Numbers and Graphs

GRAPHS AND NUMBERS

A FEW TIPS FOR ADULTS: Allow your children to work at their own pace, and respect their “refusals“!

If they close the book or skip a page, it doesn’t necessarily mean they’re giving up.

They may just need a little time to think about how to solve the problems.

“Mathematics is not only real, but it is the only reality.“ Martin Gardner Mathematics is a useful and tangible universal language that is all around us. Shapes and numbers are the building blocks of thought that we have lots of fun playing with as kids, and which we use to create great things as adults. The fantastic narration in this book allows children’s minds to explore new worlds, engaging them in problem-solving, and igniting their imagination.

Each activity requires three actions: reading, observing, and understanding.

This book contains a mountain of data, to help kids learn how to better understand the world around us.

Ask questions rather than give answers!

If your child asks you for help, don’t give them the answer. Rather, help them focus on the problem, or their mistake, by asking targeted questions.

Let your children find their own way to solve the problems, even if it’s long and convoluted. You can then help them explore other, perhaps more “clever“ ways to find solutions.

UNDERSTANDING IS THE FIRST STEP TO PROBLEM SOLVING. Help your children work through the problems before trying to solve them.

You can do this by verbalizing, drawing the steps, or using real objects.

This is the easiest, yet least fun part of problem solving!

ASK, “HOW DID YOU DO THAT?“ Gradually help them get accustomed to verbalizing and explaining their thinking processes; it’s far more important for them to know how and why they came up with an answer than to know the name of the rule applied.

CONTENTS: - tables and graphs - diagrams and representations - logical sequences - probability - classification

FOR 8 to 10 year olds.

The situations proposed in this book are of course imaginary.

Help your children discover numbers and math in everyday life.

Get your nose out of the book and go find math!

Have fun!

2

3

GRAPHS AND NUMBERS

A FEW TIPS FOR ADULTS: Allow your children to work at their own pace, and respect their “refusals“!

If they close the book or skip a page, it doesn’t necessarily mean they’re giving up.

They may just need a little time to think about how to solve the problems.

“Mathematics is not only real, but it is the only reality.“ Martin Gardner Mathematics is a useful and tangible universal language that is all around us. Shapes and numbers are the building blocks of thought that we have lots of fun playing with as kids, and which we use to create great things as adults. The fantastic narration in this book allows children’s minds to explore new worlds, engaging them in problem-solving, and igniting their imagination.

Each activity requires three actions: reading, observing, and understanding.

This book contains a mountain of data, to help kids learn how to better understand the world around us.

Ask questions rather than give answers!

If your child asks you for help, don’t give them the answer. Rather, help them focus on the problem, or their mistake, by asking targeted questions.

Let your children find their own way to solve the problems, even if it’s long and convoluted. You can then help them explore other, perhaps more “clever“ ways to find solutions.

UNDERSTANDING IS THE FIRST STEP TO PROBLEM SOLVING. Help your children work through the problems before trying to solve them.

You can do this by verbalizing, drawing the steps, or using real objects.

This is the easiest, yet least fun part of problem solving!

ASK, “HOW DID YOU DO THAT?“ Gradually help them get accustomed to verbalizing and explaining their thinking processes; it’s far more important for them to know how and why they came up with an answer than to know the name of the rule applied.

CONTENTS: - tables and graphs - diagrams and representations - logical sequences - probability - classification

FOR 8 to 10 year olds.

The situations proposed in this book are of course imaginary.

Help your children discover numbers and math in everyday life.

Get your nose out of the book and go find math!

Have fun!

2

3

BEHIND THE DOOR THE LARGE DOOR SLOWLY OPENS, ACCOMPANIED BY THE SOUND OF SCRAPING STONE. BEHIND THE DOOR, THERE’S A DARK, COLD TUNNEL. ORILDE AND FRORIN WALK STRAIGHT INTO IT, AND GANDOLF FOLLOWS THEM. “THIS ISN’T EXACTLY WHAT I WAS EXPECTING...“, HE GRUMBLES. THE PRINCE LAUGHS. “SOMETHING A BIT MORE MAJESTIC, MAYBE? JUST WAIT A COUPLE OF MINUTES, AND YOU’LL SEE!“ EXACTLY TWO MINUTES LATER, THEY COME OUT OF THE TUNNEL INTO A CAVE.

WHAT INFORMATION CAN GANDOLF GET ABOUT THE CITY FROM THE DATA ORILDE SHOWS HIM? MARK WHETHER THE STATEMENT IS TRUE (T) OR FALSE (F) WITH A CROSS.

