November 13Th, 2012 MAC 2 M 3 (Mega-Math-Mystery)

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November 13th, 2012 – MAC^2 M^3 (Mega-Math-Mystery)

Come and join us at our next MAC2 get together to participate in and to create a Mega- Math-Mystery!

Our November monthly meeting is open to all MAC2 members, and any friends they’d like to bring along who are interested in learning and teaching mathematics, elementary or secondary. The fun begins at 5pm at St. Joseph’s High School, 243 Cundles Road East, BARRIE, ON – starting in the St. Joseph’s Cafeteria, and will go till about 7pm.

We will start with a quick introduction to the activity in the cafeteria, and by 5:15 we will break into groups and solve a Mega-Math- Mystery that has been created specially for this night’s meeting.

Somewhere between 5:45 pm and 6pm all participants will regroup in one of the St. Joseph’s classrooms (to be determined) where we will debrief the activity, and then begin to create a Mega-Math-Mystery that can be used in our own classrooms (working with teachers from the same grades or divisions).

What is a Mega-Math-Mystery you ask? It is a problem-solving based activity that students can do in groups (though could be adapted to be done solo) which involves travelling from one location to another to find clues, solve math problems, and eventually find a solution to “the mystery”. The Mega-Math-Mystery can be mediated using various forms of technology – GPS, iPhone apps, QR codes, website URL links (all of which we will be using during our starter activity), though a scavenger hunt, with clues printed out on paper will work just as well in a low-tech classroom (and we will be discussing both types of approaches during the debrief). A typical Mega-Math-Mystery involves searching for clues by travelling outside the classroom, around the school building or grounds, which is great for kinesthetic learners, and a change of pace, though this aspect of visiting different places for clues can also be simulated inside a classroom or study area like the school library.

To help the MAC2 committee prepare for the event in two weeks, please visit the link below and fill out the quick form Mega Math Mystery

Trying out some QR Codes Mega Math Mystery

NEWS BULLETIN

The Toronto Triangulists have threatened to take over the textbooks and terrorize all theorems and truisms taught in trigonometry and tabulating classes … .and by extension … anything under the topic of Mathematics!

This radical group wields terrible Weapons of Math Destruction, and their Mission Statement is this: “Triangles rule all !”

Their triabolical plan is to eradicate all mention of any shapes other than triangles from the curriculum, from all textbooks, and from our lives. If they succeed, mathematicians will no longer be able to enjoy the beauty of a circle, the comfort of a perfectly formed square, or the playfulness of a perky parallelogram.

The Triangulists have issued a challenge, and given us one last chance to prove that indeed the current math standards demonstrate plenty of knowledge and mastery of their beloved triangles. If we can solve the puzzles presented, they will be satisfied, and will remove their threat to wipe out mathematical education as we know it.

As members of MAC2, the Mathematics Association for Cottage Country, your mission along with your team-mates is to follow the clues and solve the problems posed by the Toronto Triangulists using all the geometric and algebraic knowledge you have at your disposal. Work as a team, and make us proud!

The first challenge begins outside the doors to the parking lot closest to the cafeteria.

Good luck! Mega Math Mystery - NOTES about Challenges / Answers / Setup

CHALLENGE # 1

You have three different diagrams from your team-mates. Solve this challenge, then meet up with your team mates to compare your answers. The Computer Expert will have the instructions needed for the team in order to proceed to the next challenge.

Solve for the missing angles in the following diagrams.

HOW TO FIND CHALLENGE # 2

Each team member should have found three missing angles. Have each team member arrange their three answers in ascending order, and give you the middle number.

Find the sum of all three middle answers . (from the Computer Expert, Scientist and Detective – do not include the Interpol agent, as that answer should be the same as someone else on your team).

The next challenge will be near the outside doors closest to the classroom with the same number as this sum.

ANSWER:

ROOM 110

30 + 35 + 45 Mega Math Mystery

CHALLENGE # 2

You should work as a team to solve this challenge. The Detective will have the instructions needed for the team in order to proceed to the next challenge.

Classify each of the triangles below as i) acute, obtuse, right angled triangles and ii) equilateral, isosceles, scalene triangles

Create a Venn diagram that summarizes both classifications at once.

Study the Venn diagram, and isolate the pieces indicating the acute angled triangles and the scalene triangles. Those two sets of triangles will yield two words that should describe a location specific to the school.

The next challenge will be near the outside doors closest to that location.

