Exemplars
A Quarter From The Tooth Fairy
Your friend has just lost a tooth. The tooth
fairy always gives your buddy 25 cents each
time she loses a tooth. The tooth fairy’s piggy
bank is full of coins. Determine the ways the
tooth fairy can pay your friend.
Exemplars
TM
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
A Quarter from the tooth Fairy
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Exemplars
Grade Level 3–5
A Quarter From The Tooth Fairy
Your friend has just lost a tooth. The tooth fairy always gives your buddy 25 cents each time
she loses a tooth. The tooth fairy’s piggy bank is full of coins. Determine the ways the tooth
fairy can pay your friend.
Context
These students have been working with money and finding different combinations that equal
different sums.
What This Task Accomplishes
This task allows the teacher to determine how well students can group coins to equal a sum
of money, as well as how well they can organize their approach to find all combinations.
Time Required for Task
One class period was required (about 45 to 60 minutes).
Interdisciplinary Links
This task could link to a unit on currency. Recently, the US mint published some interesting
facts about coins:
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.
The number of coins produced in 1998 includes 10,257,508,500 pennies, 11,323,623,000
nickels, 2,335,250,000 dimes, and 1,867,380,000 quarters. As a study of number sense,
students could determine how much cash those coins equal.
The US has also started making quarters designed in honor of each state. This would be an
interesting study as students could link an investigation to US geography.
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
The Tooth Fairy (cont.)
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Exemplars
Teaching Tips
Give students play coins with which to work, allowing them numerous opportunities to
“play”. They should also practice making change before attempting this task. 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
Possible Solutions
The correct solution is that there are 13 ways:
Pennies
25
20
15
15
10
10
5
5
5
0
0
0
0
Nickels
0
1
0
2
1
3
0
2
4
5
3
1
0
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
Dimes
0
0
1
0
1
0
2
1
0
0
1
2
0
Quarters
0
0
0
0
0
0
0
0
0
0
0
0
1
The Tooth Fairy (cont.)
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Exemplars
Benchmark Descriptors
Novice
The novice may make an attempt to solve the problem but may not have a complete
understanding of what the task requires The solution documented will be vague and
difficult to understand. Little math reasoning will be present, and little math language
used.
Apprentice
The apprentice will have an approach that will work for solving the task, butwill not
reach a correct answer either due to a reasoning error, a computation error, or a lack of
organization. Some parts will be clear, but math language will be limited.
Practitioner
The practitioner will reach a correct solution that includes all combinations of 25 cents
Work will be organized so the solution will be complete. Math language will be used,
and representations will be labeled and accurate.
Expert
The expert will show a unique understanding of the task, resulting in a correct
solution. Work will be clear and labeled, showing the relationships between monetary
values. The expert will use math language throughout and will make mathematically
correct representations. The expert will also make mathematically relevant comments
about the solution.
Author
Shawn Parkhurst is a grade four teacher at the Canadian Academy in Kobe, Japan. He is on a
leave of absence from his work as a multi–age teacher at the Williston Central School in
Williston, Vermont.
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
The Tooth Fairy (cont.)
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Exemplars
Novice
The student has little
or no understanding of
the problem.
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
The Tooth Fairy (cont.)
- Page 5-
Exemplars
Apprentice
Some parts of the
solution are correct.
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
The student is unable to
find all combinations.
The Tooth Fairy (cont.)
A math representation
is attempted.
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Exemplars
Practitioner
The student achieves
all combinations.
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
The student’s solution
is organized.
The Tooth Fairy (cont.)
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Exemplars
Practitioner (cont.)
The student summarizes
the solution.
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
The Tooth Fairy (cont.)
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Exemplars
Expert
A correct answer
is achieved.
The student makes
mathematically
relevant observations.
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
The Tooth Fairy (cont.)
Accurate math
language is used.
The student’s
representation is accurate
and appropriate.
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