Exemplars
Nine Cents
Kevin told Beth and Lisa that he had nine
cents in his pocket. Beth said he must have
five coins in his pocket. Lisa said he must have
nine coins in his pocket. Kevin said that both
of them could be correct. How could Beth and
Lisa both be right?
Exemplars
TM
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
Nine Cents
- Page 1-
Exemplars
Grade Level K–2
Nine Cents
Kevin told Beth and Lisa that he had nine cents in his pocket. Beth said he must have five
coins in his pocket. Lisa said he must have nine coins in his pocket. Kevin said that both of
them could be correct. How could Beth and Lisa both be right?
Context
This task was given to a group of first graders in October. The teacher wanted to assess
student knowledge of the value of pennies and nickels.
What This Task Accomplishes
This task allows the teacher to assess which students understand that the same sum can be
achieved with different addends. It also assesses students’ concepts of coins.
Time Required for Task
One 45 minute period.
Interdisciplinary Links
Recently the US mint published some interesting facts about pennies: the US Mint has
produced over 312 billion pennies over the last 30 years, but 198 billion have dropped from
circulation. They are probably stashed away in penny jars, or hidden in car ashtrays, etc. This
leaves 114 billion pennies in circulation, or more than 426 pennies for every man, woman,
and child in the nation. It would be fun to have students investigate the number of pennies
they have stashed at home.
A 3–5 task that would present more of a challenge to students using similar mathematics is A
Quarter From The Tooth Fairy also featured on Best of Math Exemplars II.
Children’s literature that links to this task includes Benny’s Pennies by Pat Brisson, and Two
Ways to Count to Ten by Ruby Dee.
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
Nine Cents (cont.)
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Exemplars
Teaching Tips
Give students play coins with which to work, allowing them numerous opportunities to
“play.” Marilyn Burns has some wonderful teaching activities that can be used before giving
students this task, better preparing them for success.
Suggested Materials
Play money, although none of the students who piloted this task chose to use it.
Possible Solutions
9 cents can be made with 9 coins using all pennies. It can also be made using 5 coins: a nickel
and 4 pennies.
Benchmark Descriptors
Novice
The novice will demonstrate little or no understanding of the task. The student may not
show understandiing of the concept of "nine" or may not have a concept of coins and
their value. Little or no math language will be used, although the student may attempt
to create some sort of diagram for a solution.
Apprentice
The apprentice will show understanding of part of the task. S/he may understand that 9
cents can be made with 9 pennies but may not know another way to represent 9 cents.
Some math language may be used to communicate the solution.
Practitioner
The practitioner will have a correct solution. S/he will demonstrate understandiing of
the value of pennies and nickels. Math language and representations will be used to
communicate the solution.
Expert
The expert will show/explain mathematical reasoning used in solving thetask and
achieving a correct solution. All work will be shown, and accurate math language will
be used throughout. The expert will also make mathematically relevant comments
about the solution.
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
Nine Cents (cont.)
- Page 3-
Exemplars
Author
This task was written by Deb Armitage, K–8 Mathematics Assessment Consultant at the
Vermont Department of Education. The task was piloted by teachers and students in
Vermont.
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
Nine Cents (cont.)
- Page 4-
Exemplars
Novice
Little or no understanding of
the task is demonstrated.
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
Nine Cents (cont.)
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Exemplars
Novice (cont.)
Some language of money is
used, but there is little evidence
of understanding the task.
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
Nine Cents (cont.)
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Exemplars
Apprentice
The student is able to attempt
part of the task correctly, but
is unable to proceed.
It is unclear whether the
student understands the
term “coin”.
Some language of
money is used.
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
Nine Cents (cont.)
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Exemplars
Practitioner
The student uses money
notation correctly but
does not name the coins.
The student is able to visually
discriminate between the
coins and their value.
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
A correct answer
is achieved.
Nine Cents (cont.)
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Exemplars
Practitioner (cont.)
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
Nine Cents (cont.)
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Exemplars
Expert
All work is
shown.
A correct answer
is achieved.
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
Accurate math language
is used throughout.
Nine Cents (cont.)
The student makes
mathematically relevant
observations about the solution.
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