#46 Extend and Connect

Extend and Connect

Come up with a function that brings smaller and smaller results as you repeat it. In economics, when you work more and more to achieve smaller and smaller results, the process is said to have “diminishing returns.”

Collect and sort functions by how they iterate. You can iterate some functions forever, for example, doubling or singing “The Bear Went Over the Mountain” song. Some functions only iterate for a while, like breaking a cookie into ever smaller pieces or cutting paper in half repeatedly. Some functions don’t iterate at all, or stop changing from iteration to iteration, such as subtracting a number from itself. Invite children to come up with ideas for keeping the iterations going, such as introducing negative numbers or creating a “reset” option.

Write a recursive formula in a spreadsheet ( for example, A2=A1-2) and drag it down the column. Invite kids to observe and modify the pattern. Like many activities that have to do with cycles, it is more engaging than it sounds from this description.