unit 1 crime scene decoders geometry: shapes, lines & angles

© 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


CSD: The eviDenCe

name:_______________________________

1.

Clue

___________ 2.

Clue

___________ 3.

Clue

___________


4.

Clue

___________ 5.

Clue

___________ 6.

Clue

___________ CrypTiC TexT meSSage

SuSpeCT

___________


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


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


Name: Hank

Occupation: Engineer

Favorite Number:

21,016


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 =______


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.

______=______


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


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


Who is Euclid Swaggster?

Name: Kofi

Occupation: Musician

Favorite Number: -230

Name: Safiya

Occupation: Librarian

Favorite Number: 0

Name: Andy

Occupation: Writer


Name: Chloe

Occupation: High School Teacher

Favorite Number: 970

Name: Ting Fen

Occupation: Speech Pathologist


Name: Hank

Occupation: Engineer



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


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


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


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


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

unit 1 crime scene decoders geometry: shapes, lines & angles

Documents