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A Remainder of One
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A Remainder of One

4.04 of 5 stars 4.04  ·  rating details  ·  312 ratings  ·  95 reviews
When the queen of her bugs demands that her army march in even lines, Private Joe divides the marchers into more and more lines so that he will not be left out of the parade.
Paperback, 32 pages
Published August 26th 2002 by HMH Books for Young Readers (first published January 2nd 1985)
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May 07, 2012 Dolly rated it 4 of 5 stars  ·  review of another edition
Recommends it for: parents reading with their children
This is a fun book with a math lesson about groups of different numbers woven into the tale. I love that the little beetle tries several different combinations of groups to find one that will allow him to join the formation. After three failed attempts, Joe did not give up, which by itself is a terrific lesson on perseverence and pushing on despite failure.

We discussed the mathematical principles and the division and multiplication properties of each combination that he tried and I think this w
Tara Sheehan
"A Remainder of One" is a story about a bug named Joe who is struggling to fit in with the marching infantry. He is constantly the remainder or odd one out of the crowd, which the queen does not fit. The book is more squared shaped than other picturebooks, and has bright yellow endpages to represent the vibrant determination of Joe. The book jacket features a short description of the bug Joe and the problems he encounters in the storyline. The illustrations blend well together as they are a patt ...more
I used this book in my third grade placement for my lesson on division with remainders. It was the very first time students were introduced to this concept and this book really helped to engage students prior to the lesson. I actually incorporated the book in my lesson and had students mimic the story by dividing the unifix cubes "ladybugs" and make a straight line; any unifix cubes that made the line uneven became remainder Joe. An alternative can be to use this book for multiplication and stud ...more
Jordan Santoro
This colorful and fun children's book is a creative way to look at a math concept: remainders. The cover is very colorful and the typeface is unique. The end pages are bright yellow which correspond with and represent the lightheartedness of this book. The text and the vibrant, bordered illustrations compliment each other nicely and effectively. Children will probably enjoy the fact that the story rhymes and has a nice flow to it, and hopefully also understand the educational message this story ...more
Edward Lee
Joe the ladybug goes out to find out the real meaning of remainders; a soldier for the queen, his group paired into two, except for Joe, because he smelled of poo. The queen was disappointed by the odd number of troopers, so she kicked Joe out, and so he was sent packing out and about. He had become the remainder, a remainder of one, which for Joe couldn't have been much fun. Joe tried to get into line again, now in forms of 3 but no line was free. And again that night Joe was left alone, perhap ...more
Dannita Stanley
A Remainder of One is a cute story that is great for teaching students about division and a remainder. The author did a wonderful job of laboring the point by giving several examples of having a remainder. The different splits of the number 25 shown through the division of the ants is the most powerful aspect of this book. I think the different visuals will make the most meaning for students who have trouble understanding what a remainder is.

I would recommend this book to others. I would partic
Genre: Concept Book - Math

Age: 3rd-5th grade

Summary: The 25th infantry marches in rows past the queen, but poor Joe never fits in. The bugs keep trying different arrangements until Joe is no longer a remainder.

Curriculum Connection: This book helps teach division and remainders.

Personal Reaction: I liked the way the book rhymed and how the bugs kept trying to find a way for Joe to fit in. It would be fun to use with a class, so that they could guess what was coming next.

