Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 72141
Land for the Twins
Students are asked to solve a design problem in which a triangular tract of land is to be partitioned into two regions of equal area.
Subject(s): Mathematics
Grade Level(s): 9, 10, 11, 12
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, equal area, partition, triangle
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_LandForTheTwins_Worksheet.docx
MFAS_LandForTheTwins_Worksheet.pdf
FORMATIVE ASSESSMENT TASK
Instructions for Implementing the Task
This task can be implemented individually, with small groups, or with the whole class.
1. The teacher asks the student to complete the problems on the Land for the Twins worksheet.
2. The teacher asks follow-up questions, as needed.
TASK RUBRIC
Getting Started
Misconception/Error
The student is unable to draw a diagram that reflects the parameters of the modeling situation.
Examples of Student Work at this Level
The student:
Does not recognize the given lengths as a Pythagorean triple and draws a triangle other than a right triangle.
page 1 of 4 Does not correctly locate the segment representing the fence.
Questions Eliciting Thinking
What is the greatest common factor of 600, 800, and 1000? What kind of triangle is a 3-4-5 triangle?
What does the problem say about the location of the fence?
Instructional Implications
Remind the student that 6-8-10 is a Pythagorean triple so 600-800-1000 is as well, since each of these values is a perfect square multiple of 6, 8, and 10. Be sure the
student understands that this means the model of the tract of land should be a right triangle. Ask the student to draw a right triangle that includes the lengths given in the
diagram. Review what is said about the location of the fence and guide the student to add a segment to the diagram that represents the fence.
Next, guide the student to represent the length of the fence with a variable (e.g., l). Ask the student to calculate the area of the original triangular region. Then explain
that each smaller region must have an area that is half the area of the original region. Ask the student to determine how the area of the triangular half-region can be found
and to define any additional variables needed (e.g., the height of the triangular half-region, h). Guide the student to write an equation that models the area (e.g.,
).
Review similar triangle relationships and guide the student to write a proportion that relates the heights and bases of the original triangular region and the triangular halfregion (e.g.,
). Explain that the two equations written can be used to find the length of fence needed. Ensure that the student understands that providing
these two equations answers the second question.
Provide additional opportunities to use geometric methods to model and solve design problems.
Moving Forward
Misconception/Error
The student is unable to identify variables that are needed to model the problem.
Examples of Student Work at this Level
The student draws an appropriate diagram and may label the length of fence with a variable. But the student is unable to determine that the height of the triangular halfregion is also unknown and needed to model the area of this region.
Questions Eliciting Thinking
How can you find the area of the original triangular tract of land?
What do you need to know to find the area of the triangular half-region?
Instructional Implications
If needed, guide the student to represent the length of the fence with a variable (e.g., l). Ask the student to calculate the area of the original triangular region. Then
explain that each smaller region must have an area that is half the area of the original region. Ask the student to determine how the area of the triangular half-region can be
found and to define any additional variables needed (e.g., the height of the triangular half-region, h). Guide the student to write an equation that models the area (e.g.,
).
Review similar triangle relationships and guide the student to write a proportion that relates the heights and bases of the original triangular region and the triangular halfregion (e.g.,
). Explain that the two equations written can be used to find the length of fence needed. Ensure that the student understands that providing
these two equations answers the second question.
Provide additional opportunities to use geometric methods to model and solve design problems.
Almost There
Misconception/Error
The student is unable to correctly write equations to model the problem.
page 2 of 4 Examples of Student Work at this Level
The student draws an appropriate diagram and labels both the length of fence and the height of the triangular half-region with variables. The student may write one
equation that can be used to find the length of the fence but is unable to write a second equation.
Questions Eliciting Thinking
What is the relationship between the triangular half-region and the original triangular tract?
What is the relationship between the sides of these two triangles.
Instructional Implications
If needed, ask the student to determine how the area of the triangular half-region can be found and to define any additional variables needed (e.g., the height of the
triangular half-region, h). Guide the student to write an equation that models the area (e.g.,
).
Review similar triangle relationships and guide the student to write a proportion that relates the heights and bases of the original triangular region and the triangular halfregion (e.g.,
). Explain that the two equations written can be used to find the length of fence needed. Ensure that the student understands that providing
these two equations answers the second question.
Provide additional opportunities to use geometric methods to model and solve design problems.
Got It
Misconception/Error
The student provides complete and correct responses to all components of the task.
Examples of Student Work at this Level
The student draws a diagram such as the following:
and provides a solution such as:
Let l be the length of the fence and h be the height of the triangular half of the tract. The total area of the region is
the area of the triangular half to be 120,000 sq.ft., that is,
the equations
and
. Since the triangular half-region is similar to the original triangular region,
. We want
. So
can be used to solve for l.
Questions Eliciting Thinking
Is it possible to partition the tract into two equal area triangles?
Instructional Implications
Ask the student to use the equations he or she wrote to solve for the length of the fence.
ACCOMMODATIONS & RECOMMENDATIONS
page 3 of 4 Special Materials Needed:
Land for the Twins worksheet
SOURCE AND ACCESS INFORMATION
Contributed by: MFAS FCRSTEM
Name of Author/Source: MFAS FCRSTEM
District/Organization of Contributor(s): Okaloosa
Is this Resource freely Available? Yes
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
MAFS.912.G-MG.1.3:
Description
Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical
constraints or minimize cost; working with typographic grid systems based on ratios). ★
page 4 of 4