A student had gotten 40 points out of 100 on a test. When the teacher announced that this test and next week’s test would be averaged together for their grade, this student asked if he could still get a C if he made a 100 on the next test. The teacher asked him what he thought. He said, “I think my average (mean) would be 70, and that is a C, because half of 40 is 20 and half of 100 is 50. That’s a C because 20 plus 50 is 70.” Does his method always work? Explain.

(Source: Kamii, C., Pritchett, M., & Nelson, K. (1996). Fourth graders invent ways of computing averages. Teaching Children Mathematics, 3(2), 78-82.)