crime scene decoders algebra: variables and expressions

© 21st Century Math Projects

Crime Scene Decoders Algebra: Variables and Expressions

Standard Focus : Number, Number Sense, and Operations

Time Range : 1-3 Days

Supplies : Pencil and Paper

Topics of Focus :

- Order of Operations

- Translating Verbal and Algebraic Expressions

- Open Sentences

- Distributing

- Combining Like Terms

This particular was mapped to the curriculum in Glencoe Algebra 1 Chapter 1 and can be used as an enrichment or review activity.

Expressions and Equations 6.EE 2. Write, read, and evaluate expressions in which letters stand for numbers.

Expressions and Equations 6.EE 2a. Write expressions that record operations with numbers and with letters

standing for numbers.

Expressions and Equations 6.EE 2c. Evaluate expressions at specific values of their variables. Include

expressions that arise from formulas used in real-world problems.

Expressions and Equations 6.EE

2d. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).

Expressions and Equations 7.EE

4. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

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 Algebra: Variables & Expressions

Detectives,

As you know we are after a group of international evil geniuses, the Mathemagicians. Our evidence indicates they have plans to build a world conquering device – to conquer the world. It seems that one of the anonymous henchmen, Otto Pemdas, has committed a string of robberies all over Australia. We fear this is another step in the Mathemagician’s attempt to build a world conquering device.

Fortunately, the Mathemagicians are arrogant about their work and have a reputation for leaving behind a trail of notes and a cryptic text message. The text message when substituted correctly will calculate to the Otto’s favorite number. So far there are six suspects that police have questioned. It is hoped that someone with a relatively strong number sense can crack some codes that have puzzled the detectives on the case so far.

Your job is to bring Otto Pemdas to justice and save the planet. You need to be prepared to state your case and demonstrate your understanding of the following skills that Otto is known to use in the notes.

- Order of Operations

- Translating Verbal and Algebraic Expressions

- Open Sentences

- Distribution

- Combining Like Terms

Be sure to include:

- Other examples of the concepts

- Definitions

- Any other relevant information.

This is not a time to be sloppy. 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 Otto Pemdas?

Name: Bianca

Occupation: Baker

Favorite Number: 3

Name: Randal

Occupation: Dentist

Favorite Number: -8

Name: Donnie

Occupation: Factory Supervisor

Favorite Number: 62

Name: Sue

Occupation: Corrections Officer

Favorite Number: 44

Name: Alex

Occupation: Politician

Favorite Number: 98

Name: Stu

Occupation: Chef

Favorite Number: 24


Scene #1 Sydney Opera House -- New South Wales

Last night, Otto Pemdas broke into the Opera House and stole three parabolic shell ribs from the unique roof. Since he moves at ninja-like speed, the security cameras missed everything, but he left this note.

G’Day Police Officers of Australia,

To let you know upfront, the Mathemagicians plan on conquering the world. Okay, now that I have your attention, I figure I’ll give you a fighting chance to stop us. MuHahahahahaha.

x = # of sides on a triangle y = # of femurs an average man has z = # of syllables in integration

E = ________ Scene #2 The Dingo Steakhouse –- Western Australia

At a five-star restaurant just outside of Perth, a waitress stumbled upon this note on the back of the receipt. It was later discovered that the restaurant’s signature sauce was missing.

To celebrate our thefts, I took the whole Pemdas family out for a native three-course meal.

In all there was one family-sized BBQ Shrimp that cost $40, 5 grilled kangaroo legs that cost $18.50 each, 2 alligator burgers that cost $24 a piece, 7 drinks that cost $2.50 each, and 7 quadruple chocolate pavlova at $11.49 a pop. For their wonderful service, I’ve tipped the waiter $0.57 AUD!

I paid with a recently stolen $300 AUD. How much change did I get? This answer will be equal to $.

Start Here 𝑊𝑊 = 2𝑥𝑥2 − 𝑦𝑦𝑦𝑦

𝐴𝐴 = 4𝑥𝑥𝑦𝑦

+ 𝑤𝑤𝑥𝑥

E = a +(b + w) – x + (y – z)

B = (x2+z2) – a + w - yz

$ = _____


Scene #3 Great Barrier Reef -- Queensland

A cruise ship captain was stunned to find the following note plastered to the inside of his personal bathroom. A few guests believed they saw a stealth helicopter drop in during the middle of the night.

G’Dafternoon Mate! When everyone was asleep, I stole a dolphin right out of the reef. It was pretty easy too. Just for kicks, this might help you find me.

Find the solution set of each of the five problems using the replacement set:

Flipper = {-40, -13.5, -5, 0, ½ , 5, 300}

1.) x = 32 – 72 2.) x2 = 30 – 5 3.) x < -10

4.) x =

(9 − 23)(6 − 4)

5.) 10 – x < 7 Take a good long look at the

solution sets… there’s an unused object in the set Flipper. F is this number.

