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The Mathematics Bookshelf features outstanding trade books that support mathematics instruction in K–12 classrooms. Mathematics Review Board members have selected books that will appeal to students and enrich the teaching and learning of mathematics. Each book review includes:
- a brief summary of the story
- the main mathematical ideas
- suggestions for how to use the book
- the value of the book in standards-based instruction
- standards alignment
- a list of related ORC resources
Most of these books will be available in your school library or local public library. If not, consider using the interlibrary loan program,
OhioLink, or
INFOhio
to locate and borrow the books.
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Number / Measurement / Geometry / Algebra / Data
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Counting on the Woods
Author: George Ella Lyon
Illustrator: Ann W. Olson
Standards Alignment: Grades preK - 1
This counting book uses nature as the theme. Beautiful woodsy photographs illustrate each of the counting numbers, 1 through 10. The interdisciplinary theme of the book makes it especially worthwhile for the prekindergarten and kindergarten classroom.
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The Doorbell Rang
Author: Pat Hutchins
Illustrator: Pat Hutchins
Standards Alignment: Grades 1 - 5
Mom makes a dozen cookies for her two children to share. Just as the children determine how to divide the 12 cookies evenly among themselves, they are visited by multiple friends multiple times throughout the book. The children repeatedly evenly re-divide the cookies among themselves and their friends. Just as they begin to run short on cookies, Grandma arrives with a huge platter of new cookies, and new problems to solve.
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The Grapes of Math: Mind-Stretching Math Riddles
Author: Gregory Tang
Illustrator: Harry Briggs
Standards Alignment: Grades 1 - 5
An important objective of The Grapes of Math is to prompt children to use counting strategies beyond merely counting one by one. Grouping objects in sets of 10, for example, and then adding all the 10s is a clever way to count a large number of objects. The illustrations, as well as the rhymes, challenge young learners to look for these strategies.
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How Much Is a Million?
Author: David M. Schwartz
Illustrator: Steven Kellogg
Standards Alignment: Grades 3 - 9
Let Marvelosissimo, the Mathematical Magician, guide students into the world of large numbers. They will sail past one hundred thousand stars and see towers of children reaching toward Saturn's rings as the concepts of a million, billion, and trillion are made vivid in the mind-stretching scenes illustrated by Steven Kellogg. Elementary students will delight in the pictures, and middle grades students will enjoy checking the author's numerical claims. The assumptions underlying various estimates, for example, that it would take 95 years to count to a billion, are listed in the back of the book for easy reference.
See more about how to use this book
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If You Hopped Like A Frog
Author: David M. Schwartz
Illustrator: James Warhola
Standards Alignment: Grades 5 - 9
Through illustrations as well as text, this book introduces the concepts of ratio and proportion by comparing what humans would be able to do if they had the capabilities of different animals. For example, if you ate like a shrew, you could devour more than 700 hamburgers in a day! The last pages of the book provide all the facts that validate the claims and explain how they translate into human terms. The measurements for each ratio are listed, along with questions that help students calculate the equivalent ratio for their own measurements.
See more about how to use this book
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If You Made a Million
Author: David M. Schwartz
Illustrator: Steven Kellogg
Standards Alignment: Grades 2 - 9
This children's picture book shows different forms of money, such as coins, paper money, and checks. The author starts by showing equivalent forms of cash (10 dimes is worth the same as 20 nickels is worth the same as 100 pennies). For large amounts of money, checks are more efficient, and the author explains to young readers how banks use checks to transfer money from one person to another. Savings and the earning and compounding of interest are discussed, along with borrowing and the paying of interest. This book is an engaging introduction to some fundamentals of personal finance.
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Math Fables: Lessons That Count
Author: Gregory Tang
Illustrator: Heather Cahoon
Standards Alignment: Grades preK - 3
This is the first of two Math Fables books by Greg Tang that use verse to show how groups of objects (animals) can be broken down and regrouped. The simple verses should be easy enough for children to repeat, but some of the vocabulary (procrastinate, cooperate) may be a little beyond some children ages 3-6 for whom the book is intended. Still, they will enjoy encountering these big words in such an engaging context. Each verse concludes with a real-life "moral," such as, "They learned it's wise to plan ahead and always be prepared." At the end of the book, the author lists ideas for using and extending the mathematical decomposition of numbers.
