Topic
Whole number operations
Background Information
Sometimes one of the most useful problem-solving
strategies is to simply use manipulatives to represent
the parts of a problem. This will help you organize
the information so that you can see the results of a
variety of actions.
For young children to truly understand the effects
of adding and subtracting whole numbers, it is
important for them to act out a problem. By moving
objects around while they are trying to solve a
problem, they develop visual images of both the data
in the problem and the solution process. By taking an
active role in finding the solution, students are more
likely to remember the process they used and be able
to use it again for solving similar problems.
In this activity, the children will be using goldfish
crackers as the manipulative to represent stories read
to them by the teacher.
Key Question
How can we use a storyboard to act out mathematical
problems?
Learning Goals
Students will:
1. use their own words to describe experiences in a
mathematical setting, and
2. use manipulatives to represent number stories.
Guiding Document
NCTM Standards 2000*
• Develop a sense of whole numbers and represent
and use them in flexible ways, including relating,
composing, and decomposing numbers
• Count with understanding and recognize “how
many” in sets of objects
• Understand the effects of adding and subtracting
whole numbers
• Build new mathematical knowledge through
problem solving
• Solve problems that arise in mathematics and in
other contexts
Management
1. The storyboard can be enlarged, colored, and
laminated for extended use. Enlarged, they are
ideal to use in a flannel board format in front of
the class. They can also be copied onto overhead
transparencies and displayed using an overhead
projector.
2. It is suggested that you use colorful goldfish
crackers as the manipulative. A page of fish has
been included for you to use as an alternative to
the goldfish crackers.
3. A second option for a manipulative is shell pasta.
Macaroni shells can be purchased in three sizes at
most local grocery stories. The pasta can be dyed
by placing it in a container with a small amount of
rubbing alcohol and a few drops of food coloring.
Stir the shells until they reach the color intensity
desired, then place them on newspaper to dry.
Math
Counting
Whole number operations
addition
subtraction
Problem solving
Integrated Processes
Observing
Comparing and contrasting
Relating
Procedure
1. Give each child a storyboard and 15-20 goldfish
in a variety of colors, or invite the students to
come to the front of the class where you have an
enlarged version.
2. Read one of the following problems aloud to your
students. Then read it again while they act it out
with the goldfish either on their boards or in front of
the class with the enlarged version. Some students
may need to listen to the story several times while
they solve the problem.
Materials
Storyboard (see Management 1)
Goldfish crackers (see Management 2)
Problem-Solving Strategies
Use manipulatives
Act out the problem
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3. Tell the students to clear their boards after they
finish each question.
4. Repeat this process with as many problems as
desired.
Connecting Learning
1. Did the storyboards help you solve problems?
Explain.
2. How did you know when to add or subtract the
goldfish?
3. How did you solve Chhay’s problem with five
goldfish where two were in the medium sized bucket
and the rest were in the small bucket? Explain.
4. How did you solve the problem with three goldfish
in the water and two more goldfish on the sand
than in the water? Explain.
Kindergarten Problems
• How many goldfish do you have? Put five goldfish
in a bucket. (Creation/Recognition of a Set)
• Put some of your goldfish in the water and leave
some on the sand. Are there more on the sand or in
the water? Tell us about you picture. (Comparison
of Sets)
• If you put six goldfish in the water and four in
the small bucket, will there be more goldfish in
the water or in the bucket? How do you know?
(Comparison of Sets)
• Five goldfish are on the sand, but fewer are in the
water. How many are on the sand and how many
in the water? (Comparison of Sets)
• Juan had two goldfish on the sand and three in
his large bucket. How many goldfish did he have
altogether? (Addition, Combining)
• Four purple goldfish are in Amy’s bucket. Amy
gives two away. How many goldfish are left in the
bucket? (Subtraction, Take-Away Model)
• Chhay had five goldfish. Two were in the medium
sized bucket. The rest were in the small bucket.
How many were in the small bucket? (Missing
Addend)
• Charlie placed four green goldfish at the bottom of
the ocean, two purple goldfish in the waves, and
three red goldfish in a bucket. How many goldfish
did he have altogether? (Addition, Combining)
Extension
Have your students create their own storyboards and
math questions to go with them.
Curriculum Correlation
Butler, Christina M. Too Many Eggs. David R. Godine
Publisher. Boston. 1988.
Crews, Donald. Ten Black Dots. Greenwillow Books.
New York. 1986.
Sis, Peter. Waving. Greenwillow Books. New York. 1988.
*
Reprinted with permission from Principles and Standards for
School Mathematics, 2000 by the National Council of Teachers
of Mathematics. All rights reserved.
First Grade Problems
You may use all of the kindergarten questions and may
increase the difficulty by adding more goldfish and
using the following set of instructions and questions:
• Makenzie has eight goldfish in her pail and
Shaketa gives her three more. How many fish
does Makenzie have? Tell us about your picture.
• Three goldfish are in the water, two more are on the
sand, and one is in a bucket. How many goldfish
are there altogether? (Addition, Combining)
• Chase has five orange goldfish in the small
bucket. Rita has seven yellow goldfish in the large
bucket. Are there more goldfish in Chase’s bucket
or in Rita’s bucket? How many more? (Subtraction,
Comparison Model)
• There were four goldfish in the water and five
goldfish on the beach. A very large wave came
on shore and washed three of the goldfish off the
beach and into the water. How many goldfish were
left on the shore? How many are now in the water?
(Subtraction, Take-away Model)
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Exploring Operations
Through Storyboards
Creation/Recognition of a Set
Given a number, the child will build a set to represent the number, or given a group of objects, the child
will count the members of the set.
Comparison of Sets
The concepts of more, less, and the same as are basic relationships that are essential to develop meaning in operations. The child should construct sets to show these relationships using manipulatives, as well as
make comparisons or choices between two given sets.
Composition/Decomposition of Sets (Part-Part-Whole)
Children either build a designated quantity in two or more parts, or they begin with a designated amount
and separate it into two or more parts.
Addition of Sets: Combining (Part-Part-Whole)
To learn what joining a set of two (a part) and a set of three (a part) means, the child must manipulate two
objects and three objects and combine to make a set of five objects (the whole).
Addition: Comparison Model
If the smaller of two sets and the difference between them are known, then addition tells how many are
in the larger set. A real-world example would be Sally saying to Patty, “I have three more pennies than you
have,” and Patty knows that she is holding two pennies. Addition tells how many Sally has.
Subtraction: Take-away Model (Whole-Part-Part)
The child creates a set of a designated amount (the whole) and is asked to take away an amount (a part)
and identify what is left (a part).
Subtraction: Comparison Model
The child creates two sets, compares them, and then identifies the difference between them.
Missing Addend (Whole-Part-Part)
The child creates a set (the whole) and must cover up or hide some of the set (a part). The child is
encouraged to “think addition,” or to answer the question: “What goes with the remaining pieces (a part) to
make the whole amount?”
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