The energetic number 1.000 really enjoys his mornlng exercises. He jumps around on four Minicomputer Boards demonstrating chameleonic ability to alter his appearance while maintalnlng hls Identify as the number 1.000.
81 Roses is a love story about a little white dog and his 81-year-old "mother." The puppy explores the strange and sometimes frightening world of grown-ups. He experiences insecurity, fear, and joy.
He grows and learns. Most important, he responds with happiness and affection to the warmth of those who love and respect him. Young children, who are so sensitive to their own feelings, will empathize with the little dog and with his friends, young and old. With vivid simplicity, pictures of strings and arrows help tell the story. You may be surprised how concretely these abstract pictures speak to readers and involve them in counting or relational thinking.
A Book About Me is actually two detective stories in one, the first part concerned with identifying the narrator and the second with finding a special friend. These two friends are whole numbers. In each section, the narrator gives clues, which lead students to broaden their knowledge about certain properties of numbers and relations between numbers. Valuable allies in this task are the' nonverbal languages of Papy's Minicomputer and of arrows, certain numerical properties and symbols. As the clues build, one upon the other, readers become involved in the exciting task of narrowing the number of "possible suspects" until the "guilty one II is apprehended in each case.
In this story-workbook the young readers are taken on a fantasy journey to the curious country of the numbers. Long ago in this country, the numbers' houses were connected by little paths following a strange rule, which was invented by their leader, the number 0. The rule involved two interesting numerical relations, doubling and doubling plus one. Using the flexible language of cords, students freely explore with these two relations and the inverse of each as they search for a way to connect different pairs of numbers (30 and 50, for example). Next they are immersed in a global situation as they try to draw their idea of a map of the country. This experience leads them to examine a binary tree, which is presented artistically to show its simplicity and beauty. In the closing pages, a joke is played on 0, which causes him to have a disturbing dream. Both the joke and the dream suggest mathematical ideas that can serve as a stimulus to further thinking about the tree for those children who are interested.
If each person is to receive ten Valentine cards and no person is to send more than one card, then you need at least ten times as many senders as receivers. That's obvious! Or is it? That's the question in A Valentine Mystery.
When Zero announces that this year in the World of Numbers they will celebrate Valentine's Day in a way that only numbers can, the little boy in the story is puzzled. However, as the story progresses and Zero gradually unfolds his grandiose scheme, the boy begins to suspect that perhaps there's something about the set of whole numbers that allows things to occur in the World of Numbers that could never happen to people! Thus Zero's explanatory posters and the little boy's patient questioning give the reader a glimpse into the strange things that can occur in the realm of the infinite.
The numbers 7 and 8 live in a very strange neighborhood. No sooner does the hero of this story decide that two numbers live next door to each other than he is shown that, in fact, between their houses there are at least nine others. As the story proceeds, the reader begins to appreciate just how awesome this concept is; one feels quite dizzy just looking at the pictures of the street on which 7 and 8 live. The story of this strange neighborhood continues with a tale of mystery radio signals. The police become involved in the search for the source of these signals, but it is Zero who eventually deciphers what they mean, and hence manages to locate a sad number, whose trouble is that it is irrational (in the mathematical sense, that is).
"Clinton Street" (presented in two parts) is an intriguing mystery story which expands students' understanding of the world of numbers so artfully that the pleasure of discovery motivates them to plunge ahead into unknown territory. Cryptic pictures and notes appear in the mailbox of Spike, the detective, which show him three different ways of exploring his problem of locating a mystery house. Thus students are encouraged to be flexible in approaching a problem and to see that numbers can be represented in a variety of interesting ways. The familiar languages of Papy's Minicomputer and the red-blue arrow roads are used in the early pages of exploration. They set the stage for the introduction of another important tool, the binary abacus. In the final pages of the second part, the problem is solved as the students are given an opportunity to become more familiar with the new tool. There is also material which encourages those who have sufficient interest to do further exploration by changing the code of the abacus.
