Book title: A Remainder of One
Author: Elinor J. Pinczes
Publisher: Scholastic, Inc.
ISBN #: 0-590-12705-5
Grade levels for recommended use: Second through fourth grades
TEKS:
2.6(A): model, create, and describe contextual multiplication situations in which equivalent sets
of concrete objects are joined; and
2.6(B): model, create, and describe contextual division situations in which a set of concrete
objects is separated into equivalent sets.
Summary: During reading, students will model and discuss how to create the arrays described
in each situation. After reading, students in small groups will model, discuss, and record in math
journals possible arrays for numbers chosen randomly from a pair of dice.
Materials needed: A Remainder of One book by Elinor J. Pinczes, counting manipulatives
(beans, beads, plastic bugs, pennies, etc.) enough for each small group to have up to 60. A pair
of dice for each small group, math journals or paper to record observations
Suggested activity:
1. After teaching a lesson on arrays or basic multiplication by repeated addition, read A
Remainder of One to the class as a read-aloud. Display illustrations. As you read, ask students
for possible alternate solutions to “Joe’s” problem.
2. Put students in pairs and give each pair of students 25 of the manipulatives (to represent the
“25th Bug Squadron”).
3. Re-read A Remainder of One and pause after each formation of bugs is made to allow pairs to
recreate the arrays shown by each different formation. Allow plenty of time for students to work
together and discuss their work.
4. After the re-reading is complete, explain to student pairs that they will now be working with a
number other than 25 to see if and how many arrays can be created. Also explain that they will
be recording attempts in their math journals.
5. Have students roll 2 dice to represent the “tens” and “ones” place of their number and select
that number of manipulatives.
6. Allow time for students to make attempts at creating an array of their number. Remind them
to record attempts in math journals.
7. After the activity, have students share their results with the rest of the class.
*Extension: For numbers that could not be made into an array, have them discuss how many
more/fewer would be needed to create an even array. Ask students if there were any numbers for
which multiple arrays could be made. What other patterns did they notice?
References:
Pinczes, E. J. (1995). A Remainder of One. New York: Scholastic, Inc.
Adapted from:
Bittner, A. (2005). A remainder of one: A math manipulative lesson. Retrieved from
http://www.educationworld.com/a_tsl/archives/05-1/lesson008.shtml.
Adapted by Leah Bryars, 2012