Mathematics Benchmark
Constructed Response Marking Scheme
Grade: 3
Item Description: Broken Ruler
Mathematical Content 1 pt
3 ½ inches, 3 ½”, 3 ½ , or 3.5
Appears to have the correct answer but uses an incorrect fraction notation.
Mathematics Background: Although many students are taught to use a ruler starting at zero, this is not the mathematical idea assessed in this item. Technically measurement is a number that indicates a comparison between the attribute of an object being measured and the same attribute of a given unit of measure. Direct measure is one reading of an instrument.
In this problem, students are using the attribute of length. The identified unit of measure is inches. This means that each increment on a ruler is one inch or the distance between each number is one inch. Putting a series of these one inch increments together assists in “covering or matching” the unit measure to the length of the object.
2 points:n Indicates clear understanding that the crayon measures 3 ½”. (redrawing, marking intervals on the crayon provided, or marking the ruler below the crayon.)
n An explanation indicating that if the crayon were moved to zero then the crayon measure would be 3 ½”. (performing a rigid motion or slide)
1 point:
n Counts and reports whole unit measures. (i.e. “…because if you put the crayon from the first line it will be four inches”)
n Demonstrates understanding of reading the ruler to the ½”.
n Indicates an application of direct measurement process (i.e. “I match it up and I draw a line and it tells me what number.”)
0 point:
n Incorrect use of fraction notation.
n Explanation does not indicate application of direct measurement. (i.e. “I measured, I counted, I used numbers on the ruler, or I looked”.
n The student provides a completely incorrect explanation or justification, one that cannot be interpreted, or there is no response.
Mathematical Process Total 2 points
The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), is supported with funding from the National Science Foundation under Grant No. EHR-0314898.