YEAR 4871

INHABITANTS IN MEDIAN CITY

38 YEAR 4872

The difference between the number of inhabitants in 4871 and 4874 The number of dwarves who leave the city on public holidays

41

The total number of inhabitants in 4872 and 4875 The difference between the number of inhabitants in 4874 and 4870

YEAR 4873

43

THE MATHEMATICIAN’S EYES OPEN WIDE. IN THE MIDDLE OF THE COLOSSAL CAVE, THERE’S A MAGNIFICENT EMERALD AND SAPPHIRE CITY. “THE CITY JUST KEEPS ON GROWING“, SAYS ORILDE, PROUDLY. “LOOK HOW MANY DWARVES HAVE COME TO LIVE HERE!“ ORILDE SHOWS GANDOLF A STONE TABLET, ON WHICH – FOR EACH YEAR OF THE DWARF ERA – THE NUMBER OF CITIZENS IN MEDIAN CITY IS RECORDED.

YEAR 4874

45

T

F

T

F

T

F

T

F

YEAR 4875

50

THE ABOVE DATA HAS BEEN REPRESENTED ON A BAR GRAPH. WRITE THE MISSING NUMBERS IN THE WHITE CIRCLES.

INHABITANTS IN MEDIAN CITY 45 …

INHABITANTS

…

0 YEAR

4871

4872

4873

4874

4875

ORILDE PRESSES THE EDGE OF THE TABLET WITH HER FINGER. THE STONE CRACKS AND REASSEMBLES IN A NEW IMAGE.

8

9

BEHIND THE DOOR THE LARGE DOOR SLOWLY OPENS, ACCOMPANIED BY THE SOUND OF SCRAPING STONE. BEHIND THE DOOR, THERE’S A DARK, COLD TUNNEL. ORILDE AND FRORIN WALK STRAIGHT INTO IT, AND GANDOLF FOLLOWS THEM. “THIS ISN’T EXACTLY WHAT I WAS EXPECTING...“, HE GRUMBLES. THE PRINCE LAUGHS. “SOMETHING A BIT MORE MAJESTIC, MAYBE? JUST WAIT A COUPLE OF MINUTES, AND YOU’LL SEE!“ EXACTLY TWO MINUTES LATER, THEY COME OUT OF THE TUNNEL INTO A CAVE.

WHAT INFORMATION CAN GANDOLF GET ABOUT THE CITY FROM THE DATA ORILDE SHOWS HIM? MARK WHETHER THE STATEMENT IS TRUE (T) OR FALSE (F) WITH A CROSS.

YEAR 4871

INHABITANTS IN MEDIAN CITY

38 YEAR 4872

The difference between the number of inhabitants in 4871 and 4874 The number of dwarves who leave the city on public holidays

41

The total number of inhabitants in 4872 and 4875 The difference between the number of inhabitants in 4874 and 4870

YEAR 4873

43

THE MATHEMATICIAN’S EYES OPEN WIDE. IN THE MIDDLE OF THE COLOSSAL CAVE, THERE’S A MAGNIFICENT EMERALD AND SAPPHIRE CITY. “THE CITY JUST KEEPS ON GROWING“, SAYS ORILDE, PROUDLY. “LOOK HOW MANY DWARVES HAVE COME TO LIVE HERE!“ ORILDE SHOWS GANDOLF A STONE TABLET, ON WHICH – FOR EACH YEAR OF THE DWARF ERA – THE NUMBER OF CITIZENS IN MEDIAN CITY IS RECORDED.

YEAR 4874

45

T

F

T

F

T

F

T

F

YEAR 4875

50

THE ABOVE DATA HAS BEEN REPRESENTED ON A BAR GRAPH. WRITE THE MISSING NUMBERS IN THE WHITE CIRCLES.

INHABITANTS IN MEDIAN CITY 45 …

INHABITANTS

…

0 YEAR

4871

4872

4873

4874

4875

ORILDE PRESSES THE EDGE OF THE TABLET WITH HER FINGER. THE STONE CRACKS AND REASSEMBLES IN A NEW IMAGE.

8

9

GEOMETRIC DECORATIONS

FRORIN, ORILDE, AND GANDOLF FINALLY REACH THE MAJESTIC MINE-CITY, AND THEY WIND THEIR WAY BETWEEN THE TALL BLUE AND GREEN HOUSES. “WE LOVE MATH SO MUCH...“, SAYS THE PRINCE, “...THAT WE EVEN USE IT TO DECORATE THE SQUARES AND BUILDINGS.“

BOMBUR, THE FOREMAN, SHOWS HIS ASSISTANTS THE PATTERN FOR DECORATING THE BUILDING’S FACADE. HELP THE DWARVES FINISH DECORATING THE FACADE. ATTACH THE MISSING SHAPES, USING MASTER BOMBUR’S PATTERN TO HELP YOU. YOU’LL FIND THE PIECES AMONG THE STICKERS AT THE BACK OF THE BOOK.

