The cumulative progress indicators for grade 4 appear below in boldface type. Each indicator is followed by activities which illustrate how it can be addressed in the classroom in grades 3 and 4. Investigate and describe patterns that continue indefinitely. Using the constant multiplier feature of a calculator, students see how many times 1 must be doubled before one million is reached. They might first guess the number of steps to one million, and to half a million.
Students start with a long piece of string.
They fold it in half and cut it in two, setting aside one piece. Then they take the remaining half, fold it in half, cut it apart, and set aside half. They continue this process. They discuss how the length of the string keeps getting smaller, half as much each time, so that after about ten cuts, there is essentially no string left. Some students may understand that the process could keep going for several more steps, if we could only cut more carefully, and some may realize that in theory the process could continue forever.