F = ______

Scene #4 Aboriginal Museum in the Outback –- South Australia

The curator of an Aboriginal Museum was stunned to find one of the most-prized hollowed log coffins was stolen. The log coffin, of a noted Aboriginal poet, supposedly has mystical powers.

The Outback sure is beautiful in the spring. Aboriginal villages, marvelous rock painting, cacti, and stealing more stuff. Here’s a little map puzzle of my journey. Oh, g = -1 miles and h = 4 miles.

If you find the total distance of the path, you’ll find its magic number.

$ = 51 miles ɸ = 53 miles

E = 55 miles @ = 57 miles


Scene #5 Melbourne Cricket Ground -- Victoria

After the Aussie Rules Football match between rivals the Demons and Eagles, a security officer discovered the world’s oldest football was stolen from the museum. While it’s unsure how Otto plans to use it, the football was made out of an inflated pig bladder. Later he found this note.

FUMBLE. You shoulda been watching your ball. The coach has drawn up a complicated play. I’m not even sure he knows what it is.

MYSTERY EXPRESSION GAME!!!!!

i. Twice x Answer I:

ii. 9 less than the Answer I Answer II:

iii. The sum of Answer II and the product of 5 and t Answer III:

iv. Answer III decreased by two-fifths the cube of another number

Answer IV:

v. Half of Answer IV

Answer V:

ANSWER V is…

E (9 − 2𝑥𝑥 + 5𝑡𝑡) − 25𝑛𝑛

3

2

ɸ (2𝑥𝑥 − 9 − 5𝑡𝑡) − 25𝑛𝑛

3

2

$ (9 − 2𝑥𝑥 + 5𝑡𝑡) + 25𝑛𝑛

3

2

@ (2𝑥𝑥 − 9 + 5𝑡𝑡) − 25𝑛𝑛

3

2

The correct answer = -2 ______ = -2


Scene #6 Television Studio –- New South Wales

After a Bindi Irwin television taping, this note was found outside the studio. Otto is suspected of stealing a number of Bindi Irwin DVDs. It’s unclear whether the DVDs are related to the world conquering device or if Otto is just a big Bindi Irwin fan.

G’Daft…night. I guess you aren’t hot on my trail as it seems I can enjoy a really great television taping of “The Bindi Show” without worry. I had some extra time for this puzzle. I’m sure you won’t figure it out. What is V?

V = 36a (a – c) – 24c(2a – 3c) + 2a( -2( 3a +c)) v = ___

So you were actually able to distribute and combine like terms. Whoopdidoo. Too bad that doesn’t tell you

the value of V. Here’s the values for a and c -- I even did it for you. UNLESS I’M LYING.

4 + 3 = 3 + 4 = 7 is an example of the associative property

3 + (1+5) = (3+1) +5 = 9 is an example of the commutative property

So a = 7 and c = 9

HAHAHAHAHA see I just gave you to values! Or did I? MUHAHAHAHA. Better figure it out quick

before you plug them in to find V. I’d surely hate if you did it wrong.

CRYPTIC PUZZLE SOLVER TEXT MESSAGE

lol c if u can solve this. u need sum variables.

($ + ɸ + V) + FE$ - @$

L8r, Otto Pemdas


Who is Otto Pemdas?

Name: Bianca

Occupation: Baker

Favorite Number: 3

Name: Randal

Occupation: Dentist

Favorite Number: -8

Name: Donnie

Occupation: Factory Supervisor

Favorite Number: 62

Name: Sue

Occupation: Corrections Officer

Favorite Number: 44

Name: Alex

Occupation: Politician

Favorite Number: 98

Name: Stu

Occupation: Chef

Favorite Number: 24


Scene #1 Sydney Opera House -- New South Wales

Last night, Otto Pemdas broke into the Opera House and stole three parabolic shell ribs from the unique roof. Since he moves at ninja-like speed the security cameras missed everything, but he left this note.

G’Day Police Officers of Australia,

To let you know upfront, the Mathemagicians plan on conquering the world. Okay, now that I have your attention, I figure I’ll give you a fighting chance to stop us. MuHahahahahaha.

x=3, y=2, and z=4

W = 2x2 – yz

W=10

A = (4x/z ) + wx

A =33

B = (x2+z2) – a + w - yz

B = 25 – 33 + 10 – 8 B = -6

E = a +(b +w) – x +(y –z)

33 + (-6 + 10) – 3 +(2-4) 33+ (4) – 3 +(-2) = 32

E = ________32 Scene #2 The Dingo Steakhouse –- Western Australia

At a five-star restaurant just outside of Perth, a waitress stumbled upon this note on the back of the receipt. It was later discovered that the restaurant’s signature sauce was missing.