ANSWER:

FRON (T) / S (T) EPS Mega Math Mystery

CHALLENGE # 3

You have different diagrams from your team-mates. Solve this challenge, then meet up with your team mates to compare your answers. The Scientist will have the instructions needed for the team in order to proceed to the final challenge.

Find the perimeter of each of the following triangles.

You should work as a pair with the Scientist/Computer Expert to solve this challenge. The Scientist will have have the instructions needed for the team in order to proceed to the final challenge.

Find the area of each of the following triangles.

HOW TO FIND THE FINAL CHALLENGE

The Detective worked on a set of perimeter questions. If the largest perimeter calculated was greater than 40 cm, then the Final Challenge will be somewhere on the second floor. Otherwise, it will be somewhere on the first floor.

The Scientist and the Computer Expert both worked on area questions. Divide each area answer by 12.

If the result is not a whole number, ignore it.

If the result IS a whole number, then that digit could be part of the room number where the Final Challenge is located.

ANSWER: 1st floor / 5 / 2 (Room 152)Mega Math Mystery

FINAL CHALLENGE

Each of you have been given a final set of clues to the final design challenge. Work together as a team to create the design using all the clues from all your team members. There is a final optional clue available for each team member from the activity leader, if you need it. When you have completed your design, bring it to the activity leader to be checked.

If you are successful, then you will have proven to the Toronto Triangulists that your knowledge of triangles is sufficient to pass onto further generations, and they do not need to dastardly change the future of education.

Construct a design, using the GeoBoard provided, or a virtual geoboard on your smartphone, that meets the following criteria:

- it uses exactly 2 elastics (or virtual elastics) and will fit in a 5 x 5 geoboard - has two triangles that share a common side

AND it satisfies the criteria of your other team mates !

- the design includes an acute angled triangle, - the design also includes a right angled triangle - at least one triangle in the design is isosceles - the total area of the design is 16 square units.

- The right angle triangle is not an isosceles triangle - The isosceles triangle has area 10 square units - The side lengths of one of the triangles are consecutive whole numbers.

------Activity Design decisions:

Detective colour: 0x005500 (R0 G85 B0)

Computer Expert colour: 0x000055 (r0 g0 b85)

SCIENTIST: All clues on paper, in envelopes at “drop stations”

DETECTIVE / COMPUTER EXPERT: All clues obtained via QR codes (but also duplicated on paper, in case of tech failure)

Handouts for all: Map of SJO / News Bulletin outlining challenge Before activity : sample QR codes to try out, to ensure QR reader app works properly / installed okayMega Math Mystery

CHALLENGE # 1

SCIENTIST

Solve for the missing angles in the following diagrams. Mega Math Mystery

CHALLENGE # 2 SCIENTIST

Classify each of the triangles on the next page as i) acute, obtuse, right angled triangles

and ii) equilateral, isosceles, scalene triangles

Create a Venn diagram that summarizes both classifications at once.

Mega Math Mystery

You have different diagrams from your team-mates. Solve this challenge, then meet up with your team mates to compare your answers.

Find the perimeter of each of the following triangles.

Mega Math Mystery

Additional Info

HOW TO FIND THE FINAL CHALLENGE

The Detective worked on a set of perimeter questions.

If the largest perimeter calculated was greater than 40 cm, then the Final Challenge will be somewhere on the second floor. Otherwise, it will be somewhere on the first floor.

The Scientist and the Computer Expert both worked on area questions. Divide each area answer by 12.

If the result is not a whole number, ignore it.

If the result IS a whole number, then that digit could be part of the room number where the Final Challenge is located.

Mega Math Mystery

CHALLENGE SCIENTIST

Each of you have been given a final set of clues to the final design challenge. Work together as a team to create the design using all the clues from all your team members. There is a final optional clue available for each team member from the activity leader, if you need it.

- The design requires exactly 2 elastics (or virtual elastics) and will fit in a 5 x 5 geoboard

- The design is made of two triangles that share a common side

… AND it satisfies the criteria of your other team mates !

Good luck! When you have completed your design, bring it to the activity leader to be checked. Mega Math Mystery

CHALLENGE # 1

DETECTIVE

Introduction Challenge problems to the challenge: to solve:

Mega Math Mystery

CHALLENGE # 1

COMPUTER EXPERT

Additional Info: Mega Math Mystery

CHALLENGE # 1

DETECTIVE

Solve for the missing angles in the following diagrams. Mega Math Mystery

CHALLENGE # 1

COMPUTER EXPERT

You have three different diagrams from your team-mates. Solve this challenge, then meet up with your team mates to compare your answers. You will have the instructions needed for the team in order to proceed to the next challenge.