THERE ARE SOME DWARVES FINISHING A BEAUTIFULLY DECORATED SIDEWALK OUTSIDE A BUILDING. HELP THEM FINISH IT BY ATTACHING THE PAVING STONE STICKERS IN THE RIGHT ORDER, FOLLOWING THE SEQUENCE IN THE EXAMPLE. THE STICKERS ARE AT THE BACK OF THE BOOK.

12

13

GEOMETRIC DECORATIONS

FRORIN, ORILDE, AND GANDOLF FINALLY REACH THE MAJESTIC MINE-CITY, AND THEY WIND THEIR WAY BETWEEN THE TALL BLUE AND GREEN HOUSES. “WE LOVE MATH SO MUCH...“, SAYS THE PRINCE, “...THAT WE EVEN USE IT TO DECORATE THE SQUARES AND BUILDINGS.“

BOMBUR, THE FOREMAN, SHOWS HIS ASSISTANTS THE PATTERN FOR DECORATING THE BUILDING’S FACADE. HELP THE DWARVES FINISH DECORATING THE FACADE. ATTACH THE MISSING SHAPES, USING MASTER BOMBUR’S PATTERN TO HELP YOU. YOU’LL FIND THE PIECES AMONG THE STICKERS AT THE BACK OF THE BOOK.

THERE ARE SOME DWARVES FINISHING A BEAUTIFULLY DECORATED SIDEWALK OUTSIDE A BUILDING. HELP THEM FINISH IT BY ATTACHING THE PAVING STONE STICKERS IN THE RIGHT ORDER, FOLLOWING THE SEQUENCE IN THE EXAMPLE. THE STICKERS ARE AT THE BACK OF THE BOOK.

12

13

IN THE KITCHEN THEY WANT TO KNOW HOW MANY TIMES EACH DISH HAS BEEN ORDERED.

“LET’S EAT!“

GANDOLF, ORILDE, AND FRORIN GO AND SIT AT THE TABLE THAT’S BEEN LAID AT THE BACK OF THE ROOM. IT’S COVERED WITH AN ARRAY OF TRAYS, TANKARDS, AND FOOD. THERE ARE 7 HUNGRY GUESTS AT THE TABLE.

DISHES

NUMBER OF ORDERS

DEEP-FRIED MUSHROOMS MUSHROOM RISOTTO MUSHROOM SOUP MUSHROOMS WITH POLENTA

ORDER FORM

SAUTÉED MUSHROOMS

NAME

NUMBER OF DISHES EATEN

DISH ORDERED

GANDOLF

1

DEEP-FRIED MUSHROOMS

FRORIN

6

MUSHROOM RISOTTO

ORILDE

9

MUSHROOM SOUP

DINAIN

3

MUSHROOMS WITH POLENTA

BURBIT

2

SAUTÉED MUSHROOMS

MAMLI

5

MUSHROOMS WITH POLENTA

GLORIN

2

MUSHROOM RISOTTO

• WHICH DISH IS ORDERED THE MOST?…………………………………………………………..........

• WHICH IS ORDERED THE LEAST? ………………………………………………………………………......

• HOW MANY DINERS JUST EAT ONE DISH? ……………………………………………............

• WHICH DISH IS ORDERED THE LEAST, SAUTÉED MUSHROOMS OR MUSHROOMS WITH POLENTA?………

COLOR THE BOXES TO COMPLETE THE GRAPH. THE DISHES ARE INDICATED ON THE HORIZONTAL AXIS, AND THE NUMBER OF DWARVES WHO ORDERED THEM ARE ON THE VERTICAL AXIS.

9 8 7 NUMBER OF DWARVES

KIMLI, THE WAITER, NEEDS HELP TAKING THE ORDER. EVERYONE ASKS HIM QUESTIONS, AND THE CHEF EVEN ASKS HIM FOR A DRAWING. TRY ANSWERING THE QUESTIONS WITH HIM.

6 5 4 3 2 1 DEEP-FRIED MUSHROOMS

16

MUSHROOM RISOTTO

SAUTÉED MUSHROOMS

MUSHROOM SOUP

MUSHROOMS WITH POLENTA

17

IN THE KITCHEN THEY WANT TO KNOW HOW MANY TIMES EACH DISH HAS BEEN ORDERED.

“LET’S EAT!“

GANDOLF, ORILDE, AND FRORIN GO AND SIT AT THE TABLE THAT’S BEEN LAID AT THE BACK OF THE ROOM. IT’S COVERED WITH AN ARRAY OF TRAYS, TANKARDS, AND FOOD. THERE ARE 7 HUNGRY GUESTS AT THE TABLE.

