© 21st Century Math Projects - Amazon S3Add these together. The sum will equal m) ... not a horizontal reflection 3) ... Century Math Project

© 21st Century Math Projects


Project Title : CSI Geometry: Transformations

Standard Focus: Geometry and Spatial Sense Time Range : 1-3 Days

Supplies : Pencil and Paper

Topics of Focus :

- Translations, Rotations and Reflections

- Dilations

- Tessellations

This particular was mapped to the transformations curriculum of most geometry textbooks

and can be used as an enrichment or review activity.

Geometry 8.G 1. Verify experimentally the properties of rotations, reflections, and

translations:

Geometry 8.G

2. Understand that a two-dimensional figure is congruent to another if the

second can be obtained from the first by a sequence of rotations, reflections,

and translations; given two congruent figures, describe a sequence that

exhibits the congruence between them.

Geometry 8.G 3. Describe the effect of dilations, translations, rotations, and reflections on

two-dimensional figures using coordinates.

Geometry 8.G

4. Understand that a two-dimensional figure is similar to another if the

second can be obtained from the first by a sequence of rotations, reflections,

translations, and dilations; given two similar twodimensional figures, describe

a sequence that exhibits the similarity between them.

Building

Functions F-BF

3. Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx),

and f(x + k) for specific values of k; find the value of k given the graphs.

Experiment with cases and illustrate an explanation of the effects on the

graph using technology. Include recognizing even and odd functions from

their graphs and algebraic expressions for them.

Congruence G-

CO

4. Develop definitions of rotations, reflections, and translations in terms of

angles, circles, perpendicular lines, parallel lines, and line segments.

Congruence G-

CO

5. Given a geometric figure and a rotation, reflection, or translation, draw the

transformed figure using, e.g., graph paper, tracing paper, or geometry

software. Specify a sequence of transformations that will carry a given figure

onto another.

Congruence G-

CO

6. Use geometric descriptions of rigid motions to transform figures and to

predict the effect of a given rigid motion on a given figure; given two figures,

use the definition of congruence in terms of rigid motions to decide if they


are congruent.

Similarity, Right

Triangles, and

Trigonometry

G-

SRT

1. Verify experimentally the properties of dilations given by a center and a

scale factor:

Similarity, Right

Triangles, and

Trigonometry

G-

SRT

1a. A dilation takes a line not passing through the center of the dilation to a

parallel line, and leaves a line passing through the center unchanged.

Similarity, Right

Triangles, and

Trigonometry

G-

SRT

1b. The dilation of a line segment is longer or shorter in the ratio given by

the scale factor.

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


CSI Geometry: Transformations

Detectives,

We can literally count the seconds until the Mathemagicians deploy their world conquering device. For

their last crime spree, an associate by the name of Optimus Composite has terrorized South America.

Based on our intel, we believe Optimus is the leader of the evil genius terrorist group.

As the Mathemagicians have done time and time again, they have scattered six

mathematical puzzles and a cryptic text message that must be solved. After solving the

puzzles, you can decode the message which will lead to Optimus’s favorite number. So

far there are six suspects that police have questioned. It is hoped that someone with a

relatively strong geometry and reasoning skills can crack the codes that have puzzled

the detectives on the case so far.

Since you are being brought in as a specialist you have to have definitive proof in

order for any arrest to hold up in court. You need to be prepared to state your case

and demonstrate your understanding of the following skills that Optimus is known to

use in the notes.

- Translations, Rotations and Reflections

- Dilations

- Tessellations

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


CSI: The Evidence

Name:_______________________________

1.

Clue

___________

2.

Clue

___________

3.

Clue

___________


4.

Clue

___________

5.

Clue

___________

6.

Clue

___________

Cryptic Text Message

Suspect

___________


Who is Optimus Composite?

Name: Freddy

Occupation: Shift Supervisor

Favorite Number: 1000

Name: Linda

Occupation: Retired

Favorite Number: 1

Name: Shaquille

Occupation: Engineer


Name: Guadalupe

Occupation: Lawyer


Name: Luigi

Occupation: Restaurant Owner


Name: Pat

Occupation: DMV

Representative



Scene #1 El Dorado Café –- Caracas, Venezuela Optimus Composite snuck into a Venezuelan coffee shop dedicated to the legendary lost city of

gold, El Dorado. It appears that Optimus stole what the owner believes is a treasure map.

Hola! Optimus Composite is ready to transform

Latin America! I found this great map. Follow the

steps to find the lost El Dorado Gold!