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Math For All Seasons: Mind-Stretching Math Riddles
Author: Gregory Tang
Illustrator: Harry Briggs
Standards Alignment: Grades preK - 3
This book teaches problem solving through the use of riddles, rhymes, and colorful illustrations of fanciful problems based on the four seasons. Students aged 5-8 are encouraged to think intuitively about numbers and to apply various counting strategies. There are four problem-solving techniques suggested in the riddles. The first is to be open-minded and consider many approaches. The second is to think strategically by grouping numbers in ways that make adding easier. A third approach that works for some problems is to add easy groups and then subtract off a few items to arrive at the total. A fourth technique is to look for patterns and symmetries. Suggestions for ways to solve each problem are provided at the end of the book.
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Math Potatoes: Mind-Stretching Brain Food
Author: Gregory Tang
Illustrator: Harry Briggs
Standards Alignment: Grades 1 - 5
Another in a series of mathematically related rhyming books by Greg Tang, these counting riddles involve food and other visual items engagingly illustrated by Harry Briggs. The items to be counted are laid out in patterns that allow the reader to form numerical groupings that make counting larger numbers of objects easier for many students. Solutions are given in the back of the book, but students may come up with other ways to group and count the objects, leading to some lively discussions.
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Math-terpieces: The Art of Problem-Solving
Author: Gregory Tang
Illustrator: Greg Paprocki
Standards Alignment: Grades 1 - 5
Math-terpieces uses works of art from the Impressionists to Andy Warhol to provide settings for modeling the addition of numbers. The artwork and poems provide information about the artist and the painting. Each poem ends with a challenge to the reader to find a specific number of different combinations that equal a distinct number, 7-10. Each number can be represented in several ways, using two or more addends. This book provides an excellent opportunity for children to practice composition and decomposition of numbers. The solutions are shown at the end of the book along with Art Notes about the styles of painting. What a wonderful book to introduce art appreciation into the mathematics classroom!
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On Beyond a Million: An Amazing Math Journey
Author: David M. Schwartz
Illustrator: Paul Meisel
Standards Alignment: Grades 6 - 11
This book provides a context for exploring extremely large numbers, including googol and beyond. Students involved in popping popcorn for an assembly have a popcorn machine that is out of control, and they are curious to find out the number of kernels popped. Since it is impossible to count fast enough, Professor X suggests “power counting” using powers of 10 to do the job. Many interesting facts involving large quantities emerge along the way.
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One Hundred Hungry Ants
Author: Elinor J. Pinczes
Illustrator: Bonnie MacKain
Standards Alignment: Grades 3 - 6
With "a hey and a hi dee ho," one hundred hungry ants scurry off to a picnic in search of yummies for their empty tummies. As the 100 ants move in single file formation, the littlest ant suggests that they could get there much faster if they were in more columns with fewer ants per line. The ants agree and form 2 lines of 50 and continue their journey. The littlest ant continues to prod them to go faster by increasing the number of columns. This story will prompt students to think about the various factor pairs for 100 as the ants move faster and faster toward their lunch. At last they make it to the picnic site, only to find the food is all gone! The 99 ants with "growling tummies" go off in pursuit of the littlest ant for using up too much time rearranging them!
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Quack and Count
Author: Keith Baker
Illustrator: Keith Baker
Standards Alignment: Grades preK - 2
The number 7 is broken down into all possible sums of two smaller whole numbers. Illustrations of seven baby ducks depict each sum and its reversal (2 + 5 and 5 + 2). Some of the pictures partially "hide" one or two of the ducks, and children will enjoy finding them all.
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How Much Is a Million?
Author: David M. Schwartz
Illustrator: Steven Kellogg
Standards Alignment: Grades 3 - 9
Let Marvelosissimo, the Mathematical Magician, guide students into the world of large numbers. They will sail past one hundred thousand stars and see towers of children reaching toward Saturn's rings as the concepts of a million, billion, and trillion are made vivid in the mind-stretching scenes illustrated by Steven Kellogg. Elementary students will delight in the pictures, and middle grades students will enjoy checking the author's numerical claims. The assumptions underlying various estimates, for example, that it would take 95 years to count to a billion, are listed in the back of the book for easy reference.
See more about how to use this book
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If You Hopped Like A Frog
Author: David M. Schwartz
Illustrator: James Warhola
Standards Alignment: Grades 5 - 9
Through illustrations as well as text, this book introduces the concepts of ratio and proportion by comparing what humans would be able to do if they had the capabilities of different animals. For example, if you ate like a shrew, you could devour more than 700 hamburgers in a day! The last pages of the book provide all the facts that validate the claims and explain how they translate into human terms. The measurements for each ratio are listed, along with questions that help students calculate the equivalent ratio for their own measurements.
