A Remainder of One


This is an activity based on the picture book A Remainder of One

Achievement Objectives
NA2-1: Use simple additive strategies with whole numbers and fractions.
Specific Learning Outcomes
  1. Students will be able to model the answer to division problems by equal sharing as a set of equal groups and a whole number remainder.
  2. Students will be able to express a division problem as an equation and explain what each number in the equation represents in relation to their model.
Description of Mathematics
  1. There are a limited number of ways that each whole number can be evenly divided by other whole numbers.
  2. If a number cannot be divided evenly by another number, then the left over amount can be expressed as a “remainder”.
Required Resource Materials
Unifix blocks or ping pong balls

Egg cartons

A Remainder of One by Elinor J. Pinczes


This activity is based on the picture book: A Remainder of One

Author: Elinor J. Pinczes
Illustrator: Bonnie MacKain
Publisher: Houghton Mifflin (1995)
ISBN: 978-0-618-25077-6

A group of 25 bugs are on the parade ground marching in front of the queen. But the problem is that this queen demands tidy rows in their marching arrays with no remainders. Poor Joe, he’s always the odd one our when they try different formations, until they try 5 rows of 5. The story illustrates the concept of remainders within the context of arrays.

Lesson Sequence:

  1. Prior to reading, revisit any learning related to arrays and how the rows always have the same number and are even. Use an egg carton to demonstrate. Set a few problems involving small or large egg cartons and packing eggs (unifix blocks or balls).
    For example: The farmer has 24 eggs. How many small cartons (6 eggs each) can be filled? How can we record that in numbers?
    24 ÷ 6 = 4
    What does each number mean? Show me with the eggs and cartons. The next day the farmer has 25 eggs. How many big cartons can be filled? What do we do with this one? How will we write that down?
  2. Share the book with your students. Discuss the title and ask them what this might mean. As you read stop at each place where the bugs are shown in their marching order and demonstrate with 25 blocks what each formation looks like. Record the division equations as you go along.
  3. After reading, review all the marching arrays the bugs used. Ask: Are there any other ways they could have marched in an array without a remainder?
  4. Ask students to spread out around the room. Say: Today we have ___ students here. How many groups of 3 can we make? Is there a remainder? Try other divisors.
  5. On another day, the class can explore the learning object Divide it Up: Kittens.

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