Spaghetti and Meatballs for All!

Written by Marilyn Burns
Illustrated by Debbie Tilley

Recommended grade level: K-5

NCTM Content Standards: Number and Operation, Geometry, Problem Solving, Connections, Representation

Summary: Mr. and Mrs. Comfort decide to host a dinner part. They invite 32 of their nearest and dearest. They rent 8 square tables to seat their guests-- each seats 4. As the guests arrive on the day of the party, they begin to push the tables together so that they can all sit with the Comforts. Mrs. Comfort warns the guests that their table configuration will not accommodate all 32 guests, but they do not listen to her. Ultimately, everyone recognizes that the only way to solve the seating situation is to separate all 8 tables. Mrs. Comfort is exasperated but in the end, everyone has a seat.

Uses for this book: For younger children, teachers can have students count and then document the number of guests who arrive at the party. Slightly older children can discuss the amount of food that the Comforts purchase for their party and how much each guest can eat (i.e. ½ a loaf of garlic bread, 3 meatballs, etc.) However, this book is ideal for helping students to understand that different shapes with the same area can have different perimeters. A teacher can begin by holding a discussion where the class figures out why Mrs. Comfort continuously says, “But that won’t work.” Students can use square shaped magnets or laminated pieces of card stock to rearrange the table setup as you read each part of the story. This activity can either be done as a whole class or by each student at his or her desk. Students can calculate perimeter and area after each arrangement and talk about their findings at the end of the story. Additionally, students can be asked to calculate how many tables it would take to seat 12, 16, 24 or 36 people—this activity allows them to apply what they learned from the story to other scenarios. And finally, students can plan their own parties, complete with menus and table setups based on how many people they plan to invite.

Uno's Garden

Title: Uno's Garden

Author and Illustrator: Graeme Base

Recommended Grade Level: 3-5

NCTM Content Standards: Number and Operations, and Algebra

Summary of the Book: This book is about a character named Uno, who goes to visit a forest one day. He decides that he would like to move to the forest and make it his permanent home. He is amazed at the beautiful plants and unique animals. As more and more people make their way to this forest, and more buildings are put up, the animals and plants start to disappear. Eventually the forest is no longer full of plants and animals and the occupants decide to leave. Uno and his family stay and slowly allow for the plants and animals to come back.

Suggestions for Use: The three different mathematical patterns, subtraction, squares, and doubles, are not explained explicitly in the story, so students could figure out what pattern is being used in the increasing or decreasing amounts that are represented. Once they understand the concepts, students could write out words or word problems to describe the content on a certain page. For example they could deal with 9 times 9 equals 81 plants and have to say “there are 9 different types of plants, and there are 9 of each of these different types, how many plants are there in total?” You could also have them go through and write a word problem using subtraction, multiplication, division, squares, and doubles. This book could also extend beyond mathematics instruction and spark a conversation about environmental concerns.

-Lindsay

Chasing Vermeer

Title: Chasing Vermeer

Author: Blue Balliett

Recommended Grade Level: 5-8

NCTM Standards: Geometry, Algebra, and Problem Solving

Summary: Blue Balliett introduces readers to a pair of precocious kids on a quest full of patterns, puzzles, and the power of blue M&Ms. Eleven year old Petra and Calder may be in the same sixth grade class, but they barely know each other. It’s only after a near collision during a museum field trip that they discover their shared worship of art, their teacher Ms. Hussey, and the blue candy that doesn’t melt in your hands. Their friendship is strengthened when a creative thief steals a valuable Vermeer painting en route to Chicago, their home town. When the thief leaves a trail of public clues via the newspaper, Petra and Calder decide to try and recover the painting themselves. But tracking down the Vermeer isn’t easy, as Calder and Petra try to figure out what a set of pentominos (mathematical puzzle pieces), a mysterious book about unexplainable phenomena and a suddenly very nervous Ms. Hussey have to do with a centuries old artwork. When the thief ups the ante by declaring that he or she may very well destroy the painting, the two friends know they have to make the pieces of the puzzle fit before it’s too late!

Uses/Activities: This book would be a great tie-in for mathematics and English. Students can read the story for English, and use the pentominos in math class. The pentominos can be used to make different shapes--useful in geometry class--and students can create their own set of petominos. There are also many activities in the back of the book regarding mathematics. Students can come up with their own patterns and codes using mathematical formulas. It's a great hands-on activity and they can write reflections on what they have learned.

You Can, Toucan, Math

Written by David A. Adler
Illustrated by Edward Miller

Recommended Grade Level: 2-4

NCTM standards: Number and Operations, Problem Solving

Summary: From Two Toucans to Crows in Rows, this book presents twenty-one bird-themed rhyming word problems. These number riddles ask readers to decide whether to use addition, subtraction, multiplication, or division to solve the word problem. For younger grade levels, children can also discover the answer by simply counting the birds in the colorful illustrations. A typical riddle goes: "Two toucans, / and seven, / and four toucans more -/ how many toucans / are two, seven, and four?"