See more about how to use this book
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Sir Cumference and the Great Knight of Angleland
Author: Cindy Neuschwander
Illustrator: Wayne Geehan
Standards Alignment: Grades 3 - 7
This story is about a young man named Radius, the son of Sir Cumference and Lady Di of Ameter, and the quest he must pursue to become a knight. He uses his family's prized possession, a medallion in the shape of a circle, to help him on his quest. He uses geometry and his knowledge of different kinds of angles to help him in his adventures.
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Sir Cumference and the First Round Table: A Math Adventure
Author: Cindy Neuschwander
Illustrator: Wayne Geehan
Standards Alignment: Grades preK - 3
Inspired by King Arthur's Knights of the Round Table, this book tells the story of how one Knight, Sir Cumference, and his wife, Lady Di of Ameter, and their son Radius overcome seating issues for the Knights. Beginning with a long rectangle, they try tables shaped like a square, a parallelogram, a triangle, an octagon, and an oval, before settling on a round table as the best solution. King Arthur is so pleased with their work that he decrees that the circumference, diameter, and radius of a circle shall be so named in honor of his worthy subjects.
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Sir Cumference and the Great Knight of Angleland
Author: Cindy Neuschwander
Illustrator: Wayne Geehan
Standards Alignment: Grades 3 - 7
This story is about a young man named Radius, the son of Sir Cumference and Lady Di of Ameter, and the quest he must pursue to become a knight. He uses his family's prized possession, a medallion in the shape of a circle, to help him on his quest. He uses geometry and his knowledge of different kinds of angles to help him in his adventures.
See more about how to use this book
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Sir Cumference and the Sword in the Cone
Author: Cindy Neuschwander
Illustrator: Wayne Geehan
Standards Alignment: Grades 5 - 9
King Arthur has issued a challenge. The first knight to find the sword Edgecalibur will be the next king. Join Sir Cumference, Lady Di of Ameter, and their son, Radius, as they race to help their friend, Vertex, find the sword. With their aid, he cuts out 2-dimensional shapes and folds them to make solid figures. He then makes a data table to explore the relationship between faces, vertices, and edges of polyhedra. The last two conditions in King Arthur's clue help Vertex unravel the mystery of the location of the sword.
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Anno's Magic Seeds
Author: Mitsumasa Anno
Illustrator: Mitsumasa Anno
Standards Alignment: Grades 2 - 8
Jack receives two beans from a wizard, eats one, and plants the other. A year later, a plant grows bearing two seeds. Over time, Jack decides to plant both seeds, and the reader sees a pattern begin to emerge. However, the situation becomes more complicated when Jack decides to plant some seeds, store some seeds, sell some, and eat some. Carefully detailed illustrations make the increasingly complex scenario understandable, though still challenging. Eventually the seeds make Jack wealthy, until a hurricane wipes away all of his plants. Fortunately, his wife has saved ten seeds and they can begin the process again.
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The King's Chessboard
Author: David Birch
Illustrator: Devis Grebu
Standards Alignment: Grades 5 - 11
A king offers to reward a wise man for his service. The wise man requests his reward to be as follows: "Tomorrow, for the first square of your chessboard, give me one grain of rice; the next day, for the second square, two grains of rice; the next day after that, four grains of rice; ... for each square give me twice the number of grains as the square before it, and so on, for every square of the chessboard." The remainder of the story illustrates how the amount of rice to be given to the wise man each day grows quickly. The king comes to realize it is impossible to meet the wise man's request and learns a valuable lesson about patterns that involve "doubling."
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Anno's Magic Seeds
Author: Mitsumasa Anno
Illustrator: Mitsumasa Anno
Standards Alignment: Grades 2 - 8
Jack receives two beans from a wizard, eats one, and plants the other. A year later, a plant grows bearing two seeds. Over time, Jack decides to plant both seeds, and the reader sees a pattern begin to emerge. However, the situation becomes more complicated when Jack decides to plant some seeds, store some seeds, sell some, and eat some. Carefully detailed illustrations make the increasingly complex scenario understandable, though still challenging. Eventually the seeds make Jack wealthy, until a hurricane wipes away all of his plants. Fortunately, his wife has saved ten seeds and they can begin the process again.
See more about how to use this book
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Sir Cumference and the Sword in the Cone
Author: Cindy Neuschwander
Illustrator: Wayne Geehan
Standards Alignment: Grades 5 - 9
King Arthur has issued a challenge. The first knight to find the sword Edgecalibur will be the next king. Join Sir Cumference, Lady Di of Ameter, and their son, Radius, as they race to help their friend, Vertex, find the sword. With their aid, he cuts out 2-dimensional shapes and folds them to make solid figures. He then makes a data table to explore the relationship between faces, vertices, and edges of polyhedra. The last two conditions in King Arthur's clue help Vertex unravel the mystery of the location of the sword.
See more about how to use this book
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