Sheri's work on the Tower Puzzle
8. 9/20/00 Many sessions before this day, Sheri had worked on the Tower Puzzle (see ch. 6).
On this day, Sheri figured out the rule for the Tower Puzzle, her work shown below:
In the process she found patterns in the table of values- the differences go up 2, 4 8, 16, 32.., in powers of 2. Don reminded her about writing numbers these as powers of 2, see her work on the right above. The y-numbers she noticed were 1 less than these powers of 2. Don wrote 7 as 23 - 1 then Sheri wrote the others this way and wrote the rule as 2x - 1= y. Don asked Sheri to graph the rule and graph negative values of x. In the process Sheri got into negative exponents and statements like 1/4 - 1 = - 3/4, which they talked about. See her work above. Her graph (an exponential function) is below:
9. On 9/21, Don asked Sheri to write about what she did the day before with the Tower Puzzle. As can often be the case, students put away their work and forget about it. Don asked her this, explaining that the reason he asked was to make sure she understood and could explain what she did. She started to do this and when Don saw her slowing down, he changed the subject. He suggested she finish at home. (Sheri hasn't finished this yet, as of 11/2/00.. it's difficult to get young people to write down things like this. Don will persist!)