Step 1: ∆ABC has vertices A(-5, 3) B(0,7) C(1, -1)

Step 2: Reflect ∆ABC over the y-axis to make

∆A’B’C’

Step 3: Translate ∆A’B’C’ up 2 units and to the

left 5 units to make ∆A’’B’’C’’

Step 4: Reflect ∆A’’B’’C’’ over the x-axis and

inside the triangle you will find the correct chest.

This letter will be equal to the number 79.

____ = 79

Scene #2 Ecuador Tile Manufacturer –- Quito, Ecuador

After the robbery at the café, Optimus took a taxi to Ecuador, broke into a warehouse and stole super-

sized geometric stone tiles. It is unclear how the tile will be used for the world conquering device.

When I’m done with all these thefts, I’m going to refinishing my bathroom floor! My significant

other is a little picky and I can only use a pattern that is a semi regular tessellation! How many of

these patterns could I use?

How many patterns are

semi-regular

tessellations?

This will be equal to T t=_______


Scene #3 Nazca Desert -- Peru

An entire square mile of ground was somehow excavated from earth. It’s believed this ground had

one of the famed Nazca Lines on it. Optimus Composite carved this note into the leftover dirt.

Carved into the desert are a number of drawings that can only be seen from a helicopter. See if you can

see my dilation inspired drawings of the drawings! Fill in the missing four pieces (either the scale

factor, 𝑨𝑩̅̅ ̅̅ or 𝑨’𝑩’̅̅ ̅̅ ̅̅ ) with correct values from the “Number Bank”.

The Hummingbird

The Monkey

The “Trapezoid”(even though it’s not)

The Whale

Number Bank What is leftover in the

Number Bank? (Add these together. The sum will equal m)

m=____

130 ¾ ½

89.25 2/7 110


Scene #4 Amazon River –- Colombia

On a cruise, Optimus dove into the Amazon and took a dozen mutated, pregnant piranhas.

El Eternauta vs. LaS YacumamaS

Famed South American Superhero El Eternauta needs to destroy three infamous Yacumamas, alien life

forms that live in the Amazon River. Eternauta has a strangely shaped power blast and he only has one

charge left and needs hit all of Las Yacumamas!

Which is a correct order of transformations that will

allow El Eternauta to defeat Las Yacumamas?

Shift 12 units to the right, Shift

1 unit up, Reflect over x-axis

a = -100

Shift 12 unit to the right, Shift 1

unit down, Reflect over x-axis

c = -300

Shift 1 unit up, Reflect over x-

axis, shift 12 units to the right

e = -500

Scene #5 El Tatio Geysers –- Santiago, Chile

High in the Andes Mountains, Optimus filled a hundred balloons with pure geyser steam.

Find the transformed Chilean Flag to the left that meets these three requirements:

1)it is congruent 2)not a horizontal reflection 3)rotated clockwise 135o

The number of the flag that meets the three requirements is equal to i. i =___


Scene #6 Estádio do Maracanã -- Rio de Janeiro, Brazil

For Optimus’s final heist, a crane and bulldozer were hotwired and taken from the stadium. It

may only be a matter of time until the world conquering device is built and activated. Later,

investigators were sent what may be the final cryptic text message.

The Mathemagicians are about to reach

our GOOOOAAAAALLLLLL. Can you

reach yours? Which of these three sets

of transformations will score a goal? If

the ball lands on a vertex with a player,

the play fails. (All plays start at (0,4))

Which play scores?

(This letter will be equal to 500)

_____ = 780

CRYPTIC PUZZLE SOLVER TEXT MESSAGE

Putting on the final touches, world ends

soon. Love ya, Optimus Composite

M + A + T + E + M + A + T + I + C + A

Play

A

1. (x + 1, y – 2)

2. reflect over the x-axis.

3. reflect over y-axis

4. (x + 1, y – 2)

Play

C

1. (x – 1, y – 3)

2. reflect over the y-axis.

3. reflect over x-axis

4. (x + 1, y – 4)

Play

E

1. (x – 3, y – 2)



4. (x – 2, y – 3)


Thank you for being my Math Friend!

If you liked this

21st Century Math Project You might like others. (Click the logo)

Math it Up. Boomdiggy.

http://www.nextlesson.org/21st-century-math


Who is Optimus Composite?

Name: Freddy

Occupation: Shift Supervisor


Name: Linda

Occupation: Retired

Favorite Number: 1

Name: Shaquille

Occupation: Engineer


Name: Guadalupe

Occupation: Lawyer


Name: Luigi

Occupation: Restaurant Owner


Name: Pat

Occupation: DMV

Representative



Scene #1 El Dorado Café –- Caracas, Venezuela Optimus Composite snuck into a Venezuelan coffee shop dedicated to the legendary lost city

of gold, El Dorado. It appears that Optimus stole what the owner believes is a treasure map.