DISHES

NUMBER OF ORDERS

DEEP-FRIED MUSHROOMS MUSHROOM RISOTTO MUSHROOM SOUP MUSHROOMS WITH POLENTA

ORDER FORM

SAUTÉED MUSHROOMS

NAME

NUMBER OF DISHES EATEN

DISH ORDERED

GANDOLF

1

DEEP-FRIED MUSHROOMS

FRORIN

6

MUSHROOM RISOTTO

ORILDE

9

MUSHROOM SOUP

DINAIN

3

MUSHROOMS WITH POLENTA

BURBIT

2

SAUTÉED MUSHROOMS

MAMLI

5

MUSHROOMS WITH POLENTA

GLORIN

2

MUSHROOM RISOTTO

• WHICH DISH IS ORDERED THE MOST?…………………………………………………………..........

• WHICH IS ORDERED THE LEAST? ………………………………………………………………………......

• HOW MANY DINERS JUST EAT ONE DISH? ……………………………………………............

• WHICH DISH IS ORDERED THE LEAST, SAUTÉED MUSHROOMS OR MUSHROOMS WITH POLENTA?………

COLOR THE BOXES TO COMPLETE THE GRAPH. THE DISHES ARE INDICATED ON THE HORIZONTAL AXIS, AND THE NUMBER OF DWARVES WHO ORDERED THEM ARE ON THE VERTICAL AXIS.

9 8 7 NUMBER OF DWARVES

KIMLI, THE WAITER, NEEDS HELP TAKING THE ORDER. EVERYONE ASKS HIM QUESTIONS, AND THE CHEF EVEN ASKS HIM FOR A DRAWING. TRY ANSWERING THE QUESTIONS WITH HIM.

6 5 4 3 2 1 DEEP-FRIED MUSHROOMS

16

MUSHROOM RISOTTO

SAUTÉED MUSHROOMS

MUSHROOM SOUP

MUSHROOMS WITH POLENTA

17

THE NUMBERS PATH

FRORIN, ORILDE, AND GANDOLF ARE IN THE LAST HUGE WAREHOUSE. THERE ARE NARROW NUMBERED PASSAGES BETWEEN THE ROWS AND ROWS OF STACKED CRATES. “I’VE FORGOTTEN THE NUMERICAL SEQUENCE FOR FINDING THE RIGHT WAY,“ SAYS FRORIN, MORTIFIED.

7

14

11

18

15

DO YOU KNOW HOW TO RECONSTRUCT THE NUMERICAL SEQUENCES TO FIND THE RIGHT PATH? FOLLOW THE INSTRUCTIONS THAT GANDOLF HAS WRITTEN UNDER THE CHESTS. “DON’T WORRY“, SMILES GANDOLF, “I REMEMBER THE WAY!“

22

19

26

…

…

36

28

…

…

…

ADD 7, THEN TAKE AWAY 3. WHEN YOU REACH 30, GET ON THE MINECART: IT’LL TAKE YOU TO THE NEXT NARROW TUNNEL.

4

6

18

10

12

ADD 2, MULTIPLY BY 3, TAKE AWAY 8. AT 82, CHOOSE THE GALLERY THAT WILL TAKE YOU TO THE NEXT TUNNEL.

400

390

385

375

370

360

…

…

340

…

101

108

…

102

…

…

…

WHAT’S THE RULE? SCOPRILA E A 330 PRENDI IL TUNNEL ROSA.

100

107

98

YOU’RE ALMOST THERE. ONE FINAL EFFORT. AT 103, YOU’LL FIND THE RIGHT WAY.

24

25

THE NUMBERS PATH

FRORIN, ORILDE, AND GANDOLF ARE IN THE LAST HUGE WAREHOUSE. THERE ARE NARROW NUMBERED PASSAGES BETWEEN THE ROWS AND ROWS OF STACKED CRATES. “I’VE FORGOTTEN THE NUMERICAL SEQUENCE FOR FINDING THE RIGHT WAY,“ SAYS FRORIN, MORTIFIED.

7

14

11

18

15

DO YOU KNOW HOW TO RECONSTRUCT THE NUMERICAL SEQUENCES TO FIND THE RIGHT PATH? FOLLOW THE INSTRUCTIONS THAT GANDOLF HAS WRITTEN UNDER THE CHESTS. “DON’T WORRY“, SMILES GANDOLF, “I REMEMBER THE WAY!“

22

19

26

…

…

36

28

…

…

…

ADD 7, THEN TAKE AWAY 3. WHEN YOU REACH 30, GET ON THE MINECART: IT’LL TAKE YOU TO THE NEXT NARROW TUNNEL.

4

6

18

10

12

ADD 2, MULTIPLY BY 3, TAKE AWAY 8. AT 82, CHOOSE THE GALLERY THAT WILL TAKE YOU TO THE NEXT TUNNEL.

