62). We are going to meet exactly in between our coordinates. Where will we be meeting?
X coordinate -> -24.98 + -29.82 = -54.80 / 2 = -27.40 Y Coordinate -> 31.58 + 30.62 = 62.20 / 2 = 31.10 adding them together is 3.70 so…
Add your x and Y coordinates together to find r and the clue for this puzzle
r =____ 3.70
highgate Invitational
A i r s -5x + y = -2
y = 5x - 2
y = 9/2 x + 10
Travels through points (0, -5) and (6, -2)
Y = ½ x – 5
Travels through the point (-2, -1) and is perpendicular to the
line y = -¼ x + 2 Y = 4x + 7
x=9
20-2y
© 21st Century Math Projects
Scene #6 MuseuMAfricA -- Johannesburg, South Africa
Last night, Euclid Swaggster repelled into the heavily alarmed MuseuMAfricA. Swaggster most definitely has soft feet and great swagg. He left with hundreds of tokens and headrests from African history
I’ll be eBaying these headrests later. You can check out my listings @SwaggfromtheSwaggster14. Before I’m out, I’ll be taking a trip on the luxury Blue Line train.
Wonderboom Street and President Steyn Street are parallel to each other. If you can figure out angles A and E, you might have a chance to stop me. LOL!
50+50 C =_______ 100
CRYPTIC PUZZLE SOLVER TEXT MESSAGE
Good luck. Lol. Stay Swaggin.
S • A + (F • R)I – C + A
Euclid Swaggster
© 21st Century Math Projects
From Puzzle 1 f = 150
From Puzzle 2 s = 6
From Puzzle 3 i=67
From Puzzle 4 A = 5
From Puzzle 5 r = 3.70
From Puzzle 6 C = 100
(6) • (5) + (150 • 3.7)67 – (100) + (5)
(6) • (5) + (555)67 – (100) + (5) 30 + 37185 – (100) + (5)
37215 – (100) + (5)
37115 + (5) = 37120