Hola! Optimus Composite is ready to transform

Latin America! I found this great map. Follow

the steps to find the lost El Dorado Gold!

Step 1: ∆ABC is at points A(-5, 3) B(0,7) C(1, -1)

Step 2: Reflect ∆ABC over the y-axis to make

∆A’B’C’

Step 3: Translate ∆A’B’C’ up 2 units and to the

left 5 units to make ∆A’’B’’C’’

Step 4: Reflect ∆A’’B’’C’’ over the x-axis and

inside the triangle you will find the correct chest.

This letter will be equal to the number 79.

A____ = 79

Scene #2 Ecuador Tile Manufacturer –- Quito, Ecuador

After the robbery at the café, Optimus took a taxi to Ecuador, broke into a warehouse and stole super-

sized geometric stone tiles. It is unclear how the tile will be used for the world conquering device.

When I’m done with all these thefts, I’m going to refinishing my bathroom floor! My significant

other is a little picky and I can only use a pattern that is a semi regular tessellation! How many of

these patterns could I use?

How many patterns are

semi-regular

tessellations?

This will be equal to T t=_______4


Scene #3 Nazca Desert -- Peru

An entire square mile of ground was somehow excavated from earth. It’s believed this ground had

one of the famed Nazca Lines on it. Optimus Composite carved this note into the leftover dirt.

Carved into the desert are a number of drawings that can only be seen from a helicopter. See if you can

see my dilation inspired drawings of the drawings! Fill in the missing four pieces (either the scale

factor, 𝑨𝑩̅̅ ̅̅ or 𝑨’𝑩’̅̅ ̅̅ ̅̅ ) with correct values from the “Number Bank”.

The Hummingbird

The Monkey

The “Trapezoid”(even though it’s not)

The Whale

Number Bank What is leftover in the

Number Bank? (Add these together. The sum will equal m)

m=____90

130 ¾ ½

89.25 2/7 110


Scene #4 Amazon River –- Colombia

On a cruise, Optimus dove into the Amazon and took a dozen mutated, pregnant piranhas.

El Eternauta vs. LaS YacumamaS

Famed South American Superhero El Eternauta needs to destroy three infamous Yacumamas, alien life

forms that live in the Amazon River. Eternauta has a strangely shaped power blast and he only has one

charge left and needs hit all of Las Yacumamas!

Which is a correct order of transformations that will

allow El Eternauta to defeat Las Yacumamas?

Shift 12 units to the right, Shift

1 unit up, Reflect over x-axis

a = -100

Shift 12 unit to the right, Shift 1

unit down, Reflect over x-axis

c = -300

Shift 1 unit up, Reflect over x-

axis, shift 12 units to the right

e = -500

Scene #5 El Tatio Geysers –- Santiago, Chile

High in the Andes Mountains, Optimus filled a hundred balloons with pure geyser steam.

Find the transformed Chilean Flag to the left that meets these three requirements:

1) it is congruent 2)not a horizontal reflection 3)rotated clockwise 135o

The number of the flag that meets the three requirements is equal to i. i =___6


Scene #6 Estádio do Maracanã -- Rio de Janeiro, Brazil

For Optimus’s final heist, a crane and bulldozer were hotwired and taken from the stadium. It

may only be a matter of time until the world conquering device is built and activated. Later,

investigators were sent a cryptic text message.

The Mathemagicians are about to reach

our GOOOOOOAAAAAAALLLLLL.

Can you reach yours? Which of these

three sets of transformations will

score a goal? If the ball lands on a

vertex with a player, the play fails. (All

plays start at (0,4))

Which play scores?

(This letter will be equal to 500)

e_____ = 780

CRYPTIC PUZZLE SOLVER TEXT MESSAGE

Putting on the final touches, world ends

soon. Love ya, Optimus Composite

M + A + T + E + M + A + T + I + C + A

Play

A

1. (x + 1, y – 2)

2. reflect over the x-axis.

3. reflect over y-axis

4. (x + 1, y – 2)

Play

C

1. (x – 1, y – 3)



4. (x + 1, y – 4)

Play

E

1. (x – 3, y – 2)



4. (x – 2, y – 3)


From Puzzle 1 A____ = 79

From Puzzle 2 t=_______4 From Puzzle 3 m=____90 From Puzzle 4 c = -300 From Puzzle 5 i =___6 From Puzzle 6 e_____ = 780

M + A + T + E + M + A + T + I + C + A 90+79+4+780+90+79+4+6+(-300)+79 =911

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© 21st Century Math Projects - Amazon S3Add these together. The sum will equal m) ... not a horizontal reflection 3) ... Century Math Project