Exemplars
Maya Temple Task
Ian Roderer constructed the model of a Maya
Temple you can see below using Legos®. He
found the picture in one of his Legos
magazines. Since we are studying the Maya, I
thought this would be a fun investigation:
Determine the number of nubs the whole
temple would be made of if it were a solid
figure.
Exemplars
TM
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
Maya Temple Task
- Page 1-
Exemplars
Grade Level 6–8
Maya Temple Task
Ian Roderer constructed the model of a Maya Temple you can see below using Legos®. He
found the picture in one of his Legos magazines. Since we are studying the Maya, I thought
this would be a fun investigation: Determine the number of nubs the whole temple would be
made of if it were a solid figure.
Context
We were studying the Maya, when a student in my class brought me a picture of the temple
above from his magazine. I asked if he could build it for us, and he agreed. Students in this
6th grade class had learned about exponents earlier in the year and had done some tasks that
used exponents as the underlying mathematics. I wrote this task to see which students could
see the application of this concept in a problem–solving situation months later.
What This Task Accomplishes
This task requires students to visualize parts of a solid that they cannot see. It also requires
students to apply the concept of area. Students who identify patterns, and notice how
exponential notation can be used, will find the solution with greater ease.
What the Student Will Do
Most students break the task into 3 parts. First, they find the area of each layer of the pyramid
and add them together. Then students find the nubs required to build the steps. Finally they
tackle the top which requires the most use of spatial sense. When they have the 3 amounts,
they add them together to get a total.
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
Maya Temple Task (cont.)
- Page 2-
Exemplars
Time Required for Task
One 45 minute period – Some students required longer.
Interdisciplinary Links
As mentioned earlier, our class was studying the Maya so this was a natural link. We had
learned about how Maya temples were symmetrical, allowing archeologists to reconstruct
them from partial ruins. Students also learned the purpose and uses of temples during the
height of the Maya civilization. The Voyage of the Mimi II is a primary resource used in this
study.
Teaching Tips
I photographed the temple for your understanding, but ideally you should have one of your
students create the temple shown. I’m sure students would be very excited to do so. The
Legos magazine is a great source of ideas for other structures that your students may want to
investigate. I would look for ones that have other important underlying mathematical
concepts or would require students to find and extend patterns.
Suggested Materials
A model of the temple
Possible Solutions
Nubs in Pyramid
For N layers,
[2 (N+6)]2 = number of nubs in the Nth layer of the pyramid
Stairs: 16 x 9 x 4 = 576
64(N-1)= numbs in stairs
Temple: 596
Total: 5620 + 576 + 596 = 6792
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
Maya Temple Task (cont.)
- Page 3-
Exemplars
Benchmark Descriptors
Novice
The novice will not understand the task enough to achieve an approach that would work.
The novice may only count the nubs that are showing and cannot visualize ones that cannot
be seen. The novice may also confuse area with perimeter. Little or no math representations,
and little or no math language will be used.
Apprentice
The apprentice will have a partially correct solution. The apprentice may be able to determine
the nubs for the pyramid but may not be able to accurately determine the stairs or the top.
Computation errors may also be the cause of incorrect answers. Some math language will be
used, and a math representation (most likely a chart) will be used to communicate the
student’s solution.
Practitioner
The practitioner will achieve a correct solution to all parts of the task. Math language will be
used throughout. Math representations will be accurate and appropriate, and it will be clear
how the student achieved the solution.
Expert
The expert will achieve a correct solution to all parts of the task. Math language will include
exponential notation. Math representations will be accurate and appropriate and will
probably include a chart or a graph that shows the exponential growth. The expert may use a
rule to solve the problem and may make other mathematically relevant comments or
observations.
Author
Carol McNair teaches grade 6 at the Camels Hump Middle School in Richmond, Vermont.
She has a master’s degree from the University of Vermont in curriculum and instruction. She
has worked as the mathematics assessment consultant for the Vermont Department of
Education’s Portfolio assessment program, and acts as a consultant to school districts and to
publishing companies. She is also an associate editor for Exemplars.
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
Maya Temple Task (cont.)
- Page 4-
Exemplars
Novice
The total makes
no sense.
Little or no math
language is used.
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
A representation
is attempted.
Maya Temple Task (cont.)
It is not clear how the
student got these answers.
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Exemplars
Apprentice
The student’s work is
somewhat organized.
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
Some work is
correct.
Maya Temple Task (cont.)
The student has an approach
for part of the problem.
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Exemplars
Practitioner
The student’s approach
and reasoning are
explained.
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
Maya Temple Task (cont.)
- Page 7-
Exemplars
Practitioner (cont.)
This rule is
incorrect.
The student achieves
a correct solution.
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
The chart is organized
and labeled.
Maya Temple Task (cont.)
The student sees the
application of exponents.
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Exemplars
Practitioner (cont.)
The diagram helps communicate
the student’s solution.
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
Maya Temple Task (cont.)
- Page 9-
Exemplars
Expert
The student shows how the rule
can be generalized by applying it
to more than one other case.
The student finds a rule for getting
the number of nubs per layer of the
temple’s pyramid base.
The student creates an
accurate and labeled table.
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
Exponential notation
is used accurately.
Maya Temple Task (cont.)
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Exemplars
Expert (cont.)
All work is
shown.
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
A correct answer
is achieved.
Maya Temple Task (cont.)
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