Have a play around with this task, and please share any questions, extensions, simplifications, modifications, or lines of inquiry in the comment box below. The idea is to collect loads of suggestions that can then be used for effective differentiation. The full set of these tasks, along with additional notes, can be found here: http://www.mrbartonmaths.com/richtasks.htm
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I look forwards to using it in the class. thanks
A wonderful example of a rich task which can be student led. Thanks for sharing!
How is the “limiting value” related to the original 3 numbers?<br /> <br /> Which 3 numbers give you a “nice” limiting value?<br /> <br /> Does the order of the 3 numbers matter?<br /> <br /> Is there a pattern in the limiting value if the original 3 numbers are consecutive?<br /> <br /> How about if they are in a sequence?<br /> <br /> How about if some of the numbers are the same?<br /> <br /> What about square numbers, Fibonacci numbers, etc ?...<br /> <br /> Can you convince people using algebra?<br /> <br /> Try starting with 2 numbers<br /> <br /> Or 4<br /> <br /> Or 5<br /> <br /> Try drawing a graph of each of the values<br /> Which graphs oscillate?<br /> Which graphs approach like a staircase?<br />
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