Exemplars
Bridge Building on
Lake Champlain
Bridges are made of trusses. Examples of Warren
Trusses are shown below:
1 Truss:
2 Trusses:
3 Trusses:
5 meters long
10 meters long
15 meters long
A new bridge is being built across the Lake Champlain
Islands.
The bridge will be 1 kilometer long.
Task Part 1: If the engineers build the bridge using
Warren Trusses, how many trusses will need to be built?
Task Part 2: How many beams (______ ) will this new
bridge require?
Exemplars
TM
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
Bridge Building on Lake Champlain
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Exemplars
Grade Level 3–5
Bridge Building on Lake Champlain
Bridges are made of trusses. Examples of Warren Trusses are shown below:
1 Truss: 5 meters long
2 Trusses: 10 meters long
3 Trusses: 15 meters long
A new bridge is being built across the Lake Champlain Islands.
The bridge will be 1 kilometer long.
Task Part 1: If the engineers build the bridge using Warren Trusses, how many trusses will
need to be built?
Task Part 2: How many beams ( __________ ) will this new bridge require?
Context
This task can be used during a unit on measurement but is most appropriately given during
a unit on patterns, functions, and algebra.
What This Task Accomplishes
To successfully complete this task, students need to be able to create and extend patterns, and
then to generalize patterns. The teacher can assess which students are able to apply this
higher level thinking skill. This task also assesses students’ ability to convert kilometers to
meters.
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
Bridge Building on Lake Champlain (cont.)
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Exemplars
What the Student Will Do
Most students will make a data chart in which to record the information presented in the
task. Students will identify, then develop a rule for the pattern. Then students will realize
that in order to go across the lake, they need 1,000 meters of trusses. They need to divide
1,000 by 5 to get the necessary 200 trusses needed. They will use the rule in the table to find
the number of beams required in 200 trusses.
Time Required for Task
This task takes 1 or 2 forty–five minute class periods.
Interdisciplinary Links
This task obviously links well to the study of bridges. A study of rivers and lakes would
work as well. There are many different types of trusses that students can be introduced to,
each having its own pattern. A book entitled Building Toothpick Bridges by Jeanne Pollard has
other ideas for teaching about bridges, and shows the different types of trusses.
Teaching Tips
To personalize this task, you may want to substitute a lake or river near you. Before giving
this task to students, they need to have many opportunities to identify visual patterns and to
make function tables or in–out machines. The book Algebra Thinking, First Experiences, by
Creative Publications has many activities for introducing this concept to students.
This task can be adapted for students who have special needs by making the number of
trusses needed a smaller number. For students who need more of a challenge, you could ask
them to compare and contrast the number of beams needed for bridges with different types
of trusses.
Suggested Materials
Most students will require paper, pencils and calculators. Some students may want to build
trusses to continue to the pattern, and toothpicks are great tools for doing this.
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
Bridge Building on Lake Champlain (cont.)
- Page 3-
Exemplars
Possible Solutions
200 trusses are needed (200 trusses x 5 meters = 1000 meters = 1 kilometer)
Benchmark Descriptors
Novice
The novice solution will be mostly incorrect. The student will not be able to find a correct
pattern, nor will the novice know what to do with the measurement aspect of the task. Little
or no math language will be used, and representations will be limited to rudimentary
drawings that do not mimic the mathematical situation presented in the task.
Apprentice
The apprentice will achieve a partially correct solution. The apprentice will either not be able
to find a pattern or will not know how to determine the number of trusses needed. The
apprentice will use accurate math language, but it will be sparse. A diagram or table will be
used, but it will lack labels and accuracy in terms of consistency.
Practitioner
The practitioner will achieve a correct solution. The practitioner will find a pattern and will
be able to generalize it to the number of trusses needed. The practitioner will correctly
determine the number of trusses needed and then the number of beams needed to cross the
lake. The practitioner will use accurate and appropriate math language throughout. Tables
and diagrams used will be accurate, labeled, and will communicate clearly.
Expert
The expert will achieve a correct solution for all parts of the problem. The expert’s solution
will be clearly communicated, and all work will be documented. The expert will use algebraic
notation to describe the generalized pattern. The expert will also make mathematically
relevant comments and observations about her/his solution.
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
Bridge Building on Lake Champlain (cont.)
- Page 4-
Exemplars
Author
Carol Amico McNair, who teaches grade 6 at the Camels Hump Middle School in
Richmond, Vermont, wrote this task. The task was piloted in Carol Amos’ grade 4 classroom
located in Sutton, Vermont.
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
Bridge Building on Lake Champlain (cont.)
- Page 5-
Exemplars
Novice
The student creates a
chart that is accurate
to the solution.
The student uses an
incorrect pattern that
will never lead to a
correct solution.
It is unclear why the
student stops at
34 trusses.
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
Bridge Building on Lake Champlain (cont.)
- Page 6-
Exemplars
Apprentice
It is unclear what
the student is
trying to do here.
The student creates a
table as an attempt to
solve the problem.
The student’s approach would
take a long time to carry out
to a correct solution.
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
The student’s work
is correct as far as
it goes.
Bridge Building on Lake Champlain (cont.)
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Exemplars
Practitioner
The student creates a
table and finds a rule
that leads to a solution.
A correct answer
is achieved.
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
Accurate math
language is used.
Bridge Building on Lake Champlain (cont.)
The student explains
his/her approach.
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Exemplars
Expert
The student
shows his/her
approach.
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
The student creates
an accurate and
appropriate table.
Bridge Building on Lake Champlain (cont.)
A correct
answer is
achieved.
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Exemplars
Expert (cont.)
The student explains
his/her reasoning.
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
Bridge Building on Lake Champlain (cont.)
- Page 10-
Exemplars
Expert (cont.)
Accurate and
appropriate notations
are used.
The student generalizes
the solution to any
number of trusses.
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
Bridge Building on Lake Champlain (cont.)
- Page 11-