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.

Written and illustrated by Patricia Polacco

Recommended Grade Level: K-3

NCTM Content Standard: Numbers and Operations, Measurement, Connections

Summary: Patricia Polacco tells the story of a grandmother (Babushka) who helps her granddaughter to overcome her fear of thunderstorms. Together, grandmother and granddaughter bake a Thunder Cake. As the storm nears, they hurry to gather all of the ingredients and to get the cake into the oven before the storm hits. By the end of the story, the granddaughter has conquered her fear and the two feast on their Thunder Cake.

Uses for this book: For very young children, this book can be used as a way to learn and practice ordinal numbers (first, second, etc). Teachers can discuss the order in which Babushka and her granddaughter collected the ingredients for the Thunder Cake. For slightly older children, each student or a designated class scribe can record the ingredients being collected for the Thunder Cake as the teacher reads. Then, at the end of the story, the class can examine the recipe for Thunder Cake and go in and add amounts to the ingredients they recorded while reading. And of course, students will be thrilled if they are given the opportunity to actual bake (and eat!) a Thunder Cake. This activity will allow students to become familiar with using measurement in a real world context.

One Hundred Hungry Ants
Author: Elinor J. Pinczes
Illustrator: Bonnie Mackain
Recommended Grade Levels: K-4

NCTM Standards: Number and Operations, Algebra, Measurement

Summary:
As the title suggests the story begins with one hundred hungry ants eagerly planning on marching over to a picnic to devour the food before it is gone. At first, the ants march one after another in a long line of one hundred. However, a smart little ant begins to think of different ways the ants could march that would help them arrive at the picnic much more quickly. Throughout the book the ants change formation from one line with one hundred ants to two lines with fifty ants and eventually down to ten lines with ten ants. Unfortunately, the ants take so much time changing their formation (because they did not plan ahead) that by the time they arrive at the picnic all the food has been eaten!

Suggestions for Using this Book with Students:
The teacher could begin by reading the story to the students. Depending upon the grade level the teacher could have a wide variety of activities planned. With younger students the teacher could first discuss and document ideas students may have regarding why the ants kept changing their marching patterns. Afterwards, the teacher could line the students up one after the other (like in the beginning of the story) and time how long it takes for the whole class to reach the cafeteria. The teacher could continue to break down the class into more lines with fewer students in each line and document the time each trip to the cafeteria takes. This would enable students to see first-hand that even with more groups of students the shorter each line of students is then the quicker the students will arrive at the cafeteria.After this activity the teacher could go back to the list the students created before the activity and discuss any new ideas the students have regarding the usefulness for both the students and the ants to march in shorter lines. The marching activity would also be a great opportunity to create a graph that could contain both the time it took for each formation of students to arrive at the cafeteria and also the length of each formation's line. The teacher could then use this book to also talk about multiplication and division. With older students this book would be an especially useful starting point when discussing factoring, in particular, because it provides an in-context example of the applicability of factoring.

The Very Hungry Catperillar

Title: The Very Hungry Caterpillar

Written and Illustrated by: Eric Carle

Recommended Grade Level: Pre-k through 1st grade

NCTM Content Standard: Numbers and Operations.  This book teaches children about counting, how to represent numbers, and relationships among numbers. 

Summary: This is the story of a very hungry caterpillar who, over the course of a eight days, eats his way through a variety of foods.  Each day, the amount that he eats increases. For example, on Monday he eats one apple, on Tuesday he eats two pears, and so forth.  The caterpillar finally becomes so big and full, that he builds a cocoon for himself and rests for two whole weeks until he turns into a beautiful butterfly. 

Uses:   The teacher could give each child a pile of cards (in random order) with pictures of the different types of fruit from the story. So, for example, there would be one card with an apple, one card with two pears, one card with three plums etc. After reading the book, the students would be asked to put the cards in order from beginning to end of the story.  Another possible activity would be for the children to each make their own "Very Hungry Caterpillar" book.  The teacher could pass out the food picture cards, as well as booklets with  8 blank pages, for each day of the week from sunday to sunday. The pages would have the day of the week written at the top. The children could paste the picture cards on the corresponding pages in their booklets, and they could also draw the caterpillar on each page, as he becomes bigger and bigger.  On the last page, they could draw the beautiful butterfly! There are countless activities that can be used with this book to teach children about counting, nutrition, how caterpillars turn into butterflies, and the days of the week!

Sir Cumference and the First Round Table

Title: Sir Cumference and the First Round Table

Author: Cindy Neuschwander

Illustrator: Wayne Geehan

Grade Level: 3-6

NCTM Content Standard: Geometry

Summary: King Arthur has a problem. The long, rectangular table at which his knights meet is so long that he cannot hear what is being said at the other end. He turns to his knight, Sir Cumference, who, with the help of his wife, Lady Di of Ameter and the royal craftsman Geo of Metry, try out a series of differently shaped tables, in order to find one that works. Unfortunately, the parallelagram pokes the king in the stomach, the octagon causes fights (every knight wants his own side), and the oval leads to a big mess. It is only after being encouraged by his small son, Radius, that Sir Cumference thinks to propose a round table. This proves so successful that the king names each part of the circle in honor of the family, calling the length of the table a diameter, the outside edge a circumference, and the center to edge line a radius.

Uses: This book would serve as a very good introduction to various geometric shapes. As each shape is proposed, there is an illustrated discussion of how it is formed from the previous shape (an idea that can be played with, through the use of plastic tangrams, smaller shapes forming larger shapes). There is also a discussion of the unique features of each shape, accompanied by its name. When the circle is finally introduced at the end, the three primary features of it (diameter, radius, and circumference) are named after memorable characters in the book. Although the text does not delve into what can be done with these features of a circle, the introduction, accompanied by a specific character, will make it easier to tell each apart and avoid confusion. The ideal use for this book would be as a springboard into the larger world of geometry. It gets the vocabulary out of the way before bringing numbers into the picture.