Math is Everywhere Reasoning

THE ARCHIPELAGO AND…

… ITS INHABITANTS

These considerations led to the conceptual structure of LUMI, vividly designed as a small archipelago of seven islands, each of which represents an area of development. The islands are all connected to one another in that growth is a comprehensive process that involves a variety of cognitive, emotional, and social dominions, all of which are interconnected.

The products of the LUMI line belong to seven distinct areas, but all of them are interconnected to stimulate integral, comprehensive learning.

The contents of the activity books and board games are built according to the specific goals we have indicated and can be summarized in seven major categories, represented by the seven islands of the archipelago, that transverse the age groups.

COMMUNICATING FEELING

4

0–3 years

Logi

The little hermit crab is a sweet animal that gets its courage from its shell, where it goes to hide from predators when it needs to. It accompanies the youngest of adventurers, those who need to carry out a gradual, protected exploration and who will abandon their shell to discover new horizons and new abilities only once they have completed their growth process.

5–7 years

REASONING

CREATING

COOPERATING

There are also animals that live on these islands.

Each one acts as a little companion whose job it is to guide the explorers, according to their age group.

THINKING

Mega

The third character/guide is a whale. In our collective imagination, the whale has always been a fascinating creature, a symbol of humanity itself and of the search for knowledge. The adventurers that Mega accompanies are strong and determined, ready to leave port to navigate the seas and dive into the abysses of knowledge to discover their own individuality.

3–5 years

Uniq

Another character who lives on the islands of the LUMI archipelago is a sea turtle.

As soon as as it hatches, this creature heads bravely toward the sea, never looking back. That is why it was chosen to accompany brave explorers that are young but daring, who set out with enthusiasm to discover basic knowledge, encouraged by their achievements in physical, linguistic, and social skills.

7–9 years

Ido

And finally, in the LUMI archipelago is the friend we all know and cannot do without, the seagull.

Free, independent, determined, curious, and loyal to its flock, the seagull accompanies the more mature adventurers who are ready to leave the safe waters and make a complex exploration into the world of awareness and one day become young soldiers of knowledge.

EXPLORING 5

THE ARCHIPELAGO AND…

… ITS INHABITANTS

These considerations led to the conceptual structure of LUMI, vividly designed as a small archipelago of seven islands, each of which represents an area of development. The islands are all connected to one another in that growth is a comprehensive process that involves a variety of cognitive, emotional, and social dominions, all of which are interconnected.

The products of the LUMI line belong to seven distinct areas, but all of them are interconnected to stimulate integral, comprehensive learning.

The contents of the activity books and board games are built according to the specific goals we have indicated and can be summarized in seven major categories, represented by the seven islands of the archipelago, that transverse the age groups.

COMMUNICATING FEELING

4

0–3 years

Logi

The little hermit crab is a sweet animal that gets its courage from its shell, where it goes to hide from predators when it needs to. It accompanies the youngest of adventurers, those who need to carry out a gradual, protected exploration and who will abandon their shell to discover new horizons and new abilities only once they have completed their growth process.

5–7 years

REASONING

CREATING

COOPERATING

There are also animals that live on these islands.

Each one acts as a little companion whose job it is to guide the explorers, according to their age group.

THINKING

Mega

The third character/guide is a whale. In our collective imagination, the whale has always been a fascinating creature, a symbol of humanity itself and of the search for knowledge. The adventurers that Mega accompanies are strong and determined, ready to leave port to navigate the seas and dive into the abysses of knowledge to discover their own individuality.

3–5 years

Uniq

Another character who lives on the islands of the LUMI archipelago is a sea turtle.

As soon as as it hatches, this creature heads bravely toward the sea, never looking back. That is why it was chosen to accompany brave explorers that are young but daring, who set out with enthusiasm to discover basic knowledge, encouraged by their achievements in physical, linguistic, and social skills.

7–9 years

Ido

And finally, in the LUMI archipelago is the friend we all know and cannot do without, the seagull.

Free, independent, determined, curious, and loyal to its flock, the seagull accompanies the more mature adventurers who are ready to leave the safe waters and make a complex exploration into the world of awareness and one day become young soldiers of knowledge.

EXPLORING 5

THE SUBJECTS IN THIS BOOK The subjects chosen for this book have been inspired by the studies of Alan J. Bishop. Working in ethnomathematics, this mathematician analyzed the ways in which his discipline breaks down in the various countries and cultures of the world—from the United Kingdom to Papua New Guinea.