Dancing Friends is a story about a boy and ten of his friends who just happen to be numbers. They speak to each other, play together, and make up games. When they play after school and are free from the usual constraints placed upon them, they invent marvelous games and dance to the tune of vividly colored arrows. The games of the numbers are not frivolous. There are rules to follow and, as a result, orderly patterns emerge as they dance. They observe similarities and differences as they go from one dance to another, and 0 discovers that it plays a very important role in the whole scheme.
In this story, the Numbers' Parliament has enacted legislation requiring the decimal way of writing numbers. This means, of course, that all the numbers have to register at the City Hall using their decimal names. Many numbers, such as 1/2, 1/4, and 1/8, are greatly distressed about this because they have grown up believing that their fractional names are perfectly adequate. To their relief, they discover that assuming their decimal names does not present as much upheaval as they had feared. The situation is not so simple in the case of 1/3, however. It is sent from office to office at the City Hall, and no one seems to be able to tell 1/3 what its decimal name is. Fortunately, the Complaints Office is run by Zero, who carefully explains why 1/3 is having such problems, and promptly provides it with a manageable decimal nickname.
Halloween Puzzles comprises three intriguing little numerical mysteries, which are presented to the accompaniment of all the trappings of the season of Halloween. All three puzzles are stated in the language of arrows, and they each require that the reader attempt to identify the numbers involved in the puzzle. This task is tailored to the reader's capabilities by the progressive introduction of a graduated sequence of questions and examples. Some children will be able to solve the puzzles at a very early stage, while others will benefit from reading the development of each puzzle right through to the presentation of the last example.
I Am a Very Happy Boy is a story about a lonely child-sometimes he feels nobody notices him and he is afraid. Young children who are so sensitive to their own developing feelings will empathize with this boy. Pictures of dots, strings, and arrows reinforce the ideas in the story in a simple but powerful way and, at the same time, help students to enter the world of mathematics. In the end, the boy makes many new acquaintances and finds that he not so lonely after all.
In I Am Not My Name, 1/2 weathers a serious identity crisis and 0 has some of its pomposity deflated. Much to 0's annoyance, a small group of numbers have been playing some games in its absence. During the course of these games, 1/2 suddenly becomes aware of the fact that there is another potential occupant of its place on the number line. In great distress, 1/2 seeks comfort in the company of a human friend, who is spending an afternoon chatting with 0. Through the discussion and questions that arise, the young reader is introduced to the subject of equivalent fractions in a clever way.
Nabu Wins an Award is a story that exhibits many important aspects of the structure of the system of numbers. It is Nabu's tenth birthday. In his honor, his friends the numbers have organized a show of spectacular dances involving many numbers, some of whom Nabu has never even met before. One dance is like an earlier one danced backwards; other pairs of dances involve different dancers and different operations but have identical choreographs. The numbers 0 and 1 forget their usual rivalry in order to cooperate in the choreography of several ballets of great numerical interest. The evening reaches its climax when a special award is presented to Nabu.
This story is about seven cuddly, lovable, little puppies, one of whom is always in trouble. He gets lost when the family goes for a walk. No sooner is he given a new dish than he breaks it. Try as he will, nothing he does seems to be right. His mother must constantly scold and punish him. His situation is one with which every child can sympathize. The nonverbal languages of strings and arrows help to tell the story of the troublesome pup and his six brothers and sisters.
This story is about a little boy and his playful number friends. It is full of provocative pictures needing no words to suggest many ideas to students. Since an open situation tends to encourage students to use their creativity to develop the situation, the story is presented without any written narrative. With your encouragement and guidance, let students' help you tell a story as you explore the pictures together and discover what interesting ideas and mathematical concepts emerge and develop.
In this story-workbook, the number 37 has a very active day followed by a restless night point of view, their games provide a setting in which: during the day, 37 roller-skates with the other whole numbers. The story line, the uses nonverbal languages, and the reader's participation combine t o insure a rich mathematical experience to introduce congruence classes of whole numbers (modular arithmetic); t o give practice in the use of some elementary numerical functions;
A detective story about seven secret numbers.
A very common problem for a merchant is to determine the optimal quantity of items to buy in order to have the most profit. Nobody can be sure to make the best prediction; there is always a risk. All one can do is decide what is the most reasonable prediction. That is what Shunda, a newspaper seller, does when faced with the problem of supplying her newsstand with papers. With the help of many stimulating pictures, Shunda and the reader is gently lead through a solution of this common applied mathematics problem.
