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A Teacher's Guide to The American Revolution: A History in by Christine Compston

By Christine Compston

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Extra info for A Teacher's Guide to The American Revolution: A History in Documents (Pages from History)

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CCC 6-8 Algebra 1 (1-38) 8/6/02 4:39 PM Page 15 Follow-Up Explorations Patterns and T-Charts Figures 1–10 and 1–11 show two additional patterns that I have used with middle school students on days soon after the student exploration of the Rocket Pattern. The iterative and explicit rules are given following an illustration of the first three stages of each pattern. Notice that each of these patterns is simple and unambiguous. I do not push the students to arrive at an explicit rule at this point.

The next day in class we had a brief discussion about the reflections. ” I made a transparency of Kenya’s reflection and had her read it to the class. The other students agreed that the details she included made her explanation about the pattern and the connection of the rule to the models or drawings clearer than simply stating the rule. They also agreed that Kenya’s writing indicated understanding of the terms constant and variable as well. I acknowledged that I knew other students in the class understood these same ideas and connections, and encouraged all the students to include such information in their reflections in the future.

Soon the class had compiled the following list of common elements in the T-charts: ■ List (group or set) of starting values ■ List (group or set) of final values ■ Rule that is used to find the final value for each starting value ■ Pairs of numbers in the first and third columns of each row that all follow the same rule If the class had not offered all of these elements, I would have asked questions to elicit those responses. ”) I then explained, “In this list you have included most of the important parts—or, as mathematicians refer to them, elements or components—of a very important concept in mathematics called function.

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