A Remainder of One

by Elinor J. Pinczes, Bonnie Mackain (Illustrator)

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.

Genres: Mathematics, Picture Books, Childrens, Division, School, Animals, Fiction

32 pages, Paperback

First published January 2, 1985

Reviews

[Dolly · Rating 4 out of 5]

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 was a great way to help cement these concepts in our girls' brains. It's an especially effective way to teach about remainders. Our girls really liked the symmetry of the final combination, especially with the different bug colors.

The only gripe I had was a personal one. At first, when the story mentioned "squadron," I was hoping that the beetles would be aviators (they do have wings, after all.) But later on, the book mentions that they are marching infantry for the Army Corps. I looked up the word squadron and discovered that it can be used for all the different services and types of military units with either troops, aircraft or naval vessels. So the word is used appropriately; I just wanted them to be a bunch of fliers, like me.

Still, the lovely rhyming narrative and colorful woodcut illustrations worked very well together and we really enjoyed reading this book together. We will certainly look for more books by Elinor J. Pinczes at our local library.

[Tara Sheehan · Rating 3 out of 5]

"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 pattern of mostly purples, blues, and greens. The medium used seems to be some type of matte paint, with a tendency to use thick black lines to add texture to the story, which is perfect for illustrating the grass and plants. The typeface is classic bold black against white background and the illustrations are bordered. Joe eventually learns to fit in as he uses his problem-solving skills to do the math, and he is no longer considered a misfit. I think the book would be a perfect way to start a math lesson on remainders as it can give a child motivation to gradually understand a concept that can be somewhat difficult to them.

[Joanie · Rating 4 out of 5]

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 students can multiply how many ladybugs per line. Great book to have in any classroom.

[Jordan Santoro · Rating 4 out of 5]

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 conveys as well.

[Kori · Rating 5 out of 5]

This book clearly introduces the topic of remainders to children - I tried it with a 4th grade class and afterwards they could nearly all explain remainders to me.

[Tym · Rating 4 out of 5]

It’s a cute story and a good message. A couple of the passages were kinda clunky and it could have used another page after the final resolution, thus the four stars

[Edward Lee · Rating 4 out of 5]

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, perhaps he should have picked a different job and get out of their zone. The next morning, the mathematically illiterate bug tried again to get into line, this time by groups of 4 they aligned. But of course there was still one bug left out, fat ol' Joe left out and about. Low and behold on the final night, smart bug Joe finally got it right. 5 lines of 5 should hold nice and tight, and make the queens smile happy and bright. After the final page of the story ended, a tragic accident fell upon the group of soldier bugs, they were all swatted out, from under the rug. They didn't see it coming, the onslaught of sound, the great big newspaper sure made a pound. And soon Joe was dead, along with all his friends, the poor remainder of one should have just stayed in bed. Teaching tool, a simple and easy way to show kids that in dividing, what the remainder is.

[Kaycee · Rating 4 out of 5]

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 angry. The book goes through until it finds the number that the 25 bugs can march by that won't leave any remainders. This would be a great book to use in a math lesson. The children would be able to divide the numbers out with the book and solve for themselves whether the new number divided by would leave a remainder or not. The illustrations are colorful and engaging and the poor 'lone soldier Joe' has expressions that perfectly represent his feelings. All the bugs are very expressive and that helps to clue the reader into what they are feeling in a particular passage. This book would help a visual student understand concepts of division that they may not have understood just doing the math.

[Christi · Rating 5 out of 5]

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.


Critique:

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 four for the show, the lines all looked even til they spotted Joe.... As four lines of six marched so neatly away, Joe couldn't watch for he had to stay. Poor tag along Joe didn't have any fun, always left out a remainder of one."


Curriculum Connection: This book would be perfect to begin the math lesson on division.

[Sylvia Ulmer · Rating 4 out of 5]

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 future use if I need to cover CCSS.Math.Content.4.NBT.B.6 - Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

[Dannita Stanley · Rating 4 out of 5]

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 particularly recommend this book to math teachers. It's a great read aloud that can be utilized. I would also encourage students to write their own Remainder of One poetry books using a different number. That would be a great way to extend the text to your writing curriculum.

[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 not allowed to march with the other soldiers. Finally, they their group evenly and the soldier can march. This book does a great just of introducing division to younger children. Happy day for everyone.

[Helen Kumpel · Rating 5 out of 5]

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.
Reflection:
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 your groups will determine how many will be remaining or how you can make even groups without remainders.

[Ashley P. · Rating 4 out of 5]

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. . Record which formations leave remainders and ask students if any patterns/connections with multiplication were noticed..

[Ekassel]

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 each grouping, there is a picture of the lines, showing the remainder, so students can visualize the division.

[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 evenly. This book can also be used to talk about rhyming. The children can create their own poems about numbers using rhyming words.

[Rebecca Ashley Teague · Rating 5 out of 5]

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 well. For older grades, I would use this book to introduce division and why we sometimes have a remainder when we divide.

[Erica Garl]

This children's book introduces the basics of grouping and division in math. It begins with that 25th army squadron, the ants, lining up in hope to satisfy the queen. One of the little bugs, Joe, strives to impress the queen by adding more lines so that everyone, including him, fit into the lines evenly. Eventually he find how many rows are need so that he is not a remainder of one. This book is a great way to introduce that division is just grouping by certain number. I really like how this book shows the math problem in words and in the pictures. I also like the concept as children can easily relate.

[Kasmarine · Rating 5 out of 5]

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 is in at last.

[Nicole Agadoni · Rating 5 out of 5]

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 solve division and multiplication number sentences.

[Gina · Rating 3 out of 5]

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 numbers cannot be divided into even groups.

[Julia B · Rating 4 out of 5]

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.

[Christy Whitaker · Rating 5 out of 5]

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.

[Scott Roark · Rating 3 out of 5]

Shows how to introduce remainders when grouping numbers (division). Children can use similar idea by grouping and having remainders with dried beans or another manipulative. Author uses ants marching in lines to show how there is a remainder, since the rows are not even. The queen likes everything even, so they change the number of rows until they are even.

[Brittani Jordan · Rating 4 out of 5]

Poor soldier Joe. He was the only one that kept being a solo marcher because the numbers were uneven.He just wanted to march in the troop. 2 lines of 12 and 3 lines of 8 and so on. This book would be a great introduction to long division. You can also show students the remainders are not so bad. They can help you check your work too.

[Jenne · Rating 3 out of 5]

I wanted to like this and its companion more than I did, but I found the rhymes and context contrived so that the concept was lost on young readers. Tighter rhymes would likely improve upon comprehension. The illustrations may have been distracting with all the details surrounding the focal points of each picture.

[Velita · Rating 5 out of 5]

This is a cute book that explores math and remainders with children! The queen of the ants demands that her army marches in even lines, but one ant, Private Joe, keeps making the lines uneven. The ants keep being divided until Private Joe is no longer the"remainder of one" left out in the parade. This book is a great rhyming book for children!

[Leia-Catherine · Rating 5 out of 5]

It's funny that the little bugs are making a parade for the queen, and she finds Little Joe behind in the big parade. He finally makes it so he can be in the line, not a remainder of one (at the back).

[Sharon · Rating 5 out of 5]

The story of Joe explains what happens to numbers when they remain alone after division. While this story of Joe the ant is sad, it does provide students with a creative way to divide up manipulatives. This story can be incorporated with the use of hands-on lessons to teach division.

[Matthew · Rating 2 out of 5]

It's good if you are interested in reading a short introductory story about division. Otherwise, it wasn't the greatest book I've ever read. The rhyme scheme was simple, as was the story, but it worked. No complaints.