According to Bishop, there are six universal activities that characterize math:

COUNTING LOCATING

MEASURING

PLAYING

BISHOP’S SIX UNIVERSAL ACTIVITIES

WHAT YOU WILL FIND IN THIS BOOK AND INSTRUCTIONS FOR USE This book is aimed at children ages 5 to 7, and it has been designed according to the cognitive development of this age group. There are five chapters, each based on a different setting that is part of children’s everyday life: the park, the kitchen, the gym, a birthday party, and the bedroom.

Each setting is dedicated to one of Bishop’s universal activities.

More specifically: - locating things in the park - playing and explaining activities in the gym - numbers and sums at a birthday party - designing in the bedroom, learning to recognize shapes and geometric figures - learning measurements in the kitchen

DESIGNING

EXPLAINING

In each chapter, the level of difficulty of the activities increases to ensure that all children will eventually be able to do all the activities in the book.

This book aims to stimulate children’s (and their parents’) curiosity in mathematics and to make them want to do more.

Each of these covers a number of typical activities used in math education, from kindergarten to college, and you will find some of them in the pages of this book.

8

9

THE SUBJECTS IN THIS BOOK The subjects chosen for this book have been inspired by the studies of Alan J. Bishop. Working in ethnomathematics, this mathematician analyzed the ways in which his discipline breaks down in the various countries and cultures of the world—from the United Kingdom to Papua New Guinea.

According to Bishop, there are six universal activities that characterize math:

COUNTING LOCATING

MEASURING

PLAYING

BISHOP’S SIX UNIVERSAL ACTIVITIES

WHAT YOU WILL FIND IN THIS BOOK AND INSTRUCTIONS FOR USE This book is aimed at children ages 5 to 7, and it has been designed according to the cognitive development of this age group. There are five chapters, each based on a different setting that is part of children’s everyday life: the park, the kitchen, the gym, a birthday party, and the bedroom.

Each setting is dedicated to one of Bishop’s universal activities.

More specifically: - locating things in the park - playing and explaining activities in the gym - numbers and sums at a birthday party - designing in the bedroom, learning to recognize shapes and geometric figures - learning measurements in the kitchen

DESIGNING

EXPLAINING

In each chapter, the level of difficulty of the activities increases to ensure that all children will eventually be able to do all the activities in the book.

This book aims to stimulate children’s (and their parents’) curiosity in mathematics and to make them want to do more.

Each of these covers a number of typical activities used in math education, from kindergarten to college, and you will find some of them in the pages of this book.

8

9

At the park

COLOR IN 3 birds ABOVE the PURPLE BIRD

LOCATING

CIRCLE in BLUE at least 2 birds to the RIGHT of BRUCE

CIRCLE in RED at least 2 birds to the LEFT of BRUCE

HI, I’ M BRU

CE!

CIRCLE 2 animals ABOVE BRUCE

CIRCLE 2 animals UNDERNEATH BRUCE

UNDERLINE 2 animals to the LEFT of BRUCE

UNDERLINE 2 animals to the RIGHT of BRUCE

OBSERVE: BRUCE’S left sleeve is yellow.

12

13

At the park

COLOR IN 3 birds ABOVE the PURPLE BIRD

LOCATING

CIRCLE in BLUE at least 2 birds to the RIGHT of BRUCE

CIRCLE in RED at least 2 birds to the LEFT of BRUCE

HI, I’ M BRU

CE!

CIRCLE 2 animals ABOVE BRUCE

CIRCLE 2 animals UNDERNEATH BRUCE

UNDERLINE 2 animals to the LEFT of BRUCE

UNDERLINE 2 animals to the RIGHT of BRUCE

OBSERVE: BRUCE’S left sleeve is yellow.

12

13

EXPLAINING LOCATING

The kids in the park have a mole as their mascot.

Her name is FIONA, and her favorite activity is walking on paving stones. Unfortunately, she has very bad eyesight, so the kids have learned how to help Fiona find her way when she comes out of her den. In the example, JASMINE has managed to guide FIONA with just 3 INSTRUCTIONS:

Now, BRUCE is going to play with FIONA .

He has to help her get back to her den.

READ the directions and then DRAW the ARROWS like JASMINE did.

GO STRAIGHT: TURN RIGHT:

ARE YOU READY?