Visual Appeal: With eac
Samantha Fate
This is a cute book but once I read it I instantly disliked the queen. Why should she care if there is a remainder of one. The book overall gives a great lesson on division. Similar to "One Hundred Hungry Ants." The illustrations are very well done and depict how it would look like to be as small as these little characters. As for the math part of the book, it does a great job at showing how one number does not divide evenly every time. It is actually sad seeing how upset the ant gets when he is ...more
Julian Franklin
Joe wants to March in the parade for the Queen, but the queen wants even rows, no remainders! Joe spends the book trying to figure out how many rows the army needs so that every one in the 25 ant infantry can march!I would use this book to teach about remainders and grouping. This book can serve as a good way to introduce division/ multiplication. It teaches that some numbers cannot be divided into even groups by other numbers. It's a great way to get students thinking about how to group numbers ...more
Rebecca Ashley Teague
A Remainder of One tells the story of 25 bugs in an army who are trying to arrange themselves into even lines for the queen. Each day they try to divide themselves into a different amount of even lines, but Joe was always the remainder when dividing into 2, 3, and 4 lines. Finally, the bugs divide into 5 lines and Joe is no longer left out. This book contains rhyming throughout the story. This would be a great book to not only introduce a math concept, but to incorporate and reinforce rhyming as ...more
A Remainder of one tells a story about a queen that wants her army of 25 to march in even lines. In addition, Private Joe divides the marchers into more and more until he is not left out of the parade. This text introduces division and what works until the number is even. For a math lesson, I can implement regrouping and remainders. Throughout the entire book Private Joe tries to find a solution until he is not the remainder of one; he starts by grouping by 1, 2, 3, 4, etc. It teaches that all n ...more
A Remainder of One is a book written all in rhyming verse that introduces some difficult math concepts. This book is a visual representation of division that shows when it doesn't divide out perfectly and there is a remainder. In this book there are 25 marching soldier bugs marching for the queen and they divide into lines of 2 but there's a remainder of 1 bug marching behind and the queen gets angry. So the bugs divide by 3 the next day, but there is still a remainder of 1 and the queen is even ...more
Sylvia Ulmer
I did not end up reading this with my class because we were already starting on decimal quotients (I decided against breaking up "Remainder Joe" into ten equal pieces and distributing him evenly to each line). I think this is a great way to build a basic understanding of divisibility. I like how the ants line up in rectangle formation because it's easy to relate the picture to rectangular arrays in multiplication. I also appreciate that it is written in verse! It is definitely set aside for futu ...more
Theresa Stadt
There seems to be a theme in some children's math stories that I don't think we have to endure in adult books. They try so hard to motivate the child. They don't trust the material will be interesting in itself, so they use gimmicks or bribery; in this case, a distractingly strong emotional plot. I like math story books that quietly bring the concept to life and allow us to make associations and see relevance in our lives. Really enjoyed the illustrations, though.
Genre: Counting picture book

Summary: This is a rhyming story about ants trying to march to a picnic but they are having trouble trying to get their marching lines into even rows, without the left out remainder of one.


A. Math concepts, division
B. This catchy, rhyming story introduces division in a more concrete way so children can grasp the concept. One of the first stages in teaching division is grouping just like the ants grouped into rows to march.
C. "The troupe had divided by fou
One small soldier ant keeps being left out of the parade for the queen because he's always odd man out. He keeps trying to figure out how to divide the troops evenly so that he won't be left out. Night after night he thinks he's figured it out, but every day he's odd man out again.
Megan Brooks
A Remainder of One is a perfect book to introduce multiple and dividion. The also offers rhyme. It is about a colony of ants trying to impress the queen with prefect marches.
Jo Oehrlein
We ready this so many times when my daughter was little, almost always acting it out with manipulatives.