Solve for the missing angles in the following diagrams.

Mega Math Mystery

CHALLENGE # 1

COMPUTER EXPERT

Additional Info

Each team member should have found three missing angles. Have each team member arrange their three answers in ascending order, and give you the middle number.

Find the sum of all three middle answers . (from the Computer Expert, Scientist and Detective – do not include the Interpol agent, as that answer should be the same as someone else on your team).

The next challenge will be near the outside doors closest to the classroom with the same number as this sum. Mega Math Mystery

CHALLENGE # 2

DETECTIVE

Additional info: Mega Math Mystery

CHALLENGE # 3

DETECTIVE

Mega Math Mystery

CHALLENGE

DETECTIVE

Introduction to the final challenge: Clue 1:

Clue 2: Mega Math Mystery

CHALLENGE # 2

COMPUTER EXPERT

Introduction Challenge problems to the challenge: to solve: Mega Math Mystery

CHALLENGE # 3

COMPUTER EXPERT

Introduction Challenge problems to the challenge: to solve: Mega Math Mystery

CHALLENGE

COMPUTER EXPERT Introduction to the final challenge: Clue 1:

Clue 2:

Mega Math Mystery

CHALLENGE # 2

DETECTIVE

You should work as a team to solve this challenge. You will have the instructions needed for the team in order to proceed to the next challenge.

Create a Venn diagram that summarizes both classifications at once. Mega Math Mystery

CHALLENGE # 2

DETECTIVE

Additional Info

Study the Venn diagram, and isolate the pieces indicating the acute angled triangles and the scalene triangles. Those two sets of triangles will yield two words that should describe a location specific to the school.

The next challenge will be near the outside doors closest to that location. Mega Math Mystery

CHALLENGE # 2

COMPUTER EXPERT

Create a Venn diagram that summarizes both classifications at once. Mega Math Mystery

CHALLENGE # 3

DETECTIVE

You should work as a pair with the Computer Expert to solve this challenge. The Scientist will have have the instructions needed for the team in order to proceed to the final challenge.

Find the area of each of the following triangles. Mega Math Mystery

CHALLENGE # 3

COMPUTER EXPERT

You should work as a pair with the Detective to solve this challenge. The Scientist will have have the instructions needed for the team in order to proceed to the final challenge.

Find the area of each of the following triangles. Mega Math Mystery

CHALLENGE

DETECTIVE

- The design includes an acute angled triangle.

- The design also includes a right angled triangle. … AND it satisfies the criteria of your other team mates !

Good luck!

When you have completed your design, bring it to the activity leader to be checked. Mega Math Mystery

CHALLENGE

COMPUTER EXPERT

- At least one triangle in the design is isosceles.

- The total area of the design is 16 square units.

… AND it satisfies the criteria of your other team mates !

Good luck!

When you have completed your design, bring it to the activity leader to be checked.

Mega Math Mystery

CHALLENGE

Additional Clues

SCIENTIST

- The right angle triangle is not an isosceles triangle

DETECTIVE

- The isosceles triangle has area 10 square units

COMPUTER EXPERT

- The side lengths of one of the triangles are consecutive whole numbers. Mega Math Mystery

CHALLENGE

Additional Clues

SCIENTIST

COMPUTER EXPERT DETECTIVE

Mega Math Mystery

CHALLENGE

Solution Ideas for a mega-math mystery.

Alien invasion. The aliens have landed and solving math problems will help you identify where they are now and what they're doing.

Alien abduction. The aliens are searching for someone and it is your job to use math to discover who is thereafter.

Alien identification. The aliens are wondering all around the school and if they are leaving traces of themselves where ever they go. Solving the math problems and searching for clues will help you identify what these aliens really look like. This is a great project that could involve cross curricular activities including those links from sciences.

Math murder mystery. A good old whodunit mystery. Use math to whittle down the list of suspects until you find the person who committed the crime.

Spies on the run. Your school has just been hit by a gang of international academic espionage agents. By analyzing the clues left behind and solving the math puzzles you can determine where they're going to hit next.

Eye spy. And international academic espionage agent has infiltrated the school and is stealing math tests to sell on the black market overseas. Solve the math puzzles to find out which spy from a list of well-known spies provided by interpool is the culprit so that you can comprehend them.

Where am I? . Solve the math puzzles to determine a special location somewhere in the school or in the world.

Who am I? . Solve the math puzzles to determine a special person somewhere in the school or in the world.

What am I? . Solve the math puzzles to determine a special thing somewhere in the school or in the world.