TURN LEFT:

READY!

3 PAVING STONES!

By following Jasmine’s instructions, FIONA has moved forward 3 paving stones!

MOVE FORWARD

YOU DID IT!

MOVE FORWARD

START!

MOVE FORWARD 2 PAVING STONES.

TURN!

TURN RIGHT!

2 PAVING STONES!

TURN LEFT.

MOVE FORWARD 3 PAVING STONES.

YOU DID IT!

H U R R AY !

Now, TRY repeating the MOVES made by FIONA , using just the ARROWS .

16

REPEAT the MOVES FIONA made to get home, using just the ARROWS .

17

EXPLAINING LOCATING

The kids in the park have a mole as their mascot.

Her name is FIONA, and her favorite activity is walking on paving stones. Unfortunately, she has very bad eyesight, so the kids have learned how to help Fiona find her way when she comes out of her den. In the example, JASMINE has managed to guide FIONA with just 3 INSTRUCTIONS:

Now, BRUCE is going to play with FIONA .

He has to help her get back to her den.

READ the directions and then DRAW the ARROWS like JASMINE did.

GO STRAIGHT: TURN RIGHT:

ARE YOU READY?

TURN LEFT:

READY!

3 PAVING STONES!

By following Jasmine’s instructions, FIONA has moved forward 3 paving stones!

MOVE FORWARD

YOU DID IT!

MOVE FORWARD

START!

MOVE FORWARD 2 PAVING STONES.

TURN!

TURN RIGHT!

2 PAVING STONES!

TURN LEFT.

MOVE FORWARD 3 PAVING STONES.

YOU DID IT!

H U R R AY !

Now, TRY repeating the MOVES made by FIONA , using just the ARROWS .

16

REPEAT the MOVES FIONA made to get home, using just the ARROWS .

17

EXPLAINING DESIGNING

A Messy Gym The gymʼs a mess.

Help BRUCE clean it up.

Draw lines to CONNECT the sports equipment to the correct bins and shelves.

BALLS

BLUE OBJECTS

RED OBJECTS 26

SHOES

YELLOW OBJECTS 27

EXPLAINING DESIGNING

A Messy Gym The gymʼs a mess.

Help BRUCE clean it up.

Draw lines to CONNECT the sports equipment to the correct bins and shelves.

BALLS

BLUE OBJECTS

RED OBJECTS 26

SHOES

YELLOW OBJECTS 27

EXPLAINING PLAYING

Let’s Pack the Bags Practice is over and it’s time for the kids to pack their bags and go home. CHOOSE what to put in the bags, and then DRAW the objects inside them.

This bag’s for everything that’s THE COLOR ...

You decide!

30

This bag’s for everything NEEDED FOR ...

You decide!

This bag’s for everything YOU WEAR ...

And what goes in this bag?

You decide!

You decide!

31

EXPLAINING PLAYING

Let’s Pack the Bags Practice is over and it’s time for the kids to pack their bags and go home. CHOOSE what to put in the bags, and then DRAW the objects inside them.

This bag’s for everything that’s THE COLOR ...

You decide!

30

This bag’s for everything NEEDED FOR ...

You decide!

This bag’s for everything YOU WEAR ...

And what goes in this bag?

You decide!

You decide!

31

Let’s Celebrate and Play

COUNTING PLAYING

It’s MIRAN Š birthday, and all his friends are here to celebrate with him.

Nothing is missing: there are balloons, banners, gifts, and treats.

Look for the numbers 6 and 8 . They can be numerals or they can be objects to count. FIND THEM ALL! FA I R Y TA L E S

Y Y A PP H D

!

STORIES THE ANCIENT ROMANS

A B C

HA B I R T SEV

34

T EN

H

35

Let’s Celebrate and Play

COUNTING PLAYING

It’s MIRAN Š birthday, and all his friends are here to celebrate with him.

Nothing is missing: there are balloons, banners, gifts, and treats.

Look for the numbers 6 and 8 . They can be numerals or they can be objects to count. FIND THEM ALL! FA I R Y TA L E S

Y Y A PP H D

!

STORIES THE ANCIENT ROMANS

A B C

HA B I R T SEV

34

T EN

H

35

Dates of Birth

COUNTING PLAYING

All the guests decide to write down the day they were born so everyone will know each other’s BIRTHDAY!

When were you born? WRITE the month and year you were born on the calendar, and then mark the date with an X.

