Gum-dilly

Exemplars
Gum-dilly-icious!
You have each been given packages of the
following gums:
Bubblicious
Trident Bubble Gum
Big Red
Conduct an investigation to determine which
has the least packaging in relation to the gum
it contains.
Exemplars
TM
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
Gum-dilly-icious!
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Exemplars
Grade Level 6–8
Gum–dilly–icious!
You have each been given packages of the following gums:
Bubblicious
Trident Bubble Gum
Big Red
Conduct an investigation to determine which has the least packaging in relation to the gum it
contains.
Context
This task was given to 6th grade students who were studying fractions, decimals and
percents. Students were very motivated to solve the task, as they were promised they could
keep the gum once they completed the task.
What This Task Accomplishes
This task allows students to apply skills in measurement to a problem-solving situation. It
also requires students to apply concepts of fractions, decimals, percents, ratios and
proportions.
Time Required for Task
This task takes approximately three 45 minute class periods to complete.
Interdisciplinary Links
This task can be linked to a study of consumerism, environmental issues, and truth in
packaging. Students were very amazed at the differences in wrapping materials between the
3 types of gum. Students could choose their own products to compare such as juice boxes,
potato chips, or medications.
There are 2 fun web sites that students can access to find all they want to know about gum.
The Wrigley Company even has part of its web site dedicated to the environment!
www.wrigley.com
www.nacgm.org (The National Association of Chewing Gum Manufacturers)
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
Gum-dilly-icious! (cont.)
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Exemplars
Teaching Tips
When presenting the task, I made several different measuring tools available to students so as
not to guide their decision making. Some students chose to compare weights, while others
chose to compare volume. It was important for students to think about the difference between
surface area and volume when choosing to use linear measurements.
I purchased the gum at a discount food warehouse in bulk so it was not that expensive.
Students were very motivated by gum, but also enjoyed having a real object to measure,
manipulate and compare.
Suggested Materials
Triple beam balances, rulers (metric and standard), measuring tapes, graph paper,
spreadsheet and computer graphing programs.
Possible Solutions
Big Red Mass
Mass of gum
Mass of wrapper
16.5 grams
3.1 grams
Ratio of wrapper to gum
Ratio of wrapper to whole package
Big Red Volume
Dimensions of gum
3.1/16.5 = 18.787878788 = 19%
3.1/19.6 = 15.816326531 = 16%
7.2 x 1.9 x .2 x 5 = 13.68 cm3
Dimensions of wrapper
Outside wrapper
Aluminum wrappers
Red paper wrappers
Total Wrapper
7.8 x 9.6 x .01 = 0.7488 cm3
4.7 x 8.9 x .01 x 5 = 2.0915 cm3
6.6 x 5.2 x .01 x 5 = 1.716 cm3
4.5563 cm3
Ratio of wrapper to gum
4.5563/13.68 = 33.30628655 = 33%
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
Gum-dilly-icious! (cont.)
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Exemplars
Bubblicious Mass
Mass of gum
Mass of wrapper
39.7 grams
1.9 grams
Ratio of wrapper to gum
Ratio of wrapper to whole package
Bubblicious Volume
Dimensions of gum
1.9/39.7 = 4.7858942065 = 5%
1.9/41.6 = .693877551 = 1%
2.2 x 1.9 x 1.2 x 5 = 25.08 cm3
Dimensions of wrapper
Outside wrapper
Individual wrappers
Total Wrapper
12.3 x 9 x .01 = 1.107 cm3
7.1 x 5 x .01 x 5 = 1.755 cm3
2.862 cm3
Ratio of wrapper to gum
2.862/25.08 = 11.411483254 = 11%
Trident Mass
Mass of gum 9.1 grams
Mass of wrapper 1.5 grams
Ratio of wrapper to gum
Ratio of wrapper to whole package
Trident Volume
Dimensions of gum
1.5/9.1 = 16.483516484 = 16%
1.5/10.6 = 14.150943396 = 14%
3.2 x 1.3 x .3 x 5 = 6.24 cm3
Dimensions of wrapper
Outside wrapper
Paper wrappers
Small wrappers
Total Wrapper
8.7 x 9.4 x .01 = .8178 cm3
8.9 x 7 x .01 =
.623 cm3
5.5 x 3.8 x .01 x 5 = 1.045 cm3
2.4858 cm3
Ratio of wrapper to gum
2.4858/6.24 = 39.836538462
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
Gum-dilly-icious! (cont.)
0.4 = 40%
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Exemplars
Benchmark Descriptors
Novice
The novice will few parts, if any, of the problem correct. It will be unclear what the
student is trying to accomplish. The novice may try to interchange metric and
standard measurements, or linear and mass measurements. Little or no reasoning
will be used, and little math language will be evident.
Apprentice
The apprentice will have a partially correct solution. The apprentice will achieve an
incorrect answer due to a computation or measurement error. The student may also
confuse volume and linear measurements. Representations will be attempted, and
some math language may be used.
Practitioner
The practitioner will have a correct answer that will be clearly communicated. All
work will be present, and accurate math language used. Representations will be
clear, accurate, and will help the student draw a conclusion.
Expert
The expert will have a correct solution with the approach and reasoning used
described in detail. The expert will use math language throughout the solution, and
representations will draw conclusions about the data. The expert will go beyond the
task requirements by doing cost analysis, comparing to another brand of gum, etc.
Author
Carol McNair teaches 6th grade at the Camels Hump Middle School in Richmond, Vermont.
She has a master’s degree in curriculum and instruction from the University of Vermont. She
has worked as a mathematics consultant to the Vermont Department of Education and is an
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
Gum-dilly-icious! (cont.)
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Exemplars
Novice
It is unclear what these
calculations are showing.
The work lacks labels, and it is unclear
what the student is attempting to do.
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
Gum-dilly-icious! (cont.)
Little or no math
language is used.
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Exemplars
Apprentice
The work is
somewhat organized.
The student does not seem
to know how to proceed
after measuring the gum.
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
Some math language
is used.
The student attempts to solve
the task, but neglecting that the
gum is 3–dimensional will not
lead to a solution.
Gum-dilly-icious! (cont.)
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Exemplars
Practitioner
The work is organized
and present.
The student’s
approach works.
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
Math language is
used throughout.
S/he draws an
accurate conclusion.
Correct solutions
are achieved.
The student attempts to extend
the task, but no work is present.
Gum-dilly-icious! (cont.)
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Exemplars
Practitioner (cont.)
The student creates
representations to
communicate the solution.
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
Gum-dilly-icious! (cont.)
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Exemplars
Expert
The student explains
the approach and
reasoning used.
Accurate and appropriate
math language is used
throughout the solution.
The student
achieves a correct
solution.
S/he analyzes an
aspect of the
solution.
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
Gum-dilly-icious! (cont.)
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Exemplars
Expert (cont.)
Correct answers
are achieved.
All work is
shown.
The student goes beyond the
requirements of the task and
determines the cost.
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
Gum-dilly-icious! (cont.)
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Exemplars
Expert (cont.)
Note: Original
student work
included colors.
S/he creates
several
representations
to communicate
the solution.
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
Gum-dilly-icious! (cont.)
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Exemplars
Expert (cont.)
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
Gum-dilly-icious! (cont.)
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Exemplars
Expert (cont.)
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
Gum-dilly-icious! (cont.)
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Exemplars
Expert (cont.)
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
Gum-dilly-icious! (cont.)
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Exemplars
Expert (cont.)
Exemplars
271 Poker Hill Rd., Underhill, VT 05489
Phone 800-450-4050
Gum-dilly-icious! (cont.)
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