Exemplars
Starring the Washington Monument!
Robert and his father were looking at pictures of the
Washington Monument and noticed that it was
surrounded by one flag for each state in the United States.
Robert and his father got into a discussion about how many
stars there are in all if you combine all the stars on the flags.
Robert said that one flag had 50 stars, and commented that
two flags would have 100 stars.
Determine the number of stars there are in all on the flags
surrounding the Washington Monument.
Find a rule for determining the number of stars on any
number of flags.
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
Starring the Washington Monument!
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Exemplars
Grade Level 3–5
Starring the Washington Monument!
Robert and his father were looking at pictures of the Washington Monument and noticed that
it was surrounded by one flag for each state in the United States.
Robert and his father got into a discussion about how many stars there are in all if you
combine all the stars on the flags.
Robert said that one flag had 50 stars, and commented that two flags would have 100 stars.
Determine the number of stars there are in all on the flags surrounding the Washington
Monument.
Find a rule for determining the number of stars on any number of flags.
Context
This task would be a good task to give at the beginning of the school year to obtain
pre–assessment information.
What the Task Accomplishes
This problem can be given as a pre–assessment of students’ multiplication concepts and
skills, allowing the teacher to identify the students’ strategies for solving multiplication tasks.
The teacher can determine which students use repeated addition, manipulatives, or have
some command of multiplication. The teacher can also determine student strategies for
multiplying numbers with zeros in the ones place.
Time Required for Task
Less than 1 hour.
Interdisciplinary Links
The most logical link is to geography and the study of the United States. This problem could
have been changed to reflect a thematic study on regions of the United States. The task could
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
Washington Monument! (cont.)
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Exemplars
also link to studies of the US government or studies of Washington, DC. Another good
connection for this problem could be in the study of history and that of Betsy Ross; the
creator of the American Flag.
Teaching Tips
The students will almost immediately begin this problem by setting up a table or chart. We
have done a lot of work with in/out and function machines so this was a natural for them.
This really helped many of the children to see the problem and pattern. A good number of the
children weren’t sure about the number of states, and many went to maps and atlases and
began counting. The students didn’t take very long to see the pattern once they got started.
To make the problem more challenging, you could give the students the measurements of the
length and width of the stripes (both short and long ones) and ask them to determine the
total number of yards of red and white fabric needed for making the stripes on of the flags
surrounding the Washington Monument.
For students who need a more simple problem, the following could be used: On Memorial
Day, the cemetery was full of flags. As Robert and his father were walking, they saw that each
flag had 6 white stripes. Then Robert noticed that 12 flags had 12 white stripes. Determine the
number of white stripes Robert would see if he noticed 20 flags. What if he saw 50 flags? Can
you see a pattern?
Suggested Materials
Maps, atlases, CD-ROM atlas programs, PC Globe or PC Atlas, cutouts of flags (for some
students), pictures of the Washington Monument so that visualizing the problem can occur,
(calculators are optional if this is a pre–assessment of multiplication concepts, you may ask
that students not use a calculator).
Possible Solutions
Depending on the student’s count of the states:
50 states; the answer would be 2500
52 states; the answer would be 2600
The pattern that the students should have identified is n x 50
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
Washington Monument! (cont.)
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Exemplars
Some students may say that if 2 flags have 100 stars, then you only need to multiply 25 (or
26) by 100. Students may use a variety of strategies for multiplying 50 by 50.
Benchmark Descriptors
Novice
The novice will show limited understanding of the problem, and will lack communication
skills. The novice will have weak organization, and the novice’s use of math language will be
limited. Representations may not connect to the problem or to the student’s solution.
Apprentice
Apprentices will show some understanding of the problem. They will create math
representations or use some math language to communicate the solution. The solution will be
incorrect either due to computation errors or lack of understanding of the problem. The
explanation of how the student approached the problem will be weak, and labels will be
missing from the work.
Practitioner
The practitioner will show a clear understanding of the problem and an ability to see the
pattern. The practitioner may be able to use some algebraic notation accurately to show the
pattern seen, but this is not required. The math representations are accurate for the task and
are clearly labeled throughout. The explanations are clear, but they could use a few more
details in regard to reasoning behind decisions. Math language is used consistently.
Expert
The expert will understand the problem, solve the problem efficiently, and clearly state the
pattern. The expert will go above and beyond the problem by making mathematically relevant comments or observations, such as noticing the number of stripes. Math language will
be sophisticated, and will probably include algebraic notation.
Author
Shawn Parkhurst was a multi–age third and fourth grade teacher at Williston Central School
in Williston, Vermont. He is currently on leave teaching overseas in Japan.
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
Washington Monument! (cont.)
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Exemplars
Novice
The student uses
some math
language.
It is unclear why the
student does this
calculation.
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
Washington Monument! (cont.)
The student shows no
reference to the number
of states or flags.
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Exemplars
Apprentice
Little or no math
language is used.
The representation
is labeled and
accurate.
There are some gaps in the
student’s documentation of
what was done and why.
The student makes a
computation error.
The student obtains a solution for
only part of the problem.
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
Washington Monument! (cont.)
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Exemplars
Practitioner
The chart is
labeled and
accurate.
The student explains
his/her approach.
The student obtains a rule for
finding any number of flags.
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
Washington Monument! (cont.)
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Exemplars
Expert
Chart is labeled
and accurate.
The student gets a
correct answer.
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
Student finds a rule for any
number of flags.
Washington Monument! (cont.)
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Exemplars
Expert (cont.)
The student extends
her/his solution by
finding number of
stripes.
The student makes
a mathematical
observation.
Math computation
is accurate.
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
Washington Monument! (cont.)
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Exemplars
Expert (cont.)
Student uses solution to learn
more about multiplication
properties.
The student experiments
to find third situation and
reaches a conclusion.
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
Washington Monument! (cont.)
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