## Thursday, December 10, 2015

### Day 67: Solving for Y and Recursive Sequences

The estimation was a box of tree lights. The best reasoning for an estimation was it looks about 30 feet long and there's one light bulb per foot, so about 30 bulbs. That was a close estimate.

When starting a new chapter, I switched up the groups. Chapter 5 starts with changing standard form to y=mx+b form. Students first reviewed the equation from John's Giant redwood tree and identified the starting height and the growth rate. I emphasized that they weren't just numbers from y=4x+5 and that they needed units that reflected the context of the word problem. For example, it's not a growth rate of 4, it's 4 feet PER year and it's not a height of 5, it's 5 feet.

Then they predicted what the growth rate and y-intercept of -6x+2y=10. The most common predictions were -6 for the growth rate and a y-intercept of 10. After using algebra tiles to solve for y, they then identified the actual growth and y-intercept. I asked students how the predictions were different from the actual answers but still good predictions.

In accelerated students investigated the difference between discrete and continuous graphs. Sequences are discrete because you can't have term 1.5, only whole numbers. Functions are continuous therefore you connect the points. They also practiced writing an explicit equation t(n) for an sequence. For example, if the sequence adds 4 each time and term zero is 6, the rule is t(n)=4x+6.  They then were introduced to a recursive equation which starts with t(n+1)=t(n)+4 in this case. What that means is to find the next term in the sequence you take a term and add 4 to it.

At the staff holiday party I got to meet Mrs. Wards baby girl Orla. Isn't she cute?