Love the way it shows divisibility.
Ashley P.
This book tells the story of a bug parade of 25 bugs. When the parade is divided into lines of 2, 3, 4, etc., Joe, a beetle, always seems to be the "remainder of one. Finally, the parade troops divide evenly when 5 is used. I like this book b/c it shows students a way division might be used otside of school. THe concept of dividing is presented in a very informal, non-alogrithm-ized way. After reading you could have students divide a set number of beans into parade lines of 2,3, 4,5, 6, etc. . R ...more
Helen Kumpel
Who this book would be for: 2-5
Activity: Read book and then reread while students use manipulatives to show how the ant was unable to fit into the group. Once the groups of ants were divided evenly the ant was no longer a remainder.
This book is a great example of how a large group can be divided into smaller groups and sometimes in order to create equal groups there may be remainders. Using manipulatives with your students will help them understand that depending on how you separate y
Nicole Agadoni
A Remainder of One features a bug named Joe who is constantly struggling to fit in with the marching infantry. He is always the odd one out, or the remainder, which does not please the queen. This is obviously a great book to introduce division, especially for students who learn best with visual examples. I also love the idea of incorporating literacy and math. After reading the book, the students could create their own infantries with plastic bugs or manipulatives, and use them to form and solv ...more
A Remainder of One is a children fiction picture book that helps teach about counting, division, remainder, rhyming, overcoming the emotion of left-out, sadness, loneliness,and disappointment. The Queen of bugs wants that her infantry march in even line. Well, poor Joe wants to be in the march, but he It is about every time the lines are uneven and he has to stand aside. This makes him sad and determines to study the problem and rearranges the 25 bugs in his squadron in five lines of five - Joe ...more
Genny Flett
In this book, there are 25 soldiers (bugs) marching for the queen. The are trying to form marching lines so they first divide into lines of 2 but that doesn't work. There is a remainder of one and that makes the queen angry. So, the bugs divide by 3 the next day, but there is still a remainder, making the queen angry. The book goes through consecutive numbers until the soliders are able to make equal lines with no bug left out.

A great book for talking about division with remainders.
Kalisha Mohammed
After reading A Remainder of One, I will give each student twenty-five plastic bugs. The students will work individually.I will then reread A Remainder of One. While the story is being reread, the students are going to use the plastic bugs to model the formation of the bug squadron. They will recreate each bug squadron from the story. I will pause following each bug squadron formation to assure that all students are participating and correctly modeling the formations.
Raenie Brown
What a fun way to teach division! I would have never though a story in a picture book could solidify learning division. I feel by doing this you can create a better understanding of the concept to students. I would say that it would be good to have previous knowledge of division concepts before reading this book just because someone too young might not understand how it's all working. The story follows a colony of Ants who's queen wants her army to mark in equal/ even lines.
Julia B
This book is a great way of introducing the concept of remainders in a concrete way to students. Besides doing a Read Aloud, this book could be used a as a center. Students can count out materials and divide them into sets of 2, 3, 4, etc. They could then determine the remainders in the different division sentences and then write the sentences out. On the whole I really enjoyed this book and I'm excited to turn it into an instructional activity in the classroom.
A Remainder of One by Elinor Pinczes is about an army of bugs that want to assemble their lines evenly for the queen, but there is always a bug (Joe) that makes the line uneven and he is deemed remainder Joe. This book is great for a lesson on introducing division and remainders with the students in third grade. Students could be given unifix cubes, beans, or other types of manipulatives to model the army of bugs and the remainder joe along with the book.
Christy Whitaker
Joe the beetle is meant to teach students how and why we have remainders when dividing. One bug is left when the 25th squadron breaks off into pairs, then sets of three, and sets of 4 (always leaving a remainder of 1). Finally, when breaking off into sets of five, every bug is included. This book is excellent for introducing dividing and remainders in a classroom. For an added bonus, the book is written in rhymes- which seems to be a favorite in all grades.
Lauren Owens
This is a cute story that illustrates what happened to the bug who was always the odd one out because the team could not divide evenly without excluding him until the end of the book. It introduces the multiplication concept of arrays, odds and evens, and dividing. This book could lend itself into a discussion about what to do with remainders and what remainders mean.
Recommended grade levels: 3-5
Chloe Jackson
A Remainder of One is a story about an ant named Joe who wants to march in the Queen's but he cannot be in the parade whenever the lines are uneven. The ants have to work together and divide themselves evenly to see how many rows they can make and if they will have a remainder or not. I would introduce this lesson/book to third grade students because it allows the students to use their prior knowledge.
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