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.
- Does not square the horizontal and vertical components.
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| 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.
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| 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.
- After calculating AB = 20, takes the square root of 20 and says AB =
 .
- Does not include a unit or writes a unit incorrectly.
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| 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.
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| 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. |
