Treasure Hunt Primary

8/10/2019 Treasure Hunt Primary

1/16

MathematicalTreasure Hunt

KEY STAGE 2GRADES 3-5


2/16

Mathematical Treasure Hunt

IntroductionTe mathematical treasure hunt is a great activity or un and engaging mathemat-ics lessons: the pupils ollow a trail o clues and mathematical problems aroundthe school site; each clue contains a hint to where the next clue is hidden.

Tis document includes clues and questions intended or Key Stage 2 (UK) orgrades 68 (US).

Te treasure hunt works best when the class is divided into groups o about 5 chil-dren o different abilities. Working in a team, and in a competition, supports teamworking skills, and even children with difficulties in mathematics can participate.

Te questions are taken rom a wide range o different topics, and ofen not di-rectly related to the mathematics curriculum. Some o the problems lend them-selves to urther discussion aferwards; ofen there is an article on that topic in theMathigon World o Mathematics.

Te answer to each problem is an integer, and all the answers once decoded intoletters spell the location o the treasure.: the library.

Te QuestionsName Locations Solution Order of eams

A Cryptography 18 1 9 7 5 3B Combinatorics 18 2 10 8 6 4C Graph Teory 2 3 1 9 7 5D Number Pyramid 9 4 2 10 8 6E Pascal's riangle 8 5 3 1 9 7F Prime Numbers 25 6 4 2 10 8G Probability 20 7 5 3 1 9H Platonic Solids 12 8 6 4 2 10I angram 1 9 7 5 3 1J Secret Numbers 5 10 8 6 4 2

PreparationFirst choose 10 locations in your school where to hide the the different questions(see previous table). Either use the prepared clues (pages 910) or come up withyour own clues (pages 1112) to lead to these questions. Print the clues once oreach team.

Make sure that the class is able to solve all the problems. Print the introductorysheets and questions (pages 38) once or every team and cut them in the middle.Print and cut the additional materials or various problems (pages 1315).

Put the questions, materials as well as the clues leading to the next question intoan envelope, and hide the 10 envelopes around the school site. Keep the two intro-ductory sheets or each team, as well as a different clue or each team the onesleading to their rst problem.

At the beginning o the lesson, divide the class into a couple o teams and giveeach team the two introductory sheets, as well as their rst clue. Te treasure ishidden in the library usually chocolate works well

able of ContentsPage 3 Introductory SheetsPages 48 ProblemsPages 910 Clues

Pages 1112 Customisable CluesPages 1315 Additional Materials

Copyright NoticesTe mathematical treasure hunt is part o the Mathigon Project and PhilippLegner, 2012. Graphics include images by the sxc.hu users ba1969, slafo andspekulator . o be used only or educational purposes.

Instructions for Teachers


3/16

Mathematical Treasure Hunt

Professor Integer was one of the worlds most famous mathematicians,who made discoveries that changed the world forever: from algorithms forcomputers and internet to statistical calculations and quantum mechani-cal predictions.

When he died, he had no relatives or close friends but a very large for-tune. He believed that only the best mathematicians deserved to nd histreasure and created a trail of puzzles and problems.

Many of his diary pages, notes and letters are archived at the Universityof Cantortown, and they all include clues and hints regarding the locationof the treasure.

This treasure hunt will require you to move around your school, ndthe hidden clues and solve mathematical problems. Each questionwill contain a clue about where the next problem will be hidden, butevery team solves the problems in a different order.

When you nd an envelope, take one problem page and one clue. Tryto solve the problem, sometimes using additional materials in the en-velope; then look for the next problem. You may not nd the problemsin the correct order!

There are many other children in the school, so avoid any unneces-sary noise. Dont leave your solutions behind for the next team to see,and dont take more than one copy of each problem otherwise fol-

lowing teams might not be able to solve the problem.

You are now ready to receive the rst clue and a copy of the last letterwritten by Professor Integer.

