Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 55448
Perimeter and Area of a Right Triangle
Students are asked to find the perimeter and the area of a right 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, right triangle
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_PerimeterAndAreaOfARightTriangle_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 problems on the Perimeter and Area of Right Triangle worksheet.
2. The teacher asks follow-up questions, as needed.
TASK RUBRIC
Getting Started
Misconception/Error
The student is unable to correctly calculate the lengths of the sides of the triangle.
Examples of Student Work at this Level
The student attempts to use the distance formula to calculate lengths but makes errors in its application. For example, the student:
Subtracts a y-coordinate from its corresponding x-coordinate.
page 1 of 4 Does not square the horizontal and vertical components.
Questions Eliciting Thinking
Can you write out the distance formula? What do the parts of the distance formula [e.g.,
] actually calculate?
How did you substitute the coordinates of the endpoints into the distance formula?
Instructional Implications
Review the distance formula and assist the student in correctly applying it to find the length of one of the sides. Directly address any errors the student initially made when
using the formula. Ask the student to find the lengths of the remaining two sides and provide feedback.
Provide additional opportunities to find lengths of 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 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 an Obtuse Triangle (G-GPE.2.7).
Moving Forward
Misconception/Error
The student is unable to correctly calculate area.
Examples of Student Work at this Level
The student correctly calculates the lengths of the sides of the triangle. However, when calculating area, the student:
Does not identify a height that corresponds to the selected base.
Identifies and uses and incorrect formula.
Questions Eliciting Thinking
Can you explain how you found the area of the triangle?
How did you determine what could serve as the base and what could serve as the height?
Instructional Implications
Review the formula for the area of a triangle. Explain the meaning of the terms base and height. Be sure the student understands that any side can serve as the base.
However, the height is always perpendicular to the base. Consequently, in a right triangle it is often convenient to use the legs as the base and height. Ask the student to
identify the length of a base and its corresponding height and to revise his or her calculation.
Consider using MFAS task Perimeter and Area of a Rectangle (G-GPE.2.7) or Perimeter and Area of an Obtuse Triangle (G-GPE.2.7).
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:
Substitutes one coordinate incorrectly into the distance formula, for example, substitutes 3 instead of -3.
Makes one minor computational error.
page 2 of 4 After calculating AB = 20, takes the square root of 20 and says AB =
.
Does not include a unit or writes a unit incorrectly.
Questions Eliciting Thinking
You made a mistake in one of your calculations. Can you find and correct it?
What is the unit of measure for perimeter? For area? Did you write these units correctly?
What is the difference between
and 150
? Which is needed here?
Instructional Implications
Provide feedback to the student concerning any errors made and allow the student to revise his or her work.
If needed, review the units of measure for length and area. Guide the student to write the units using appropriate notation.
Consider using MFAS tasks Perimeter and Area of a Rectangle (G-GPE.2.7) or Perimeter and Area of an Obtuse 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
The student either uses the distance formula or the Pythagorean Theorem to determine the following: AB = 20, BC = 15 and AC = 25. The student correctly calculates
the perimeter as 60 units and the area as 150 square units.
Questions Eliciting Thinking
Can you think of another way to find the area of this triangle?
How is the unit of measure for perimeter different from the unit of measure for area?
Instructional Implications
Challenge the student to find the area and perimeter of composite figures drawn in the coordinate plane.
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Perimeter and Area of a Right Triangle worksheet
page 3 of 4 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.
page 4 of 4