400

390

385

375

370

360

…

…

340

…

101

108

…

102

…

…

…

WHAT’S THE RULE? SCOPRILA E A 330 PRENDI IL TUNNEL ROSA.

100

107

98

YOU’RE ALMOST THERE. ONE FINAL EFFORT. AT 103, YOU’LL FIND THE RIGHT WAY.

24

25

TOWARDS THE CORE OF THE MOUNTAIN

FRORIN, ORILDE, AND GANDOLF FIND THEMSELVES ON THE SLOPE OF A MOUNTAIN. “THIS WAY!“, SAYS THE PRINCE OF THE DWARVES, AS HE REACHES A DARK WELL WITH A CAGE LIFT HANGING ON IT. “WHAT’S THAT?“ “OUR WAY INTO THE CORE OF THE MOUNTAIN! IT’S QUITE A LONG WAY DOWN...“ “HOW BORING!“, GROANS GANDOLF. “LET’S DO SOMETHING IN THE MEANTIME!“ AND THEY IMMEDIATELY START PLAYING A LOGIC GAME!

“TWELVE, THIRTY-SIX, TWENTY-FOUR, ARE MULTIPLES OF … AND …“

..

..

HELP FRORIN AND ORILDE PLAY THE LOGIC GAME AGAINST GANDOLF. LOOK AT THE EQUATIONS, AND THEN FIND THE RIGHT ANSWER AMONG THE THREE OPTIONS. FIND THE STICKER AT THE BACK OF THE BOOK, AND STICK IT IN THE SPACE NEXT TO IT.

SUDDENLY, THE CAGE LIFT STARTS SHAKING OMINOUSLY. SNAP! A ROPE BREAKS AND THEY START TO FALL. “OH NOOOOO!“ GANDOLF CONCENTRATES HARD, DRAWING ON HIS MAGIC WISDOM TO CAST A SPELL TO STOP THE FREEFALL.

..

..

..

..

COMPLETE THE DIAGRAM TO FINISH THE SPELL.

MULTIPLES OF ……

..

“THANKS, GANDOLF!“ THE TWO DWARVES BREATHE A SIGH OF RELIEF. THE MATHEMATICIAN SMILES, BUT IMMEDIATELY BECOMES SERIOUS AGAIN: “LET’S GO! THIS ADVENTURE HAS ONLY JUST BEGUN!“

..

..

..

..

MULTIPLES OF ……

28

29

TOWARDS THE CORE OF THE MOUNTAIN

FRORIN, ORILDE, AND GANDOLF FIND THEMSELVES ON THE SLOPE OF A MOUNTAIN. “THIS WAY!“, SAYS THE PRINCE OF THE DWARVES, AS HE REACHES A DARK WELL WITH A CAGE LIFT HANGING ON IT. “WHAT’S THAT?“ “OUR WAY INTO THE CORE OF THE MOUNTAIN! IT’S QUITE A LONG WAY DOWN...“ “HOW BORING!“, GROANS GANDOLF. “LET’S DO SOMETHING IN THE MEANTIME!“ AND THEY IMMEDIATELY START PLAYING A LOGIC GAME!

“TWELVE, THIRTY-SIX, TWENTY-FOUR, ARE MULTIPLES OF … AND …“

..

..

HELP FRORIN AND ORILDE PLAY THE LOGIC GAME AGAINST GANDOLF. LOOK AT THE EQUATIONS, AND THEN FIND THE RIGHT ANSWER AMONG THE THREE OPTIONS. FIND THE STICKER AT THE BACK OF THE BOOK, AND STICK IT IN THE SPACE NEXT TO IT.

SUDDENLY, THE CAGE LIFT STARTS SHAKING OMINOUSLY. SNAP! A ROPE BREAKS AND THEY START TO FALL. “OH NOOOOO!“ GANDOLF CONCENTRATES HARD, DRAWING ON HIS MAGIC WISDOM TO CAST A SPELL TO STOP THE FREEFALL.

..

..

..

..

COMPLETE THE DIAGRAM TO FINISH THE SPELL.

MULTIPLES OF ……

..

“THANKS, GANDOLF!“ THE TWO DWARVES BREATHE A SIGH OF RELIEF. THE MATHEMATICIAN SMILES, BUT IMMEDIATELY BECOMES SERIOUS AGAIN: “LET’S GO! THIS ADVENTURE HAS ONLY JUST BEGUN!“

..

..

..

..