Good luck!

INSTRUCTIONS

The Integer FilesArchive of the University of Cantortown Item 0

Item 0: Last letter of Prof. Integer Catalogue Nr. 0010

Dear Mathematicians,When you read this letter, I will be deand my treasure will be hidden in a vlocation. Only the best mathematician deserve to find it.In my notes and diaries, I have left 10 problems which you need to solve. Tanswer to every problem is a single nwhich you can write down here: A B C D E F G H I J

Once you have solved all problems, tthe numbers into letters (1-a, 2-b,3-c so on) and bring the letters into the coorder to spell the location of the treas _ _ _ _ _ _ _ _ _ _Hurry, though, because otherteams may be onto it as wellRegards and good Luck!Prof. Integer


4/16


5/16


Item 3: Spiral Bound Notebook No 2 Catalogue Nr. 5478


Item 4: Old piece of paper 1 Catalogue Nr. 1271

Pro bl em D : N u mber Pyr ami d

Last ni ght I wa s thinkin g about a large nu mber p yramid. Unfortunately I s pilled myc offee, and Ilos t many o f the numbers only 6 rema ined legi b le.I was thinking about it f or somet ime, and I think i t is possib le to reco n struct t he whole p yramidu singo nly those6 numbe r s!

P r o bl e m C : G r a ph T h e o r y

La s t n i g h t I wa s d o o dl i n g o n a sh e e t o f p a p e r a n d d i s c o v er e d s o me t h in g c u r i o u s : s om e s h a p e s ca n b e d r a wn al l a t o n c e ,wi t h o u t l i ft i n g t h e p en o f t h e p ap e r , a n d wi t h o u t d r a wi n g a ny l i n e t wi ce . Bu t f o r s o me s h a p e s t h at i s i mp o s s ib l e .

Ho w ma n y o f t h e s e sh a p e s a r e IM P OS S I BLE to d r a w wi t h o u t l i f ti n g t h e p e n a n d d r a wi ng a l i n e t wi c e ?

Ca n y ou wo r k o u t wh y ?

8 2

4 7 5 5

2 0

6 1 1

The answer !


6/16


7/16

This shape is called an Icosahedron. All faces are equilateral triangles, and itlooks the same from every direction.Therefore it is called a Platonic Solid,named after the Greek mathematicianPlato. Plato showed that there are only

five solids of this kind. He though thatthey corresponded to the four classical elements

fire, air, earth and fire, as well as the universe.

Here is a table showing all 5 platonic solids. Can you find a pattern and fill in the gaps?


Item 8: Old piece of paper 2, Icosahedron Catalogue Nr. 5512


Item 7: Old notebook, box of marbles Catalogue Nr. 4652

Problem H: Platonic Solids

Name Model Faces Vertices Edges

Tetrahedron 4 6

Cube 6 8 12

Octahedron 8 6

Dodecahedron 20 30

Icosahedron 20 30

Maybe Think about Faces + Vertces!

T o d a y I w a s p l a y i n g a

g a m e w i h

m a r b l e s . I h a d a b a g w i h 5 0 m a r b l e s ,

s o m e o f w h i c h w e r e r e d a n d s o m e o f

w h i c h w e r e b l u e .

I r e p e a e d l y p i c k e d a m a r b l e a

r a n d o m a n d h e n

p u i b a c k . O n

a v e r a g e , h e c h a n c e o f g e t i n g a r e d

m a r b l e w a s 4 0 % .

H o w m a n y r e d m a r b l e s w e r e h e r e i n

h e b a g ?

P r o b l e m G

: P r o b a b i l

i t y

Marbles by the Minnesota Historical Society on Wikipedia


8/16


Item 10: Spiral Bound Notebook No 2 Catalogue Nr. 9612


Item 9: Two letters by Prof. Integer, Tangram Catalogue Nr. 1972

1

7

8

6

2

4

3

5

T oday when browsing a shop in C hinatown, I discovereda fantastic game, called T angram: it consists of geometric shapeswhichcan be combined to makenew ones.

