How much is a million? This question is familiar to many elementary teachers who have challenged their students to think about and explore large numbers. Much has been written about the importance of having children explore large numbers, think about large amounts of something, estimate large quantities of objects, and be able to gain a sense of how much is “a lot.” Explorations with these goals in mind often invite students to use a familiar context or an everyday object to think about how much a million or some other very large number is. The children's book How Much Is a Million? (Schwartz 1993) is well known in many classroom settings and frequently used as a springboard for lessons posing this kind of challenge. In fact, there may be millions of resources available to teachers who are looking for ways to help their students conceptualize large numbers.
Three years ago, the mathematics teachers from grades 4-12 in our school met for two weeks during the summer for an in-service program related to assessment and decided to begin using portfolios with our students in the fall. I was enthusiastic, although I had no idea at that time how drastically my approach to assessment—and to teaching in general—would change a a result of the portfolio decision.
Experiences with many children in the middle grades indicate that they have poor decimal concepts and lack fundamental skills in working with decimal values. For example, when asked to identify which of 0.36 or 0.339 is greater, children frequently choose 0.339 because 339 is greater than 36.
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