Performance Assessment Task
3rd Grade: Number and Operations - Fractions
3.NF.3 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
A. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.
B. Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model.
C. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram.
D. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
Materials:
Attached assessment.
Manipulatives, if needed
Directions:
Explain to students that they are to look at the fractions and then choose from the statement which one they believe to be true. Have them use pictures or words to support their answers.
Considerations:
· Can students identify which statement is true?
· Are they able to support their thinking? Can they explain why 3/1 is larger? Do they discuss how 3/1 is equivalent to a whole number? That it is equal to 3?
· When talking about the fractions are they able to use math vocabulary? Ex. Denominator and numerator vs. bottom and top?
Collecting Data:
Student performance can be scored with a provided task rubric or a rubric created by the teacher. Data can be recorded on a score sheet.
Look at the fractions below.
Which statement is true? Circle your answer.
a. =
b. >
c. <
d. You cannot compare them because they have different denominators.
Explain how you know the statement is true. Use pictures or words to explain your answer.
Not yet: Student shows evidence of misunderstanding, incorrect concept or procedure / Got It: Student essentially understands the target concept.
0 Unsatisfactory:
Little Accomplishment
The task is attempted and some mathematical effort is made. There may be fragments of accomplishment but little or no success. Further teaching is required. / 1 Marginal:
Partial Accomplishment
Part of the task is accomplished, but there is lack of evidence of understanding or evidence of not understanding. Further teaching is required. / 2 Proficient:
Substantial Accomplishment
Student could work to full accomplishment with minimal feedback from teacher. Errors are minor. Teacher is confident that understanding is adequate to accomplish the objective with minimal assistance. / 3 Excellent:
Full Accomplishment
Strategy and execution meet the content, process, and qualitative demands of the task or concept. Student can communicate ideas. May have minor errors that do not impact the mathematics.
Adapted from Van de Walle, J. (2004) Elementary and Middle School Mathematics: Teaching Developmentally. Boston: Pearson Education, 65
Ó Elementary Mathematics Office • Howard County Public School System • 2013-2014