MULTIPLES OF ……

28

29

MATHEMATICAL FLAMES

75

“WE HAVE TO FIND THE SOURCE OF THE FIRE AND PUT IT OUT! QUICK! COME WITH ME!“ “THEY’RE MATHEMATICAL FLAMES“, CRIES ONE OF THE DWARVES. “TO STOP THEM, YOU HAVE TO UNDERSTAND THE LOGIC OF THEIR SPREADING“, ADDS ORILDE. GANDOLF CONTINUES: “RIGHT! TO STOP THE TONGUES OF FIRE SPREADING, WE MUST BREAK THEM DOWN INTO PRIME FACTORS!“ HELP THEM TO DO IT, AS SHOWN IN THE EXAMPLE ON THE RIGHT.

120

15

5 4

5

3

2

24

2

15 5

420

2

2 3

12 4 2

42

48

3 2

12 2

2

4 2

10

6

4 2

32

30

3 2

7

5

2

3

“THERE’S TOO MANY FLAMES“, SHOUTS ORILDE. “GANDOLF, WHAT DO WE DO?“ “GET OUT OF HERE!“ THE MATHEMATICIAN IS GRIMMER THAN EVER. “THESE AREN’T NORMAL FLAMES. ONLY LOGIC AND KNOWLEDGE CAN KEEP THEM AT BAY.“ 33

MATHEMATICAL FLAMES

75

“WE HAVE TO FIND THE SOURCE OF THE FIRE AND PUT IT OUT! QUICK! COME WITH ME!“ “THEY’RE MATHEMATICAL FLAMES“, CRIES ONE OF THE DWARVES. “TO STOP THEM, YOU HAVE TO UNDERSTAND THE LOGIC OF THEIR SPREADING“, ADDS ORILDE. GANDOLF CONTINUES: “RIGHT! TO STOP THE TONGUES OF FIRE SPREADING, WE MUST BREAK THEM DOWN INTO PRIME FACTORS!“ HELP THEM TO DO IT, AS SHOWN IN THE EXAMPLE ON THE RIGHT.

120

15

5 4

5

3

2

24

2

15 5

420

2

2 3

12 4 2

42

48

3 2

12 2

2

4 2

10

6

4 2

32

30

3 2

7

5

2

3

“THERE’S TOO MANY FLAMES“, SHOUTS ORILDE. “GANDOLF, WHAT DO WE DO?“ “GET OUT OF HERE!“ THE MATHEMATICIAN IS GRIMMER THAN EVER. “THESE AREN’T NORMAL FLAMES. ONLY LOGIC AND KNOWLEDGE CAN KEEP THEM AT BAY.“ 33

THE FIRE DRAGON

THE MAGIC BLOCKS THE TONGUES OF FIRE, WHICH ARE SLITHERING ACROSS THE BRIDGE LIKE CRAZED SNAKES. GANDOLF FINDS HIMSELF ISOLATED, PROTECTED BY A THIN MAGIC BARRIER. A HUGE FIRE DRAGON IS COMING OUT OF THE FLAMES. THE STONE MELTS UNDER HIS FEET. HIS ROAR MAKES THE GROUND SHAKE. IT HAD BEEN THE DRAGON’S EYES STARING AT GANDOLF! THE DRAGON OPENS HIS JAWS TO BELLOW... MEANINGLESS PHRASES. CORRECT THE DRAGON. IN EACH BALLOON, DISCARD THE WORDS AND NUMBERS THAT HAVE NOTHING TO DO WITH THE OTHERS.

FLAME

FIRE

BLAZE

WOOD

12 16

13

DWARF KIMLI BUYS TURNIPS GANDOLF THE MAGICIAN COOKS VEGETABLES DWARF BADANDRA BUYS CARROTS

DEMON

HIPPOGRIFF

CHIMERA 53

14

28

10=2X5 9=3X3 40

7

GOAT

DWARF FRORIN BUYS TOMATOES

4 32

8

12=3X4 28=5X3X2 41

THE FIRE DRAGON

THE MAGIC BLOCKS THE TONGUES OF FIRE, WHICH ARE SLITHERING ACROSS THE BRIDGE LIKE CRAZED SNAKES. GANDOLF FINDS HIMSELF ISOLATED, PROTECTED BY A THIN MAGIC BARRIER. A HUGE FIRE DRAGON IS COMING OUT OF THE FLAMES. THE STONE MELTS UNDER HIS FEET. HIS ROAR MAKES THE GROUND SHAKE. IT HAD BEEN THE DRAGON’S EYES STARING AT GANDOLF! THE DRAGON OPENS HIS JAWS TO BELLOW... MEANINGLESS PHRASES. CORRECT THE DRAGON. IN EACH BALLOON, DISCARD THE WORDS AND NUMBERS THAT HAVE NOTHING TO DO WITH THE OTHERS.

