# Logic-Based and Strategic Problem Solving -- Final Preparations for Noetic Contest

Once again, almost every student completed the full-length practice test. Many of them came to class with questions that they could not understand even after reading the explanation. This is the most important step in the improvement process. Many of them showed a marked improvement on their scores and approaches to problem solving.

This was the final week of preparation for the Noetic Learning Math Competition. Next week we will start a unit linking probabilities to prime numbers. Two weeks ago, there was an amazing discovery out of Stanford University regarding the lack of randomness of prime numbers.

I will give the student the Noetic Test and they will take it within the 45 minute limit without parent help (except that K-1st grade can have parents read the questions to them). I will request that parents scan the test and email it to me at dkramer496@gmail.com and I will grade the test.

One of the most interesting questions we worked on this week was to find the smallest number with a sum of digits of 82. Once students started to write down numbers and add the digits, they realized the numbers with the fewest digits had the highest value digit: 9. Once again, this is all about nines. Dividing 82 by 9, they got 9 with a remainder of 1. So many of them first wrote down 9,999,999,991. When I told them that this is a number with the fewest digits but not the smallest number, they realized that they had to put the digit one on the front to get 1,999,999,999. Then I asked them to find the largest number with a sum of 82 and many of them wrote down 82 ones or  1,111,111,111,111,111,111,111,111,111,111,111,111,111,111,111,111,111,111,111,111,111,111,111,111,111,111,111. I suggested to them that they might try to add on a zero to make it 10 times bigger. Then again, and again until they realized that there is no largest number with a sum of digits of 82 because infinity is undefined.

For the K and 1st graders we worked on a 1st grade level packet together in class. and I gave them a 2nd grade packet for during the week.

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