Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 55449
Perimeter and Area of an Obtuse Triangle
Students are asked to find the perimeter and area of an obtuse triangle given in the coordinate plane.
Subject(s): Mathematics
Grade Level(s): 9, 10, 11, 12
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, perimeter, area, coordinate geometry, obtuse triangle
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_PerimeterAndAreaOfAnObtuseTriangle_Worksheet.docx
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 problem on the Perimeter and Area of an Obtuse Triangle worksheet.
2. The teacher asks follow-up questions, as needed.
TASK RUBRIC
Getting Started
Misconception/Error
The student does not have an effective strategy for calculating the lengths of the non-horizontal sides of the triangle.
Examples of Student Work at this Level
The student attempts to count lengths of diagonal segments to find AC and BC.
page 1 of 4 The student indicates that he or she does not know how to find the lengths of
and
.
Questions Eliciting Thinking
What is the unit of measure for lengths in this diagram? Are the lengths of diagonal segments that you counted along
equal to the unit lengths you counted along
?
How can you find a length in the coordinate plane that is not vertical or horizontal? Do you know the distance formula?
Is there another way to find these lengths without using the distance formula? How about the Pythagorean Theorem – would that help you find these lengths?
Instructional Implications
Be sure the student understands how to calculate horizontal and vertical lengths in the coordinate plane. Make explicit the unit of measure. Then provide instruction on
using the Pythagorean Theorem or the distance formula to find lengths of diagonal segments in the coordinate plane.
Provide additional opportunities to find lengths of diagonal segments in the coordinate plane. Encourage the student to carefully identify coordinates of vertices and to label
and show all work neatly and logically, using correct notation. Allow Got It students to share their work as good examples of how to communicate mathematics on paper.
Consider using MFAS tasks Perimeter and Area of a Rectangle (G-GPE.2.7) or Perimeter and Area of a Right Triangle (G-GPE.2.7).
Moving Forward
Misconception/Error
The student has an effective strategy for finding the lengths of the sides of the triangle but makes major errors in implementing it.
Examples of Student Work at this Level
The student uses the distance formula but:
Labels the points (
Calculates (
+
) and (
,
)
) instead of (
,
-
)
Makes multiple substitution errors
Questions Eliciting Thinking
Can you tell me what the distance formula is? What points did you use? How did you label those points? What values did you substitute into the formula?
How did you find the area of the triangle?
Instructional Implications
Guide the student through the process of substituting values into the distance formula and evaluating the resulting expression. Encourage the student to carefully identify
coordinates of vertices and to label and show all work neatly and logically, using correct notation. Allow Got It students to share their work as good examples of how to
communicate mathematics on paper. Provide additional practice with the distance formula and finding lengths of segments in the coordinate plane.
Review the Pythagorean theorem and show the student how it can be used to calculate the lengths of segments in the coordinate plane. Model creating a right triangle
using one side of the triangle as the hypotenuse and counting the horizontal and vertical segments forming the legs. Provide the student with colored pencils or highlighters
and ask him or her to trace the right triangles needed to use the Pythagorean theorem to find the lengths of the sides.
Provide practice using the distance formula. Consider using MFAS tasks Perimeter and Area of a Rectangle (G-GPE.2.7) or Perimeter and Area of a Right Triangle (GGPE.2.7).
Making Progress
Misconception/Error
The student is unable to find the height of the triangle.
Examples of Student Work at this Level
The student is identifies the length of a side of the triangle as the height.
page 2 of 4 The student calculates the area incorrectly.
The student identifies the height as a vertical segment from vertex A to
.
Questions Eliciting Thinking
What value did you use for the base of the triangle? Why?
What value did you use for the height of the triangle? Why?
In what kind of angle should the base and the height meet?
Instructional Implications
Provide the student with instruction on finding the height of an obtuse triangle. Make explicit that the height can be drawn outside the triangle and is always perpendicular
to the line that contains the base. Challenge the student to consider each side of the triangle as a base and draw its corresponding height.
Almost There
Misconception/Error
The student makes a minor computational error and/or does not communicate work completely and precisely.
Examples of Student Work at this Level
The student uses the distance formula correctly but does not simplify the radical correctly.
The student makes a minor error substituting into the distance formula.
The student substitutes into the distance formula correctly but makes a minor computation error.
Questions Eliciting Thinking
How did you find AB? BC? AC? Did you substitute correctly?
Can you check your work? Did you add correctly? Did you subtract correctly? Did you square the difference correctly?
Instructional Implications
Provide the student with additional practice with application of the distance formula. Encourage the student to carefully identify coordinates of vertices and to label and
show all work neatly and logically, using correct notation. Have the student partner with another Almost There student to compare work and reconcile any differences.
Consider using MFAS tasks Perimeter and Area of a Rectangle (G-GPE.2.7) or Perimeter and Area of a Right Triangle (G-GPE.2.7).
Got It
Misconception/Error
The student provides complete and correct responses to all components of the task.
Examples of Student Work at this Level
page 3 of 4 The student either uses the distance formula or the Pythagorean Theorem to find the following: AB = 6, BC ˜ 13.4 and AC ˜ 8.5 and correctly states that the perimeter is
approximately 27.9 units. The student uses AB as the length of the base of the triangle determines that the height of the triangle is 6. The student then states the area is
18 square units.
Questions Eliciting Thinking
Is there another way you could have found the area of this triangle?
Instructional Implications
Challenge the student to consider each side of the triangle as a base and draw its corresponding height and then find the area using another base-height pair.
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Perimeter and Area of an Obtuse Triangle 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-GPE.2.7:
Description
Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance
formula. ★
Remarks/Examples:
Geometry - Fluency Recommendations
Fluency with the use of coordinates to establish geometric results, calculate length and angle, and use geometric
representations as a modeling tool are some of the most valuable tools in mathematics and related fields.
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