Singing Friends introduces students to properties of 0 and '1/2 through fantasy. The games in Singing Friends are of two kinds. At first the numbers are exuberant and their games suggest a first notion of infinity, as greater numbers dance right off the page in unending snake dances. Then, in a quieter moment, several friends sit together thoughtfully and ponder the meaning of their relationships to one another. Finally, in a game designed to include 1/2, some numbers race toward 0 in a futile attempt to reach their leader, and this time smaller and ever smaller numbers form an infinite line of players.
This book is an account of the adventures that a group of whole numbers met with when they had the good fortune to go to summer camp together. It is not possible, however, for the reader just to sit back and absorb stories of boating, games of hide-and go-seek, mountain climbing, scuba diving, visits to caves, tree climbing, and so on. As the number 100 gives his report of the camp, he leaves it up to the reader to provide all the details required for a full understanding of what happened. This involves a lot of computation and deductive reasoning on the part of the reader as he or she attempts to fill in the missing information in the cleverly blended realistic and mathematical pictures. "Summer Camp" provides a pleasant setting in which there are many opportunities for the reader to solve problems stated in the language of arrows. In carrying out this task the reader takes one more step in the process of familiarization with this important nonverbal, mathematical language.
Did you know that the whole numbers go to school during the summer? It appears that an important part of their school day is spent presenting themselves to one another in a variety of ways. In great- grandmother's day, the numbers used bundles of sticks for their presentations. Many numbers found carrying sticks terribly inconvenient. For example, the number 24.367 had an enormous mountain of sticks to bring each day to school. How times change! With the arrival of a great modern convenience, Papy's Minicomputer, numbers no longer needed to carry anything more than a small bag of checkers. (24,367 needs no more than nine checkers; and some say even fewer!)
Did you know that the whole numbers go to school during the summer? An important part of their summer school day is spent presenting themselves to one another in a variety of ways. In great- grandmother's time, the numbers used bundles of sticks for their presentations. Many numbers found carrying sticks terribly inconvenient. For example, the number 24,367 had an enormous mountain of sticks to bring to school each day. How times change! With the arrival of a modem convenience, Papy's Minicomputer, numbers no longer need to carry anything more than a small bag of checkers. (For example, 24,367 need no more than nine checkers; and some say even fewer!) Summer School in the Old Days is a story warmly told and richly illustrated. Much information is provided both in the detailed illustrations and in the text. The careful observer can discover, for example, in which year the new school building was opened. The story offers its readers an opportunity to gain new insights into the whole numbers and to extend their perspective to include a first idea of negative numbers. (A glimpse of this wider range of numbers is given when the number 0 finds new ways to present itself.)
The birth of the second child in a family can be a traumatic experience. Suddenly the focus of attention switches from the only child to the new arrival. Feelings of rejection and resentment can follow unless the situation is handled very carefully. The Baby Is Born is the story of just such a conflict and its subsequent resolution. It is seen through the eyes of the firstborn and the reader shares with him his changing feelings. This spectrum of e emotions is illustrated, perhaps surprisingly, by means of two nonverbal mathematical languages: the language of strings and the language of arrows.
The Happy Puppet tells the story of a lovable hand puppet and the interesting games played with the puppet's friends, the dots. These games are vividly and colorfully portrayed by means of the versatile mathematical languages of strings and arrows. At one moment the dots are numbers, at another they are 100-year-old hippopotami, yet the mathematical languages can always faithfully record their exploits.
The principal character in The Hidden Treasure is a boy who has the misfortune to fall ill at Christmas time. Fortunately, for him, his grandmother is on hand to help him feel less sorry for himself. She gives him two interesting puzzles and a large box of colored pens to use figuring them out. The first puzzle has to do with Spike, the famous spy, and the mysterious case of the stolen treasure. As part of his investigation, Spike has to travel along all the possible routes from his house to the place where the treasure is hidden. Even though all the roads in the area are one-way, there are still surprisingly many possibilities. The second puzzle involves Spike's attempts to wind up his investigation by interviewing all ten suspects, four at a time. The reader discovers a very strong link between the two puzzles, and this greatly simplifies the situation.
