Lawn Mower Challenge
Randy and his sister agreed to work together to mow the
family’s 40-foot by 80-foot lawn. Randy said he would go first
and mow 1/2 the lawn and then his sister could take over and
finish the job.
Determine how many trips around the lawn Randy must make
in order to mow 1/2 of the grass if the mower cuts a path 2 feet
wide.
Lawn Mower Challenge
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Lawn Mower Challenge
Suggested Grade Span
6–8
Grade(s) in Which Task Was Piloted
8
Task
Randy and his sister agreed to work together to mow the family’s 40-foot by 80-foot lawn.
Randy said he would go first and mow 1/2 the lawn and then his sister could take over and
finish the job.
Determine how many trips around the lawn Randy must make in order to mow 1/2 of the grass
if the mower cuts a path 2 feet wide.
Alternative Versions of Task
More Accessible Version:
Randy and his sister agreed to work together to mow the family’s 20-foot by 40-foot lawn.
Randy said he would go 1st and mow 1/2 the lawn and then his sister could take over and finish
the job.
Determine how many trips around the lawn Randy must make in order to mow 1/2 of the grass
if the mower cuts a path 1 foot wide.
More Challenging Version:
Randy and his sisters agreed to work together to mow the family’s 40-foot by 80-foot lawn.
Randy said he would go 1st and mow 1/2 the lawn and then his sister Samantha could take
over and mow 1/2 of the remaining job. His sister Kate would then finish the job.
Determine how many trips around the lawn Randy and Samantha must make in order to mow
their share of the lawn if the mower cuts a path 2 feet wide.
Lawn Mower Challenge
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NCTM Content Standards and Evidence
Geometry Standard for Grades 6–8: Instructional programs from pre-kindergarten through
grade 12 should enable students to ...
Use visualization, spatial reasoning and geometric modeling to solve problems.
• NCTM Evidence: Draw geometric objects with specified properties, such as side lengths
or angle measures. Recognize and apply geometric ideas and relationships in areas
outside the mathematics classroom, such as art, science and everyday life.
• Exemplars Task-Specific Evidence: This task requires students to draw some sort of
geometric sketch to visualize the area to be mowed and also to apply geometric ideas to
"real world problems."
Time/Context/Qualifiers/Tip(s) From Piloting Teacher
This task took my students two 40-minute class periods to solve during a unit on geometry and
measurement. We had been studying the perimeter and areas of rectangles.
Links
This task could link to units on entrepreneurship and/or responsibility to community.
Common Strategies Used to Solve This Task
Most students used diagrams to solve the problem. Many used grid paper on which to draw
diagrams. All successful students divided the lawn area in half at the outset and worked toward
that number of square feet through their diagrams or by using a computational approach.
Possible Solutions
It would take Randy about 3.83 passes to mow half the lawn. The specific ending point is
dependent on the starting point. It would take three complete trips plus an additional two widths
and 1 1/2 lengthwise strips to get 1,600 square feet, or half the area of the lawn.
More Accessible Version Solution:
Each child will need to mow 400 square feet. It would take about 3.83 passes to mow 400
square feet.
Lawn Mower Challenge
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More Challenging Version Solution:
Randy would make about 3.83 trips around the yard. Samantha would need to finish the fourth
pass for Randy, then make two full passes, and then mow 48 feet of the next pass. Kate would
do the remainder of the lawn.
Task-Specific Assessment Notes
Novice
The Novice may state that half the lawn would equal 1,600 square feet, but it will be unclear
how that number was achieved. There will be little or no evidence that the Novice understands
the size of the lawn or the capability of the lawn mower. Representations will be inaccurate or
inappropriate to the task.
Apprentice
The Apprentice will be able to partially solve the task. S/he may have some basic
understanding of the task, such as how to determine half the area, but then will not have a
correct approach for dealing with how much lawn is mowed with each pass of the mower. Some
math language may be used, and diagrams will be basic and not useful in finding a solution.
Practitioner
The Practitioner will most likely make a scaled diagram as an approach that would work. S/he
will bring prior knowledge of area and scale to this new problem-solving situation. The solution
will be reasonable and documented. Connections between computation and diagrams will be
used to achieve a solution. The solution will show elements of good mathematical
communication through a methodical, organized, coherent and labeled response. It will be clear
that the student was aware of the audience while recording the solution.
Expert
The Expert will most likely use the same strategy for solving the task as does a Practitioner but
will go a step further to develop a formula to calculate the area remaining after each pass of the
mower. By the student’s own admission, this formula will work successfully only with whole
numbers. The Expert benchmark shows a student who tested the formula against the solution
found mathematically and by using the diagram. The original diagrams were in color to enhance
the readers’ comprehension of the solution, showing an awareness of audience and of purpose
for communicating.
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Novice
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Novice
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Apprentice
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Apprentice
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Practitioner
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Practitioner
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Expert
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Expert
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Expert
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Expert
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Expert
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Expert
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Expert
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Expert
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