A Broken Gumball Machine
Something was wrong with the gumball machine at the
shopping mall. If you put in 1 penny and then turned the knob,
you got 3 gumballs. If you put 2 pennies and then turned the
knob, you got 5 gumballs. If you put 3 pennies and then turned
the knob, you got 7 gumballs. If you put in 4 pennies and then
turned the knob, you got 9 gumballs.
If John put 5 pennies in the machine and then turned the knob,
how many gumballs would he get if this pattern continued? If
Joyce puts in 10 pennies and then turns the knob, how many
gumballs will she get?
Bonus
If you put in a dollar in pennies and then turned the knob, how
many gumballs would you get?
A Broken Gumball Machine
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A Broken Gumball Machine
Suggested Grade Span
3–5
Grade(s) in Which Task Was Piloted
3 and 4
Task
Something was wrong with the gumball machine at the shopping mall. If you put in 1 penny and
then turned the knob, you got 3 gumballs. If you put 2 pennies and then turned the knob, you
got 5 gumballs. If you put 3 pennies and then turned the knob, you got 7 gumballs. If you put in
4 pennies and then turned the knob, you got 9 gumballs.
If John put 5 pennies in the machine and then turned the knob, how many gumballs would he
get if this pattern continued? If Joyce puts in 10 pennies and then turns the knob, how many
gumballs will she get?
Bonus
If you put in a dollar in pennies and then turned the knob, how many gumballs would you get?
Alternative Versions of Task
More Accessible Version:
Something was wrong with the gumball machine at the shopping mall. If you put in 1 penny and
then turned the knob, you got 2 gumballs. If you put 2 pennies and then turned the knob, you
got 3 gumballs. If you put 3 pennies and then turned the knob, you got 4 gumballs.
If John put 5 pennies in the machine and then turned the knob, how many gumballs would he
get if this pattern continued? If Joyce puts in 10 pennies and then turns the knob, how many
gumballs will she get?
Bonus
If you put in a dollar in pennies and then turned the knob, how many gumballs would you get?
More Challenging Version:
Something was wrong with the gumball machine at the shopping mall. If you put in 1 penny and
then turned the knob, you got 2 gumballs. If you put 2 pennies and then turned the knob, you
A Broken Gumball Machine
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got 5 gumballs. If you put 3 pennies and then turned the knob, you got 8 gumballs. If you put in
4 pennies and then turned the knob, you got 11 gumballs.
If John put 5 pennies in the machine and then turned the knob, how many gumballs would he
get if this pattern continued? If Joyce puts in 10 pennies and then turns the knob, how many
gumballs will she get?
Bonus
If you put in a dollar in pennies and then turned the knob, how many gumballs would you get?
NCTM Content Standards and Evidence
Algebra Standard for Grades 3–5: Instructional programs from pre-kindergarten through grade
12 should enable students to ...
Understand patterns, relations and functions.
• NCTM Evidence: Describe, extend and make generalizations about geometric and
numeric patterns.
• Exemplars Task-Specific Evidence: This task requires students to continue a pattern to
find the number of gumballs that a student will get when she puts in 10 pennies.
Time/Context/Qualifiers/Tip(s) From Piloting Teacher
This task was piloted in grades three and four. It took one 45-minute class period.
This task allows the teacher to assess students’ abilities to identify and extend patterns in a
problem-solving situation. To make this task more or less complicated, you can change the
pattern. After students solve the task, you can show them how they can create a rule for solving
the problem for any number of pennies. Students can also analyze how to get the most gum for
their money from this broken machine.
Links
Many teachers do a menu of activities with bubble gum. Project AIMS has many bubble gum
activities, such as determining the number of grams of sugar in each piece of gum by weighing
the gum before and after chewing. Another Exemplars task that involves the theme of gum is
"Gum-dilly-icious."
Common Strategies Used to Solve This Task
Students will create a table to find the pattern and number of gumballs. Some students may
require manipulatives to represent pennies and/or gumballs.
A Broken Gumball Machine
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Possible Solutions
Pennies
Gumballs
1
3
2
5
3
7
4
9
5
11
10
21
100
201
x
2x + 1
More Accessible Version Solution:
Five pennies would be six gumballs. Ten pennies would be 11 gumballs. One dollar would be
101 gumballs.
Pattern is p + 1 = g where p is number of pennies and g is number of gumballs.
More Challenging Version Solution:
Five pennies would be 14 gumballs. 10 pennies would be 29 gumballs. One dollar would be
299 gumballs.
p x 3 – 1 = g where p is the number of pennies and g is the number of gumballs.
Task-Specific Assessment Notes
Novice
The Novice will not be able to proceed toward a solution. Representations may be attempted,
but little or no math language will be used.
Apprentice
The Apprentice will achieve a partial solution, but all parts of the task will not be attempted or
will be attempted unsuccessfully. Representations will be used to organize the solution, but little
math language will be used.
Practitioner
The Practitioner will have an approach that works and achieves a correct solution for both parts
of the task. Math language will be used to communicate, and representations will be used to
organize the solution.
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Expert
The Expert will have an approach that works and achieves a correct solution for both parts of
the task and for the bonus. Sophisticated math language will be used to communicate, and
representations will be used to organize the solution. The Expert will find a rule for solving the
problem for any number of pennies.
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Novice
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Apprentice
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Practitioner
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Expert
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