FLAME

FIRE

BLAZE

WOOD

12 16

13

DWARF KIMLI BUYS TURNIPS GANDOLF THE MAGICIAN COOKS VEGETABLES DWARF BADANDRA BUYS CARROTS

DEMON

HIPPOGRIFF

CHIMERA 53

14

28

10=2X5 9=3X3 40

7

GOAT

DWARF FRORIN BUYS TOMATOES

4 32

8

12=3X4 28=5X3X2 41

THE MESSAGE ON THE SLAB Despite the monstrous dragon’s incessant blows, Gandolf manages to resist.

“Go back to the abyss, you illogical flame!“ As Rog, the dragon, prepares to breath fire, he emits a sinister gurgle.

Gandolf rummages through his magic pocket, and pulls out a long stick and a sparkling sword. The mathematician wields both in his hands.

“Go back to where you came from!“ The flames touch Gandolf’s face, and he’s forced to leap backwards to avoid them.

“Go away.“ “ROARR!“ The dragon advances, ready to launch a new attack.

Gandolf raises his sword and stick, and after pointing them at Rog, he shouts: “YOU DON’T KNOW HOW TO COUNT!“ On hearing these words, the dragon looks really upset.

THE DISHEARTENED CREATURE STARTS TO SPEAK.

BUT, ONCE AGAIN, NOTHING HE SAYS MAKE SENSE. LUCKILY, GANDOLF KNOWS HOW TO REARRANGE THE LOGICAL PASSAGES IN THE DRAGON’S SPEECH! LOOK AT THE WIZARD’S NOTES, AND THEN COMPLETE THE FIRE DRAGON’S PHRASES.

I WAS GRUR WHEN GNUM SENT ME A FRUR THAT SAID: “—> YOU DO * SOLVE THE BUUR WITHIN A DAY, YOU’LL HAVE TO FIGHT FOR ME FOR THE REST OF YOUR LIFE“.

BUT —> I DO * KNOW HOW TO COUNT V REASON, HOW CAN I SOLVE IT? HE’S BROR ME!

LOGICAL OPERATIONS GANDOLF USES TO COLLECT HIS THOUGHTS: AND (^) OR (V) NOT (*) IF/THEN (—>) IF AND ONLY IF (<—>)

ABBREVIATIONS THE DEMON USES IN HIS SENTENCES: GRUR = ASLEEP BUUR = PROBLEM GNUM = THE DARK LORD BROB = MAKING FUN OF FRUR = MESSAGE

I WAS ..……………... WHEN ………….......….... SENT ME A ………...….. THAT SAID: “………. YOU DO ………. SOLVE THE ………………. WITHIN A DAY, YOU’LL HAVE TO FIGHT FOR ME FOR THE REST OF YOUR LIFE.“ BUT ………. I DO ……….. KNOW HOW TO COUNT ˆ REASON, HOW CAN I SOLVE IT? HE’S .…………………………....ME!

42

43

THE MESSAGE ON THE SLAB Despite the monstrous dragon’s incessant blows, Gandolf manages to resist.

“Go back to the abyss, you illogical flame!“ As Rog, the dragon, prepares to breath fire, he emits a sinister gurgle.

Gandolf rummages through his magic pocket, and pulls out a long stick and a sparkling sword. The mathematician wields both in his hands.

“Go back to where you came from!“ The flames touch Gandolf’s face, and he’s forced to leap backwards to avoid them.

“Go away.“ “ROARR!“ The dragon advances, ready to launch a new attack.

Gandolf raises his sword and stick, and after pointing them at Rog, he shouts: “YOU DON’T KNOW HOW TO COUNT!“ On hearing these words, the dragon looks really upset.

THE DISHEARTENED CREATURE STARTS TO SPEAK.

BUT, ONCE AGAIN, NOTHING HE SAYS MAKE SENSE. LUCKILY, GANDOLF KNOWS HOW TO REARRANGE THE LOGICAL PASSAGES IN THE DRAGON’S SPEECH! LOOK AT THE WIZARD’S NOTES, AND THEN COMPLETE THE FIRE DRAGON’S PHRASES.

I WAS GRUR WHEN GNUM SENT ME A FRUR THAT SAID: “—> YOU DO * SOLVE THE BUUR WITHIN A DAY, YOU’LL HAVE TO FIGHT FOR ME FOR THE REST OF YOUR LIFE“.

BUT —> I DO * KNOW HOW TO COUNT V REASON, HOW CAN I SOLVE IT? HE’S BROR ME!

