Engaging math activities for the summer break - Day 13
The two activities described below require nothing beyond a paper and a pencil. Both activities consist of carrying out iterative processes whose results becomes - hopefully - predictable after a few tries. When this happens, i.e., when children become able to predict the result, they can start using online simulators to verify their intuition. Until then the calculations should be carried by hand.
Activity 1
What to do? Start with a number and count the number E of even and the number O of odd digits. Write them down next to each other following by their sum S = E + O. In other words, write down the number 100E + 10O + S. Treat the result as a new number and continue the process.
What to observe? Regardless of the original selection, the final result is always 123.
Explanation and an online tool: Even, Odd and Total Number of Digits
Activity 2
What to do? Take any 3-digit number, say, 732 and write it backwards: 237. Subtract the smaller of the two numbers (237 in our case) from the larger (732). With our selection, we obtain the number 495. Write this one backwards too and compute the sum: 495 + 594.
What to observe? Regardless of the original selection of a 3-digit number, the kids keep arriving at 1089.
Explanation and an online tool: 1089 and a Property of 3-digit Numbers
Related posts:
[...] Also see the references to Ecker’s processes given by Alex Bogomolny, @CutTheKnotMath on Twitter, here and here. [...]
August 6th, 2011 at 9:36 amI want to solve for the wave number (k) in the dispersion equation (σ^2=gk*tanh(kd)) using an iterative process. I know it is easily done with a computer but would like to know how to do it by hand. It's a question of Maths Olympiad , not wave mechanics,so I am struggling!...
August 25th, 2011 at 1:25 am