IMP Day 5 - Calculator Exploration...and The Broken Eggs

On Day 5 I chose to go ahead and do the Calculator Exploration with my classes. I was very tempted to skip it because we are going to have to trim some items in the books since we are starting 7 weeks late. However, it was a Friday and I thought the students might enjoy it. What is funny is they taught me things about the TI-83 calculators that I didn't know. I have never played with any of the Apps and of course this generation is all about Apps. I also learned how to dim and brighten the screen AND how to convert decimals to fractions and vice versa. I asked at the end of class how many students were more excited about our new books now that they realize that they will get to use the graphing calculators and about 5 or 6 raised their hands. That is improvement. Right now many of the students are not happy with our new books because they are more wordy and they are required to explain and describe their reasoning more. The way the curriculum is written we will EASILY be meeting our new literacy standards. I am excited about the amount of reflection and explaining that the book asks for because I was interested in having my students journal anyway. I just have a hard time implementing journals in my classroom.  After the calculator exploration I gave my students time to start writing their POW write up for The Broken Eggs.

Thursday I had a student in my 5th period class tell me that he had come up with a way to find an endless number of solutions to The Broken Eggs. He told me verbally but he lost me! I told him to write it down and put it on my desk (the bell was about to ring). He had written down to take the previous answer, multiply it by 2, and then add 119. I used 301 as the "previous answer" and used his method and it worked. I went and showed Sonya New to see if she could help me figure out how he came up with it. We were stumped! When he came to class on Friday I asked him to explain. He said that he found 301 by adding 7 over and over again. The class had already discussed that the answer had to be an odd multiple of 7. This young man had also decided that the number had to end with a 1 because to have 1 left over when putting the eggs in packages of 5 the number had to end in a 6 or a 1 and since the number had to be odd it had to end with a 1. So...he kept adding 7 until he came to the next multiple of 7 that ended in a 1 and it was 721. Then he said he was just playing with the numbers and decided to multiply 301 by 2 to see how close it was and it was 119 away. Then he decided to try to double 721 and add 119 to see if it worked to generate another solution and it did. WOW! That seems so random to me. I am still amazed.