LOGICAL OPERATIONS GANDOLF USES TO COLLECT HIS THOUGHTS: AND (^) OR (V) NOT (*) IF/THEN (—>) IF AND ONLY IF (<—>)

ABBREVIATIONS THE DEMON USES IN HIS SENTENCES: GRUR = ASLEEP BUUR = PROBLEM GNUM = THE DARK LORD BROB = MAKING FUN OF FRUR = MESSAGE

I WAS ..……………... WHEN ………….......….... SENT ME A ………...….. THAT SAID: “………. YOU DO ………. SOLVE THE ………………. WITHIN A DAY, YOU’LL HAVE TO FIGHT FOR ME FOR THE REST OF YOUR LIFE.“ BUT ………. I DO ……….. KNOW HOW TO COUNT ˆ REASON, HOW CAN I SOLVE IT? HE’S .…………………………....ME!

42

43

CLICK!

DID YOU WORK IT OUT? COMPLETE THE SEQUENCE.

THEY SEND THE PHOTO, AND GANDOLF SIGHS WITH RELIEF. SOME WORDS APPEAR ON THE SLAB:

1 YOUR REQUEST HAS BEEN ACCEPTED. “SO, CAN I FINALLY GO BACK TO SLEEP?“, ASKS THE DRAGON, HOPEFUL. “YOU ARE UNTIL THE DARK LORD FINDS ANOTHER WAY TO MAKE YOU SERVE HIM“, REPLIES THE MATHEMATICIAN. “BUT IF YOU STAYED IN MEDIAN CITY AND LEARNED LOGIC AND MATH, IT WOULD BE HARDER FOR HIM TO DECEIVE YOU...“ “HE’S RIGHT“, SAYS ORILDE. “YOU COULD GIVE US A HAND WITH THE FURNACES, IN EXCHANGE FOR SOME LESSONS.“ ROG THE DRAGON STARES AT THEM FOR A FEW MOMENTS, UNDECIDED. THEN, WITH A LOUD BREATH OF FIRE, HE SMILES: “ALL RIGHT, THEN: I’LL STAY!“

4

2

2

8

11

9

36

9

36

……

……

……

……

……

NOW USE THE NUMBERS IN THE SEQUENCE TO FIND OUT HOW THE STORY ENDS. USE THE STICKERS AT THE BACK OF THE BOOK TO COMPLETE THE PICTURE, IN THE ORDER OF THE SEQUENCE, AS SHOWN IN THE EXAMPLE.

1

11

4

11

……………………………………………………………… ……………………………………………………………… ……………………………………………………………… ……………………………………………………………… ……………………………………………………………… ………………………………………………………………

ALL’S WELL THAT ENDS WELL. BUT THERE’S ONE LAST TEST! LOOK AT THIS SEQUENCE OF EMERALDS: WHICH RULE JOINS EACH NUMBER TO THE NEXT? FOLLOW THE COLORED ARROWS.

1

8

4

2

8

9

36

…

…

…

149

37

THE RULE IS:

50

51

CLICK!

DID YOU WORK IT OUT? COMPLETE THE SEQUENCE.

THEY SEND THE PHOTO, AND GANDOLF SIGHS WITH RELIEF. SOME WORDS APPEAR ON THE SLAB:

1 YOUR REQUEST HAS BEEN ACCEPTED. “SO, CAN I FINALLY GO BACK TO SLEEP?“, ASKS THE DRAGON, HOPEFUL. “YOU ARE UNTIL THE DARK LORD FINDS ANOTHER WAY TO MAKE YOU SERVE HIM“, REPLIES THE MATHEMATICIAN. “BUT IF YOU STAYED IN MEDIAN CITY AND LEARNED LOGIC AND MATH, IT WOULD BE HARDER FOR HIM TO DECEIVE YOU...“ “HE’S RIGHT“, SAYS ORILDE. “YOU COULD GIVE US A HAND WITH THE FURNACES, IN EXCHANGE FOR SOME LESSONS.“ ROG THE DRAGON STARES AT THEM FOR A FEW MOMENTS, UNDECIDED. THEN, WITH A LOUD BREATH OF FIRE, HE SMILES: “ALL RIGHT, THEN: I’LL STAY!“

4

2

2

8

11

9

36

9

36

……

……

……

……

……

NOW USE THE NUMBERS IN THE SEQUENCE TO FIND OUT HOW THE STORY ENDS. USE THE STICKERS AT THE BACK OF THE BOOK TO COMPLETE THE PICTURE, IN THE ORDER OF THE SEQUENCE, AS SHOWN IN THE EXAMPLE.

1

11

4

11

……………………………………………………………… ……………………………………………………………… ……………………………………………………………… ……………………………………………………………… ……………………………………………………………… ………………………………………………………………

ALL’S WELL THAT ENDS WELL. BUT THERE’S ONE LAST TEST! LOOK AT THIS SEQUENCE OF EMERALDS: WHICH RULE JOINS EACH NUMBER TO THE NEXT? FOLLOW THE COLORED ARROWS.

1

8

4

2

8

9

36

…

…

…

149

37

THE RULE IS:

50

51