A student claims all fractions greater than 3/7 have a denominator less than 7. Show that this claim is only sometimes true.
These are sample test questions from a 4th-grade math test from the Smarter Balanced Assessment Consortium (SBAC), one of the two multi-state consortia developing Common Core tests.
Question 2: C is correct answer
Item Purpose: This question attends to the coherence in the standards by integrating ideas from the Operations and Algebraic Thinking domain with those in the Number and Operations in Base 10 domain. Instead of the missing product (What is 420 x 10?), the question is seeking a missing factor using the 4th grade language of multiplicative comparison.
Question 7: Multiple correct responses possible. For example, 6/6 for part A and 7/8 for part B.
Item Purpose: In early grades, the pathway toward later mathematical proof and argumentation begins by exploring conjectures through examples. In this case, students are exploring the relationship between the value of the denominator in a fraction and the value of the number represented by the fraction. In later grades, students would be expected to more autonomously select the kinds of examples needed to evaluate a proposition or conjecture.
Question 10: There are three correct answers.
Item Purpose: The primary focus of this item is on the relationship between multiplication and division, but presented through the early grades practice of mathematical modeling (knowing that different equations can be used to represent the same situation). Each choice represents a slightly different conceptualization of the same problem. Students receive partial credit for identifying 2 of the 3 correct equations as long as they have not also selected an incorrect choice.
Question 19: 1/8 and 4/8 are correct answers.
Item Purpose: This item is intended to support reasoning about numbers and operations. It is specifically constructed so that a student can recognize that the two sides of the inequality would be equal if a 1 were entered into the box. Since the left side must be greater, the unknown value on the right must be less than 1. Students receiving solid instruction focused strongly on mathematical practice #7 (looking for and making use of structure) are likely to be able to complete this problem more easily and efficiently than those who only learn to think about the problem as substituting each number individually and “checking if it works.”
In addition to questions like the ones above, the Smarter Balanced assessments will include “performance tasks.” SBAC defines these as “extended activities that measure a student’s ability to integrate knowledge and skills across multiple standards.” To try one of these performance tasks, click here.
To try a full SBAC practice test, click here.