To celebrate our thefts, I took the whole Pemdas family out for a native three-course meal.

In all there was one family-sized BBQ Shrimp that cost $40, 5 grilled kangaroo legs that cost $18.50 each, 2 alligator burgers that cost $24 a piece, 7 drinks that cost $2.50 each, and 7 quadruple chocolate pavlova at $11.49 a pop. For their wonderful service, I’ve tipped the waiter $0.57 AUD!

I paid with a recently stolen $300 AUD. How much change did I get? This answer will be equal to $. 40+ 140.5 +17.5+80.43 +.57 = 279 21 change

$ = _____


Scene #3 Great Barrier Reef -- Queensland

A cruise ship captain was stunned to find the following note plastered to the inside of his personal bathroom. A few guests believed they saw a stealth helicopter drop in during the middle of the night.

G’Dafternoon Mate! When everyone was asleep, I stole a dolphin right out of the reef. It was pretty easy too. Just for kicks, this might help you find me.

Find the solution set of each of the five problems using the replacement set:

Flipper = {-40, -13.5, -5, 0, ½ , 5, 300}

1.) x = 32 – 72 2.) x2 = 30 – 5 3.) x < -10

4.) x =

(9 − 23)(6 − 4)

5.) 10 – x < 7 Take a good long look at the

solution sets… there’s an unused object in the set Flipper. F is this number.

F = 0

Scene #4 Aboriginal Museum in the Outback –- South Australia

The curator of an Aboriginal Museum was stunned to find one of the most-prized hollowed log coffins was stolen. The log coffin, of a noted Aboriginal poet, supposedly has mystical powers.

The Outback sure is beautiful in the spring. Aboriginal villages, marvelous rock painting, cacti, and stealing more stuff. Here’s a little map puzzle of my journey. Oh, g = -1 miles and h = 4 miles.

If you find the total distance of the path, you’ll find its magic number.

$ = 51 miles ɸ = 53 miles

E = 55 miles @ = 57 miles


Scene #5 Melbourne Cricket Ground -- Victoria

After the Aussie Rules Football match between rivals the Demons and Eagles, a security officer discovered the world’s oldest football was stolen from the museum. While it’s unsure how Otto plans to use it, the football was made out of an inflated pig bladder. Later he found this note.

FUMBLE. You shoulda been watching your ball. The coach has drawn up a complicated play. I’m not even sure he knows what it is.

MYSTERY EXPRESSION GAME!!!!!

i. Twice x Answer I:

ii. 9 less than the Answer I Answer II:

iii. The sum of Answer II and the product of 5 and t Answer III:

iv. Answer III decreased by two-fifths the cube of another number

Answer IV:

v. Half of Answer IV

Answer V:

ANSWER V is…

E (9 − 2𝑥𝑥 + 5𝑡𝑡) − 25𝑛𝑛

3

2

ɸ (2𝑥𝑥 − 9 − 5𝑡𝑡) − 25𝑛𝑛

3

2

$ (9 − 2𝑥𝑥 + 5𝑡𝑡) + 25𝑛𝑛

3

2

@ (2𝑥𝑥 − 9 + 5𝑡𝑡) − 25𝑛𝑛

3

2

The correct answer = -2 ______ = -2


Scene #6 Television Studio –- New South Wales

After a Bindi Irwin television taping, this note was found outside the studio. Otto is suspected of stealing a number of Bindi Irwin DVDs. It’s unclear whether the DVDs are related to the world conquering device or if Otto is just a big Bindi Irwin fan.

G’Daft…night. I guess you aren’t hot on my trail as it seems I can enjoy a really great television taping of “The Bindi Show” without worry. I had some extra time for this puzzle. I’m sure you won’t figure it out. What is V?

V = 36a (a – c) – 24c(2a – 3c) + 2a( -2( 3a +c)) v = -72

(36a^2-36ac)+( – 48ac +72c^2)+(-12a^2 -4ac)

24a^2-88ac+72c^2

1944 – 5544 +3528 = -72

So you were actually able to distribute and combine like terms. Whoopdidoo. Too bad that doesn’t tell you

the value of V. Here’s the values for a and c -- I even did it for you. UNLESS I’M LYING.

4 + 3 = 3 + 4 = 7 is an example of the associative property

3 + (1+5) = (3+1) +5 = 9 is an example of the commutative property

So a = 7 and c = 9 a = 9 and c = 7

CRYPTIC PUZZLE SOLVER TEXT MESSAGE

lol c if u can solve this. u need sum variables.

($ + ɸ + V) + FE$ - @$

21 + 53 + -72 – 0 + 42 =44

L8r, Otto Pemdas

crime scene decoders algebra: variables and expressions

Documents