Uses for this book: This book serves as a good introduction into basic word problem solving for students in grades 2-3. The book could be used across grades 2-4 since teachers can pick and choose the number riddles that best suit their purpose. It could be used in 4th grade to help students review or refresh their memory on the four different number operations. In addition, in 4th grade, the teacher could read one number riddle a day for three straight weeks or sporadically throughout the year. The four number operation fact table endpapers could help students to test their own knowledge of addition, subtraction, multiplication, and division facts.

One activity that students could do is to create their own number riddle. The class could decide on a topic to write their rhyming word problems on in case they want an unifying theme. Otherwise, students could select a topic of their choice to do their number riddle on. Afterwards, the teacher could collect the students' number riddles to make a classroom book of rhyming word problems.

A Drop of Water

Title: A Drop of Water

Author: Walter Wick

Recommended Grade Level: 6-8

NCTM Content Standard: Geometry

Summary: Vivid photographs illustrate the various states of water in A Drop of Water. The photos and accompanying explanations explore water from its simplest form as tiny molecules to its more complex forms as vapor, ice, snowflakes, and clouds. Water is also analyzed in its multiple stages of movement, including condensation and evaporation. Each new page contains a striking image of water to stimulate awe in the reader and a brief summary to explain the featured phenomenon. A list of potential experiments involving water are included at the end of the book.

Uses/Activities: Water is presented in its form as soap bubbles in the book. Students could read about water in this state and then use soap bubbles to learn about geometry, specifically circles. The activity would go as follows:
Groups of students receive bubble mix. Students blow bubbles and when the bubbles pop, they measure the radius, diameter, and circumference of the circles left by the bubbles (very quickly before they completely disappear)! After recording the data in a table, students work collaboratively to discover the relationship between radius, diameter, and circumference of a circle.

How Big is a Million?

Title: How Big is a Million?

Author: Anna Milbourne 

Illustrator: Serena Riglietti

Recommended Grade Level: Prekindergarten- 3rd grade

NCTM Content Standard: Number and Operations

Summary: This is a story about a small penguin named Pipkin who decides to go on a quest to find a million of something.  This proves to be harder than he imagined! First he finds ten fish, then he meets 100 penguins,  and he even sees 1,000 snowflakes. Eventually, he gives up and goes home. When he gets there, his mother has a surprise for him -she helps him find out how big a million really is! At the end of the book, there is a huge poster that folds out and shows what a million stars looks like!

Uses/Activities: This book is great for helping young children conceptualize very large numbers, and helping them to understand how numbers relate to one another. It is also a good way to show how simply adding a "zero" to the end of a number can change the value of the number dramatically. Depending on the age of the students, there are many different activities you do using this book.  For younger kids, you could have them draw their own version of the story, using a much smaller number as the ultimate goal (like 100, instead of 1 million).  For older kids, you could have them make estimates using the poster at the end.  For instance, the poster folds out into 24 squares; the teacher could ask each student to guess how many stars there are in each separate square and then solve for the correct answer. Kids of all ages will be in awe of what a million stars actually looks like!

The Phantom Tollbooth

Title: The Phantom Tollbooth

Author: Norton Juster

Illustrator: Jules Feiffer

Grade Level: 5-8

NCTM Content Standards: Geometry, numbers/operations, measurement

Summary: The Phantom Tollbooth tells the story of Milo, a lethargic young boy who chances to discover a magical tollbooth. Traveling through the booth, he finds himself in a fantasy world in the midst of a civil war between lovers of words (led by King Azaz) and lovers of numbers (led by the great Mathemagician). Accompanied by his watchdog friend Tock and the cranky Humbug, Milo journeys through the magical realms of sight, sound, and context in a quest to return the Princesses Rhyme and Reason to the land and restore peace once and for all. Facing “punny” demons, he discovers the power of knowledge and learns more about numbers and words than he ever thought important.

Uses: The Phantom Tollbooth relies heavily on speech in both the sections on words and the sections on numbers. When Milo first arrives in Digitopolis, the land of numbers, he encounters a talking Dodecahedron (who uses each of his faces to convey a different emotion) who points out the use of mathematical language in everyday speech, referencing phrases such as “high hopes” and “narrow escapes” and “wide world.” A possible activity that could employ both themes of the world in The Phantom Tollbooth could ask students to search for everyday clichés that involve mathematical vocabulary. This would connect mathematics to the world outside of school. It might also be fun for students to create characters out of geometric shapes, determining how many emotions each shape can convey, based on the number of faces it has, just like the Dodecahedron.

Another interesting episode involves Milo’s encounter with 0.58 boy. The boy explains that the average family has 2.58 children and that he is the 0.58 in his family. Milo objects that averages aren’t real, but in fact, are imaginary. The 0.58 boy argues that averages are very useful at times. Students can find such averages and statistics in the world and discuss what it would mean to be 0.58 of a person, and such.

Although not an activity, an important point of the story is that the Mathemagician’s magic wand is actually a pencil. This idea can be brought up repeatedly from time to time, having the students use their own pencils to perform magic. For example, they can make numbers disappear with the equation 4+5-9 which equals zero, an “invisible” number.

