Education Standards
OSPI Other Functions Instructional Task: Fencing Land
Overview
This resource was created by the Washington Office of Superintendent of Public Instruction.
Task
OSPI Other Functions Instructional Task E
Other Functions; Standard A-APR.1, Claim 3A
Fencing Land
Two mathematicians are neighbors. Each owns a separate rectangular plot of land that shares a boundary and has the same dimensions. They agree that each has an area of square units. Mathematician A sells his plot to the other. Mathematician B wants to put a fence around the perimeter of her new combined plot of land.
Mathematician B wants to know how many linear units of fencing she needs. Mathematician A says the perimeter of the combined plot of land would be
- Determine whether Mathematician A’s claim is True, False, or Cannot be determined. Show your reasoning using numbers and words.
Rubric
Rubric
Question Number | Standard/Claim | Description |
E | A-SSE.2/Claim 3A | A 1-point response demonstrates full and complete understanding of the standard and claim by doing all the following:
|
A 0-point response demonstrates almost no understanding of the standard and claim. |
OSPI Other Functions Instructional Task E Exemplar
OSPI Other Functions Instructional Task E Exemplar
Other Functions; Standard A-APR.1, Claim 3A
Fencing Land
Two mathematicians are neighbors. Each owns a separate rectangular plot of land that shares a boundary and has the same dimensions. They agree that each has an area of square units. Mathematician A sells his plot to the other. Mathematician B wants to put a fence around the perimeter of her new combined plot of land.
Mathematician B wants to know how many linear units of fencing she needs. Mathematician A says the perimeter of the combined plot of land would be
- Determine whether Mathematician A’s claim is True, False, or Cannot be determined. Show your reasoning using numbers and words.
The area of each plot is . That means that the dimensions of each plot are and In the diagram if the horizontal distance is and the vertical distance is the perimeter of the combined lots would be If the dimensions are reversed the perimeter of the combined lots would be which is what Mathematician B said it would be. Since we don’t know which dimension represents the length and which represents the width, we cannot determine whether Mathematician A’s claim is true or false. |