We started with more Estimation 180, at which they are getting very good. There were multiple correct answers for most of the estimations today (days 21-26). The range of answers is getting tighter too, except for Day 24 which asked "How many sheets of paper in the package?".
One student guessed 1000000. Yes, 1 million sheets. We talked about why this was a "too high" guess given that it meant that there would be over 83000 sheets in each pad of paper. I think they are starting to see that a combination of reasoning and calculations will help them get a good estimate.
Next, Frogs! This is a fun, yet challenging game.
I made them strips to work with and brought in square tiles to represent the frogs. Here is the sequence for 1 pair of frogs.
So 3 moves is the minimum. They recorded that in their table. Next, 2 pairs of frogs (feel free to play along):
This gave a minimum of 8 moves. Enter that in the table. Then on to 3 pairs:
I'll let you play with this and see what you find. I found it really helpful to have the strips as otherwise you can get lost as to which end has an empty spot. Most of my students found this challenging. Some needed help to get going and some needed me to show them (once) how to do the 3 pairs. They then had to be able to reproduce it. Not to spoil your fun, but the data here is quadratic again and once they found the pattern they entered their data in the graphing calculator to produce an equation. They were then able to answer the original question (10 pairs of frogs) using their equation.
Some finished this and another investigation into the number of diagonals in a polygon (also quadratic) before the end of the period, and others were still working through yesterday's activities. I love working with patterns and modelling so this is all right up my alley. I am so impressed with all they can do independently at this point in the course.
Tomorrow, inaccessible heights!