Math Curse

Authors: Jon Scieszka & Lane Smith

Recommended Grade Level: 3-5

NCTM Standards:
Number and Operations, Algebra, Measurement, & Data Analysis & Probability

Summary:
This highly amusing story is about a girl who has become the “victim of a math curse.” It all begins on Monday in math class when her teacher, Mrs. Fibonacci, says, “You know, you can think of almost everything as a math problem.” By Tuesday, EVERYTHING in the girl’s life has transformed into a mathematical problem. While getting ready in the morning, she finds herself wondering if she will make it to the bus on time. Then, while taking the milk out for her cereal she asks, “How many quarts in a gallon? How many pints in a quart?” Each page of the book is covered with these types of problems related to mathematics in everyday life. All of the problems involve number and operations, algebra, measurement, and data analysis and probability. At the end of the story, the heroine falls asleep and dreams that she is “trapped in a room with no doors and no windows and the room is covered with a lifetime of problems.” In order to finally break the math curse, the heroine uses fractions!

Suggestions for Using Book with Students:
We live in a mathematical world; it is important for students to understand connections between mathematical ideas and to recognize mathematics in contexts outside of the classroom. A teacher could read this book to students, perhaps a page at a time (as Aliyah suggested), to help them become aware of these connections. After reading the entire book, the teacher could tell students that he/she is putting a “math curse” on them and ask them to keep a journal for one day in which they record all of the mathematical problems/things that they notice in their everyday lives. To break the curse, the teacher should provide the class with a problem that they must work together to solve.
Reading this book to students would be a fun way to help students develop number sense and provide them with an opportunity to practice solving problems related to each of the content areas. After reading each page, I would have the class work together to solve the problems. I would encourage students to make use of different methods each day (e.g., mental calculations, estimation, paper-and-pencil, using manipulatives, or calculator). The answers to the problems are located on the back cover of the book.
After reading the page with the chart (a bar graph depicting the number of birthdays each month), the teacher could have the students work together to create their own class birthday chart. He/she could ask the students to identify which months have the most and the least number of birthdays.
A teacher could read the pages about fractions either before or after introducing students to fractions. Fractions seem to be a very difficult concept for many young students; this book would help to make fractions seem more tolerable! The teacher could then bring in some type of (non-allergenic) food that the class will have to figure out how to share amongst themselves (using fractions). (The teacher can hide extras behind his/her desk to make sure that everyone gets a whole piece at the end of the activity. Make sure that there is enough for everyone!)

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.

Inch by Inch

Title: Inch by Inch

Author/Illustrator: Leo Lionni

Grade Level: K-4

NCTM Content Standard: Measurement, Number and Operations

Summary: A quick read, "Inch by Inch" describes an inchworm's journey through measurement to save himself from being eaten by a robin. He measures many different things to prove his worth. At the end, the robin asks the inchworm to measure his song. Cleverly, the worm "inches" away to escape.

Recommended Use of Book: This book is a great introduction to measurement for any grade. For early elementary, students can count while reading to discover the length of the things measured in the story. Students can also make their own inchworms as an introduction to measuring objects. For later elementary, student can wrestle with the concept of measurement through questioning at the end of the story. Can a song be measured? Is length the best way of measuring song?

Alice in Wonderland

Title: Alice's Adventures in Wonderland

Author: Lewis Carroll

Illustrator: John Tenniel

Recommended Grade Level: Middle school - 6/7/8

NCTM content Standard: Measurement, Numbers and Operations, Algebra, Reasoning and Proof

Summary: The story is about a little girl, called Alice, who falls asleep under a tree and begins to dream about a journey through "Wonderland". It is in her dream that she is put in interesting situations with life like characters. Alice's reactions to these situations, combined with the nature of conversations that she engages in, provide a fascinating context for mathematical lessons.

Recommended use of book: I recommend that the book be used at the beginning of the school year to bring levity to the classroom setting. Students should be encouraged to role-play and read out aloud select sections from the book over the course of 3-4 weeks. These sections should be chosen with the purpose of introducing / reviewing relevant mathematical concepts. For example, the part where Alice responds "... four times five is twelve, and four times six is thirteen, and four times seven is-.." can be used to introduce/review the concept of alternative bases.
Throughout the course of the school year, the characters in the book can be referenced by asking students to contemplate how, for example, may Alice have responded to a question. This would allow exploration of alternative variants of mathematical concepts.
Note: Various editions of the story can be used to cater to most grade levels

Zero Is Not Nothing

Title: Zero Is Not Nothing

Authors: Mindel and Harry Sitomer

Illustrator: Richard Cuffari

Recommended Grade Level: 3-5

NCTM Content Standards: Number and Operations, Measurement

Summary:
This book discusses the importance of zero in the decimal system and its many uses. Zero is at once nothing and everything in our material world. For instance, zero can be the starting point of an event (a race or a rocket blast off) or measurement (rulers and scales). Zero can be the separation point between freezing and melting of water, or the “break-even” point to signify neither profit, nor deficit. Zero can also be used as a placeholder in place value systems.

Uses For This Book:
I would introduce this book for mid-to-late elementary kids who have trouble thinking of zero in more abstract terms. This book can be used as a launch pad for interdisciplinary activities, such as measuring frozen water with a thermometer or measuring one’s weight with a weight scale.