YE AR : M ON TH :

YE AR :

JASMINE was born

BRUCE was born

on 12/03/2014

M ON TH :

on 08/14/2014

And your best friend? WRITE the month and year they were born on the calendar, and then mark the date with an X .

WRITE the date of birth of three people you know

WRITE DOWN the biggest number you know!

below. Then DRAW their faces.

NAME: D AT E O F B IR /

/

NA M E:

TH:

DATE OF BI RT H: /

/

NA ME : DATE OF BIRTH : /

/

What happens if you add 1 to the number you’ve written? TELL someone what happens.

ASK a person who’s older than you to tell you

the biggest number they can think of, and then write it down.

Write your favorite number below and the reason why you like it.

36

NUMBER “ THE YEAR B I G !”

I S R E A L LY

Dates of Birth

COUNTING PLAYING

All the guests decide to write down the day they were born so everyone will know each other’s BIRTHDAY!

When were you born? WRITE the month and year you were born on the calendar, and then mark the date with an X.

YE AR : M ON TH :

YE AR :

JASMINE was born

BRUCE was born

on 12/03/2014

M ON TH :

on 08/14/2014

And your best friend? WRITE the month and year they were born on the calendar, and then mark the date with an X .

WRITE the date of birth of three people you know

WRITE DOWN the biggest number you know!

below. Then DRAW their faces.

NAME: D AT E O F B IR /

/

NA M E:

TH:

DATE OF BI RT H: /

/

NA ME : DATE OF BIRTH : /

/

What happens if you add 1 to the number you’ve written? TELL someone what happens.

ASK a person who’s older than you to tell you

the biggest number they can think of, and then write it down.

Write your favorite number below and the reason why you like it.

36

NUMBER “ THE YEAR B I G !”

I S R E A L LY

COUNTING

Each row of bags must contain a total of 10 MARBLES. PUT the correct NUMBER of marbles in each bag.

Colored Marbles It’s time to play with the colored marbles!

Before rolling them, MIRAN suggests that they all play a game.

4

5

1

GO to page 63, CUT OUT the marbles,

and PUT THEM on the plate below.

A) How many marbles

have you cut out?

0

5

5

B) How many YELLOW marbles

are there?

C) How many BLUE marbles

are there?

FIND all the possible combinations to create 5 different groups of 6 MARBLES.

COLOR all the possibilities below: 1)

4)

2)

5)

Now, YOU TRY! CREATE other ways to divide the 10 MARBLES between the bags, and WRITE the number of marbles in each bag on the labels.

3) 39

COUNTING

Each row of bags must contain a total of 10 MARBLES. PUT the correct NUMBER of marbles in each bag.

Colored Marbles It’s time to play with the colored marbles!

Before rolling them, MIRAN suggests that they all play a game.

4

5

1

GO to page 63, CUT OUT the marbles,

and PUT THEM on the plate below.

A) How many marbles

have you cut out?

0

5

5

B) How many YELLOW marbles

are there?

C) How many BLUE marbles

are there?

FIND all the possible combinations to create 5 different groups of 6 MARBLES.

COLOR all the possibilities below: 1)

4)

2)

5)

Now, YOU TRY! CREATE other ways to divide the 10 MARBLES between the bags, and WRITE the number of marbles in each bag on the labels.

3) 39

MEASURING COUNTING

The Weight of a Cookie The cookies are ready. Now all you have to do is weigh them and put them in the bags.

OMAR’S grandfather has come to visit, and he suggests they play a game.

He lays out a few kitchen utensils and some food items on the table and asks OMAR to find those that have a similar weight. You can TRY , too. LOOK for some of these objects and food items in your kitchen, and then WEIGH them.

Which of them have a SIMILAR WEIGHT ?

GET a cookie from your pantry

and WEIGH it on your scale.

WRITE how much it weighs on the screen.

How much do 10 cookies weigh?

DRAW your cookie on the bag, and WRITE the WEIGHT OF 10 COOKIES on the label.

Can you FIND anything in your kitchen that weighs the same as 10 COOKIES ? Weigh some different objects on your scale, and when you find something that weighs the same as 10 cookies, draw it here.

54

PA S TA

MILK WATER

RICE

MEASURING COUNTING

The Weight of a Cookie The cookies are ready. Now all you have to do is weigh them and put them in the bags.