The Little Donkey is a delightful story about how a little girl and her friend, a donkey, entertain themselves on a lazy afternoon. As children so often do, the little girl pretends that the pebbles she has so carefully collected are the people she knows. Then, with a stick, she draws arrows in the sand from one pebble to another to show the donkey the story of her family. As the donkey identifies the various family members, these two friends share their feelings about the people in their lives.
In The Little Dreamer, we meet a little boy who isn't too fond of schoolwork. Everything is so rigid and cut -and-dried. There is no room for fantasy and artistic expression. His parents, whom he wants to please so much, are disappointed with his school grades. The only solace he can find is in the company of his aunt, who shares his interest in clouds, birds, and trees. Using the mathematical languages of strings and arrows, she helps him "warm up" to mathematics. These languages give full rein to the imagination, making whole numbers familiar and less daunting.
The Magic Box is a story about a poor little boy with a very rich imagination. Although his working mother has little time to spend with him, she listens thoughtfully as he shares his ideas. A valentine story drawn by the little boy presents an opportunity to explore a situation, which is told completely in the language of colored arrows.
Inspired by a suggestion from the probabilist Lennart Rade, The Square Trap provides an exciting introduction to the fascinating world of probability and statistics. The hero of the story is given a spinner, and he invites the numbers 0 and 1 over to help him make the most of his new toy. The two friends oblige by each inventing a game that can be played using the spinner. Examples of the games being played are included in the narration of this story, but the readers as the story progresses perform the bulk of experimentation. Thus, students gain firsthand experience of the gradual build-up of statistical information and acquire a deeper appreciation of the probabilities at work in each situation is acquired. The first game is a random walk on a square, and the second is a very special case of what is known as "the EHRENFEST model." However, even though these games are apparently very dissimilar, the reader takes part in the major discovery that they are in fact equivalent in the sense that moves in one game parallel moves in the other, and if one game ends, the other game always end on the same move.
The delightfully illustrated tale of The Weird Story of 24 is about a boy, his cat, and a weird number " friend, 24. From the moment 24 shows up in the mailbox to the time of its odd disappearance, life is just one strange happening after another. Minicomputer boards appear on the ceiling, pictures vanish into thin air, checkers take on a life of their own-these peculiarities disturb the cat's morning snooze, but the boy takes it all with equanimity. Behind all the strange occurrences, readers have a chance to learn more about the number 24. In particular, by anticipating how the boy is going to get 24 out of the various predicaments into which it falls, the readers strengthen their knowledge of and confidence with the Minicomputer.
The number 100 is directing some friends in an interesting game. They all have to find their places in an arrow picture. As they very quickly discover, this is not as easy as it sounds. The story compels the reader to consider several challenging numerical problems presented in two non- verbal languages: the language of arrows and the language of the Minicomputer. While grappling with these problems. Students develop mathematical reasoning skills within the context of an enjoyable story.
In Two by Two, Cedric Shirtsleeves learns an intriguing new game. He finds out how he can represent the numbers he knows simply by using checkers and some colorful square boards. This story introduces the Papy Minicomputer, a simple abacus that combines the usual positional system with the fundamental notion of doubling. As the narrative unfolds, insight into the anatomy of numbers is subtly deepened. Students begin to think of numbers in many different ways and discover how numbers can be shown with checkers on, the colored squares. This positional system lends strong support to the learning of the usual system of 'writing numbers. The positions of that system acquire a physical significance, and this concreteness brings the representation of numbers to life.
Where's My Nose? is a story about an only child whose understanding grandmother amuses him with a detective story about the boy, his nose, herself, her three lovely cats, three rabbits, one squirrel, three bugs, and a charming black poodle. At first the boy is disappointed to find that his grandmother's story consists of nothing more than a picture of 14 dots, one for each of the characters. But the grandmother is patient and begins to attract the boy's interest by drawing a colored string around all the dots for animals with four legs. As more clues are given and more strings are drawn, the boy becomes absorbed in the discussion of the picture until finally he solves the mystery. .
A Supplement for Intermediate Entry Module.
