The Greedy Triangle

written by Marilyn Burns and illustrated by Gordon Silveria

Recommended Grade Level: 1-3

NCTM standards: Geometry, Connections

Summary: This book tells the story of a triangle who is initially happy with the many situations in which he finds himself: he can be a piece of pie or the roof of a house, a sailboat sail or the face of a pyramid. Over time the triangle tires of his life and visits a shapeshifter who transforms him into a quadrilateral. Again he tires of his four-sided adventures and visits the shapeshifter again, and again, and again, each time being given one more side and one more angle and each time returning, bored with his new life. As he changes shape, he begins to neglect his friends and feel isolated and confused. He returns to the shapeshifter and asks to be turned back into a triangle, unsure why he was unhappy with this life in the first place.

Uses for this book: This book is a good introduction into basic geometrical shapes and it shows the difference between shapes when one side and one angle are added, changing the shape completely. One useful activity would be a shape stroll where students walk through the school looking for shapes in the real world. After this, students could create an art project where they construct familiar objects out of cut paper polygons.

Flatland by Edwin A. Abbot, is a story told from the perspective of a character called the "square." Square describes to the reader his country called Flatland because it is the land of two dimensions. After explaining the social structure of his country, he travels to Lineland (the first dimension) and converses with the king of Lineland, but alas, Square is unable to convince the king of Flatland's existence. Similarly, once Square returns home, a sphere from Spaceland (the third dimension) tries to describe Spaceland. Square is unable to imagine it until the sphere pulls Square into Spaceland. Thus, the adventures of Square is a fun and interesting introduction to dimensions.

Recommended grade level: 7-8.
NCTM content standard: Geometry
Book uses: I would take ten to fifteen minutes a day to read a chapter of this book to the class and together discuss the concepts introduced. There's a plethora of material to discuss: social structures, angles, the relationships between 3-D shapes, 2-D shapes, lines, and points, and social commentaries of the subject of truth and heresy. Students could conceivably write story responses, draw the different lands, but mainly I think this book lends to great and fun mathematical discussions.
Cons: The book is written in an older english dialect. Also, it is heavily sexist in its treatment of females [shapes].

My Little Sister Ate One Hare

By Bill Grossman

Illustrated by Kevin Hawkes

NCTM Content Standard: Numbers and Operations and Probability

Summary: In this amusing picture book, readers follow the story of Little Sister as she eats all kinds of disgusting things and has no problem getting them down. But when Little Sister attempts to eat 10 peas, she throws up all over the place and creates a disgusting mess.

-Uses of this book:

K-1

- Counting - Ask the children if they notice a number pattern, or how the numbers change from page to page. Each time, the Little Sister eats one more disgusting thing than the page before until she reaches 10.

1-4

-Addition - Ask students to add up the total number of things that little sister eats

-Estimation - Have students estimate the total number of things that Little Sister eats, have students use a calculator to compute the total number.

4-6

-Probability - Students can play with probability and ratio by pretending all of the things that Little Sister ate were in one sack and figure out the probability of pulling out certain objects and the ratios of part to whole.

One Grain of Rice

One Grain of Rice by Demi

Illustrated by Demi

Recommended Grade Level: 5th grade

NCTM standards: Number and Operations, Algebra

This book tells the story of a selfish raja who forced the peasants in his town to give all the rice that they grew to him except for just enough for them to live off of. He said he was storing the rice in his royal storehouses so that they could have rice to eat if there was a famine. One day, there was a famine in this village and the raja did not want to give rice to his peasants fearing that he himself would starve. Along came a peasant girl named Rani who noticed that rice was leaking out of one of the bags being carried to the royal storehouses. She collected the rice in her dress and instead of keeping the rice for herself she returned the rice to the raja. He was grateful to her and asked her if he could do anything for her in return. She replied that he could give her one grain of rice, and the next day double that, and the next day double that, and so on for 30 days. The raja thought this was a very modest request. Over the course of 30 days, Rani was given all the rice in the raja's royal storehouses and she gave it to the peasants so that no one would go hungry and made the raja promise that from now on he would only take as much as he needed.

If I were teaching this book I would ask students to make predictions about how much rice Rani would be receiving on the 30th day and how much rice she would be accumulating over all. Students could make estimations and then actually calculate how much rice she would be receiving and see how far off their predictions were from the real numbers. I would also challenge students to come up with a mathematical formula to figure out how much rice Rani would be receiving on the 30th day and overall so that students wouldn't have to multiply times 2 over and over again.

Two of Everything

Title: Two of Everything

Author/Illustrator: Lily Toy Hong

Grades: K-4

A darling retelling of a Chinese folk tale about an elderly couple who finds a magical brass pot that doubles everything put inside of it. They begin to make doubles of everything: hair pins, coins and even (by accident) themselves.

NCTM Content Standards: Numbers & Operations, Algebra

How to Use: This book can be used to make predictions (They put one vase in the pot, how many will they have now?) and to see patterns, specifically doubling. The story serves as a great introduction to multiplying by twos and can be used to show the link between addition and multiplication (5 coins + 5 coins = 2(5 coins)). Students can be asked to record, prove or even act out the doublings that happen in the text (10 coins + 10 coins = 20 coins) and to continue doubling beyond the story (What would happen if we take those 20 coins and put them in the pot?). The story can be used to think about large magnitudes (How many times would you have to double the 5 coin purse before you got to 100? What about 1000?) or even to think about the concept of infinity (What happens if we keep doubling our coin purse for hours and days and years? What's the highest number we'll get to?). And finally, the story presents great opportunities for inter-subject connections with other folk/fairy tales, with topics on Chinese culture, with social concerns (e.g. poverty, wealth, materialism), and more.

The Doorbell Rang

Author and Illustrator: Pat Hutchins

Summary: two kids sit down to share a batch of a dozen cookies, when the doorbell starts to ring. With each ring more kids come in and each kid gets fewer cookies. Then, at the end of the book, grandma comes in with more cookies.

Recommended Grade Level: 1-3
How to use the book: students act out sharing 12 and other numbers of cookies or other concrete objects with each other. Different numbers of students can come to a table, and students can see how quotients change with different divisors. Once this task is mastered with concrete objects, the same problems can be done using only written numbers.

NCTM content standard: Number and Operations

-How Much Is a Million?

By David M. Schwartz pictures by Steven Kellogg

-Recommended for grades 2-5

-NCTM Content Standards: Number & Operations, Measurement

-Summary:

This book helps readers conceptualize the magnitude of large numbers. The main character, Marvelosissimo the Mathematical Magician, leads the reader through several examples of what a large quantity, for example one million, of something might look like. To illustrate how large one million is, Marvelosissimo describes how big a container would have to be to house one million goldfish, or how high one million children stacked on one another’s shoulders would stretch to.

-Recommended Uses/ Activities:

This book could be used to introduce a unit on measurement. After reading the book, students could measure each other’s heights and add them together, figuring out how far the students in the classroom if stacked upon one another’s shoulders would stretch to, or how big the city harbor/ lake might be. Furthermore, the students could find the average foot size of the classroom and find how far one million human feet might stretch.

To practice estimation, previous to reading the book, the teacher could ask the children to estimate the magnitudes of certain measurements that will be discussed in the book. After reading the teacher could lead a discussion on how their estimations compared with the book.