You aregiven a certain shape, like a square,and you have to use all of the tiles available to makethat shape.

U nfortunately I mixed up two games and couldn't gure out whichtile didn' t belong there. 8 of the tiles on thebackcan be used to make a square: nd the

one that is left over.

Pr oble m I: Tang r am

I received thisletters from Prof.Interger just acouple of daysbefore he died.

Do you think you can break the key to my safe? No? Well,I shall give you a few hints:

* it is a 6-digit number and consists of 1, 2, 3, 4, 5and 6 in some order

* the whole key is divisible by 6 * if you leave out the last digit, it is divisible by 5 * if you leave out the last two digits, the remaining

4-digit number is divisible by 4 * if you leave out the last three digits, the remaining

3-digit number is also divisible by 3 * the rst two digits of the key form a 2-digit num-

ber which is divisible by 2.

Can you work out what the 5th digit of my key is?

Problem J: Secret Number


9/16

Full of paper, books and les,

Pay the school ofce some smiles!

Bonjour, Hola, Goddag, Ni Hao, And more if languages allow.

Find the riddle that is given,Where the bits and bytes are livin.

With watercolour, crayons, pen,

The next puzzle is waiting then.

In breaktime its brawling, in lessons is still,

On the playground the next riddle finding you will.

Where smoke and where re

are common event, The following mystery I will present.

S c h o ol Offi

c e

L an g u a g e s R o om

C om p u t er R o om

A r t an d C r af t s R o om

P l a y gr o un d

C h emi s t r yL a b


10/16

No pupil may enter,

no child may come in, Where the next clue is hidden, so you can begin!

U p a n

d d o w n

a n d l e f t a n d r i g h t ,

T h e s t a i r c a s e s ,

t h e y d o e x c i t e .

The biggest room that is in sight,But try to knock it is polite.

Hurry, less than

80 days, For you to reach the problem's place.

M a t h em a t i c s R o om

S t aff C om

m onR o om

M u s i c R o om

G e o gr a ph

yR o om

H al l / A u d i t or i um

S t ar i r c a s e s

Where 10 divided 5 is 2,The next questions, it waits for you.

T rum pet f an f ares

no del a y! A nd music sounds wil l l ead your wa y.


