A Remainder of One

A Remainder of One

3.5 2
by Elinor J. Pinczes, Bonnie MacKain

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This entertaining lesson in the math concept of remainders shows Private Joe, a soldier who, when the queen bug demands her army to march in even lines, divides the marchers into more and more lines so that he won't be left out of the parade.


This entertaining lesson in the math concept of remainders shows Private Joe, a soldier who, when the queen bug demands her army to march in even lines, divides the marchers into more and more lines so that he won't be left out of the parade.

Editorial Reviews

Publishers Weekly - Publisher's Weekly
As they did in One Hundred Hungry Ants, Pinczes and MacKain apply numerical division to a practical problem-and explain it in an entertaining, visually emphatic way. Keeping to the insect theme, Pinczes introduces the ``25th Army Corps,'' a regiment of 25 beetles on parade. Their blue bug queen ``likes things tidy,'' and when the bugs march two by two, she notices that one bug brings up the rear. The unfortunate Joe has to stand aside rather than be a ``remainder''; on the days that follow, Joe tries dividing the squadron into symmetrical rows of three, then four and, finally, five, when he is at last accommodated. Rather than endorse conformity, this rhyming tale focuses on Joe's search for a solution. And lest squadron-like precision trouble readers, each big-eyed ``bug-soldier'' has a unique patterned shell. MacKain even ensures that the same beetle characters-one with a pointy nose, two wearing glasses, etc.-appear in every spread, allowing readers to play spot-the-bug. Rendered in dusty blues and pasture-green with warm yellow, red and pink accents, her linocut-style art vibrates with energy. Ages 4-8. (Mar.)
Children's Literature
A Bug Army parade seems like the right thing to do on a very hot day in this story that sets out to explain the math concept of a remainder in division. The queen bug is displeased when her army of twenty-five bugs marches by in two columns of twelve bugs each because that leaves a remainder of one. The remainder bug, Joe, is also distressed by his lack of a partner. So he sets out to arrange the Bug Army into rows and columns in such a way that he is no longer a remainder. The book is set in rhyme, which keeps the story flowing. The artwork is colorful and suggestive of whimsical woodcuts on each page. The book's rhyme and illustrations would appeal to a young child, but the math concepts are not appropriate for the same aged child. The illustrations are fun but not clear enough to aid the student old enough to be learning the concept of remainder in division. 2002 (orig. 1995), Houghton Mifflin Co, Ages 3 to 8.
— Ben Ingel
Children's Literature - Pat Simon
All Joe wants to do is to march with the other twenty-four bugs in the parade. But the squadron's lines must be even and Joe always seems to be the one left behind. Determined to march past the Queen, Joe tries again and again to arrange his bug buddies into even lines. But there's always a remainder of one. When Joe finds a solution, he marches in the parade, the proudest bug in the troop. A charming introduction to division and remainders, A Remainder of One uses poetry and vibrant illustrations to teach children a sometimes confusing concept. A good read aloud selection.
School Library Journal
PreS-Gr 3-As they did in One Hundred Hungry Ants (Houghton, 1993), Pinczes and MacKain present a mathematical concept through rhyming text and simple illustrations. Here, an army of insects is planning a parade, but each formation that the squadron comes up with for its 25 members-two lines of twelve, three of eight, four of six-leaves Joe Bug standing alone, a remainder of one. After much cogitation, Joe finally comes up with the solution: five lines of five. The rhyming has an old-fashioned tone reminiscent of Peter Newell's books. MacKain's blue bugs are large, friendly looking, and anthropomorphic. The queen has blonde curls. This will provide a fine accompaniment to a math lesson on division. Children will identify with Joe's predicament-being left out again and again-and will certainly have a clearer understanding of remainders after reading this story.-Louise L. Sherman, Anna C. Scott School, Leonia, NJ
Carolyn Phelan
From the author and illustrator of "One Hundred Hungry Ants" (1993), here's another picture book rooted in mathematics--the rhyming tale of a bug named Joe. When the 25th Army Corps of beetles proudly marches past their queen in two rows, her majesty insists that Private Joe, marching alone at the back, drop out to make the rows come out even. The next day the squadron in three rows, and the next, in four, but each day Joe is distressed to be marching alone, a remainder of one. All ends well when the bugs go marching five by five: "`Good show!' said her grace. `Your rows are divine. / We see no remainder to ruin your line.'" Using bold lines reminiscent of those in linocut prints, the colorful artwork uses visual rhythm as effectively as the verse uses meter and rhyme to punctuate the marching tempo of the text. Young children who get to know Joe's ragged regiment will understand the concept of remainders before anyone mentions long division in the classroom. With its sympathetic main character, bouncing verses, and expressive, comical illustrations, this makes an entertaining choice to read aloud.

Product Details

Houghton Mifflin Harcourt
Publication date:
Sales rank:
Product dimensions:
8.50(w) x 7.75(h) x 0.25(d)
Age Range:
5 - 8 Years

Meet the Author

Elinor Pinczes and Randall Enos have collaborated together on another book for children, My Full Moon Is Square. Ms. Pinczes is the author of several other books for young readers. She lives with her husband in Bozeman, Montana. Mr. Enos's illustrations have appeared in books, magazines, and newspapers for more than forty-five years. He lives in Easton, Connecticut, with his wife.

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