OMAR’S grandfather has come to visit, and he suggests they play a game.

He lays out a few kitchen utensils and some food items on the table and asks OMAR to find those that have a similar weight. You can TRY , too. LOOK for some of these objects and food items in your kitchen, and then WEIGH them.

Which of them have a SIMILAR WEIGHT ?

GET a cookie from your pantry

and WEIGH it on your scale.

WRITE how much it weighs on the screen.

How much do 10 cookies weigh?

DRAW your cookie on the bag, and WRITE the WEIGHT OF 10 COOKIES on the label.

Can you FIND anything in your kitchen that weighs the same as 10 COOKIES ? Weigh some different objects on your scale, and when you find something that weighs the same as 10 cookies, draw it here.

54

PA S TA

MILK WATER

RICE

ACTIVITIES, TEXT, AND STORYTELLING Agnese del Zozzo and Marzia Garzetti both have a mathematics degree, and after years of self-employment in the world of education, they began researching the teaching and communication of mathematics. They are currently PhD students, at the Universities of Trento and Bolzano, respectively.

MOLE Page 18

TO CUT OUT CAKE Page 40

MARBLES Page 38

Tecnoscienza is a group of authors and educators who for more than 15 years have been involved in the dissemination of science, technology, mathematics, and information on the environment for numerous institutions, such as museums and businesses. Their books have been published in more than 20 countries and are designed to stimulate thoughts, actions, and emotions.

ILLUSTRATIONS Camilla Garofano was born in Empoli, Italy. After years of designing theatrical costumes, Camilla decided to dedicate herself to designing imaginary worlds and creatures, which led to her career in digital media and, in particular, illustrations for children’s books. She is a member of Fuffa, an illustration studio based in Tuscany that was created by a team of four friends passionate about illustration and books.

Together they make picture, activity, and interactive books, as well as puzzles and toys. Between them, they have years of experience in the editorial field, and they share the same goal: to create something beautiful.

GRAPHIC DESIGN

Lander Project

DIE Pages 44–45

LumiTM is a trademark of White Star s.r.l. © 2022 White Star s.r.l.

Piazzale Luigi Cadorna, 6 - 20123 Milan, Italy www.whitestar.it Translation: TperTradurre, Rome, Italy Editing: Michele Suchomel-Casey All rights reserved. No part of this publication may be reproduced, stored or transmitted in any form or by any means without written permission from the publisher.

First printing, May 2022 ISBN 978-88-544-1900-1 1 2 3 4 5 6 26 25 24 23 22 Printed and manufactured in China by Allied Fortune Times Limited (AF printing)

63

ACTIVITIES, TEXT, AND STORYTELLING Agnese del Zozzo and Marzia Garzetti both have a mathematics degree, and after years of self-employment in the world of education, they began researching the teaching and communication of mathematics. They are currently PhD students, at the Universities of Trento and Bolzano, respectively.

MOLE Page 18

TO CUT OUT CAKE Page 40

MARBLES Page 38

Tecnoscienza is a group of authors and educators who for more than 15 years have been involved in the dissemination of science, technology, mathematics, and information on the environment for numerous institutions, such as museums and businesses. Their books have been published in more than 20 countries and are designed to stimulate thoughts, actions, and emotions.

ILLUSTRATIONS Camilla Garofano was born in Empoli, Italy. After years of designing theatrical costumes, Camilla decided to dedicate herself to designing imaginary worlds and creatures, which led to her career in digital media and, in particular, illustrations for children’s books. She is a member of Fuffa, an illustration studio based in Tuscany that was created by a team of four friends passionate about illustration and books.

Together they make picture, activity, and interactive books, as well as puzzles and toys. Between them, they have years of experience in the editorial field, and they share the same goal: to create something beautiful.

GRAPHIC DESIGN

Lander Project

DIE Pages 44–45

LumiTM is a trademark of White Star s.r.l. © 2022 White Star s.r.l.

Piazzale Luigi Cadorna, 6 - 20123 Milan, Italy www.whitestar.it Translation: TperTradurre, Rome, Italy Editing: Michele Suchomel-Casey All rights reserved. No part of this publication may be reproduced, stored or transmitted in any form or by any means without written permission from the publisher.

First printing, May 2022 ISBN 978-88-544-1900-1 1 2 3 4 5 6 26 25 24 23 22 Printed and manufactured in China by Allied Fortune Times Limited (AF printing)

63