11/16


12/16


13/16

Pascals TrianglePrint several times for each group, cut out and add to problem E

P a s c a l s T r i a n g l e

1

1

1

1

2

1

1

3

3

1

1

4

6

4

1

1

5

1 0

1 0

5

1

1

6

1 5

2 0

1 5

6

1

1

7

2 1

3 5

3 5

2 1

7

1

1

8

2 8

5 6

7 0

5 6

2 8

8

1

1

9

3 6

8 4

1 2 6

1 2

6

8 4

3 6

9

1

1

1 0

4 5

1 2 0

2 1 0

2 5 2

2 1 0

1 2 0

4 5

1 0

1

1

1 1

5 5

1 6 5

3 3 0

4 6 2

4 6 2

3 3 0

1 6 5

5 5

1 1

1

1

1 2

6 6

2 2 0

4 9 5

7 9 2

9 2 4

7 9 2

4 8 5

2 2 0

6 6

1 2

1

1

1 3

7 8

2 8 6

7 1 5

1 2 8 7

1 7 1 6

1 7 1 6

1 2 8 7

7 1 5

2 8 6

7 8

1 3

1

1

1 4

9 1

3 6 4

1 0 0 1

2 0 0 2

3 0 0

3

3 4 3 2

3 0 0

3

2 0 0 2

1 0 0 1

3 6 4

9 1

1 4

1

1

1 5

1 0 5

4 5 5

1 3 6 5

3 0 0

3

5 0 0 5

6 4 3 5

6 4

3 5

5 9 9 5

3 0 0

3

1 3 6 5

4 5 5

1 0 5

1 5

1

1

1 6

1 2 0

5 6 0

1 8 2 0

4 3 6 8

8 0 0 8 1 1 4 4 0 1 2 8 7 0

1 1 4 4 0 8 0 0 8

4 3 6 8

1 8 2 0

5 6 0

1 2 0

1 6

1

P a s c a l s T r i a n l e

1

1

1

1

2

1

1

3

3

1

1

4

6

4

1

1

5

1 0

1 0

5

1

1

6

1 5

2 0

1 5

6

1

1

7

2 1

3 5

3 5

2 1

7

1

1

8

2 8

5 6

7 0

5 6

2 8

8

1

1

9

3 6

8 4

1 2 6

1 2

6

8 4

3 6

9

1

1

1 0

4 5

1 2 0

2 1 0

2 5 2

2 1 0

1 2 0

4 5

1 0

1

1

1 1

5 5

1 6 5

3 3 0

4 6 2

4 6 2

3 3 0

1 6 5

5 5

1 1

1

1

1 2

6 6

2 2 0

4 9 5

7 9 2

9 2 4

7 9 2

4 8 5

2 2 0

6 6

1 2

1

1

1 3

7 8

2 8 6

7 1 5

1 2 8 7

1 7 1 6

1 7 1 6

1 2 8 7

7 1 5

2 8 6

7 8

1 3

1

1

1 4

9 1

3 6 4

1 0 0 1

2 0 0 2

3 0 0

3

3 4 3 2

3 0 0

3

2 0 0 2

1 0 0 1

3 6 4

9 1

1 4

1

1

1 5

1 0 5

4 5 5

1 3 6 5

3 0 0

3

5 0 0 5

6 4 3 5

6 4

3 5

5 9 9 5

3 0 0

3

1 3 6 5

4 5 5

1 0 5

1 5

1

1

1 6

1 2 0

5 6 0

1 8 2 0

4 3 6 8

8 0 0 8 1 1 4 4 0 1 2 8 7 0

1 1 4 4 0 8 0 0 8

4 3 6 8

1 8 2 0

5 6 0

1 2 0

1 6

1


14/16

1 2 3 4 5 6 7 8 9 1011 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100

100 Number TablePrint several times for each group, cut out and add to problem F

1 2 3 4 5 6 7 8 9 1011 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30

31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50

51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70

71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90

91 92 93 94 95 96 97 98 99 100


15/16

TangramPrint once (on coloured cardboard), cut out and add to problem I


16/16

Pro bl em D: M agic Sq uar es

D o you k now whata magic sq uar e is? A qua dratic grid ofintege rs, so t hat the sum of the nu mb ers in e very row, e very column and thetwo diagonalsis alwa ys t he same. H ere is a 3 3 magi c sq uare w iththe numbe rs from 1 to 9. The row s,col umn s anddiag onals a ll a dd up t o 15 :

Mag ic sq uares have also playe d an im por tant ro le in Chine seand Arab ic mathematic s: they

we re belie vedto have ma gical po wer s and a su pernatu ral meanin g.

I fou nd thi s 4 4 mag ic sq uare in a b ook, ex cept that s omenumber s are missi ng. Can yo u ll in the gaps a nd nd the number in t he bott om left cor ner ?

12 1413 11

16 106 15 N ot e:

Mayb e y ou sh oul d f i r st d et e rmi n e w h at t h e sum o f t h e numb e r si n e v e ry r ow and c ol umn i s..

2 7 69 5 14 3 8

KS4Big Caesar Code 18Combinatorics: Lotto 8Graph Teory: Bridges 2Magic Square 9Sequences Hard 20Sieve o Eratosthenes 25Probability 18Symmetry Groups: 13 1 = 12

Geometry 1Modular Arithmetic 5

Treasure Hunt Primary

Documents

Transcript of Treasure Hunt Primary