1. Round Robin Review
There are six discussion stations set up around the room. You must visit four of them today. The discussion stations are:
Graphs
Table of Numbers
Functions
Free Response
Write Your Own Free Response
Challenge Problem—taking things a step further
You will have 10 minutes at each station.
After you complete your discussion, fill in the reflection form for that station.
Use your reflection form to guide your studying tonight.

2. Graphs Section

7. Graph Discussion Points
Over and under estimates with LRAM and RRAM
Which is closer to the actual value, LRAM or RRAM, and why?
Try with different numbers of rectangles.
For the linear graph, can you find an actual area?
Can you draw a monotonic (either always increasing or always decreasing) graph that both LRAM and RRAM are over estimates? Under estimates?

8. Tables of Numbers

9. Finding area using a table of numbersx 2 4 6 8 10 12 y 15 9 5 3 1
How many rectangles can you use using LRAM? RRAM? MRAM?
How wide are the rectangles with each of those? Are all the rectangles the same width? Why or why not?
Can you approximate the derivative at x=5?

10. Given this table of velocities, find the distance traveled…
t (sec) 2 3 5 7 10 11 12 15
v (ft/sec) 8 16
Can you do MRAM, LRAM, RRAM on this data? Why or why not?
What is the acceleration at t=6 sec? Is this exact or approximate or maybe you can’t really tell?
What are the units on acceleration?

11. Discussion Points Do all the rectangles have to be the same width?
Can you do MRAM on all data sets? If not, what makes a data set not a good candidate for MRAM?
Can you tell if you are over or underestimating? If so, how?
Units, units, units

12. Functions

13. Use LRAM and RRAM to find the area under the following curves 0<x<4 Use 4 rectangles.
Discussion points:
How do you tell if it is an over or under estimation?
Could you do this process with more rectangles?
Which is better, more or fewer rectangles?

14. Practice some Free Response

15. Free Response

17. Write your own free response

18. Write your own
Write your own free response accumulation/consumption or given velocity find distance problem. You can use a graph or a table of values. You should have units. You should have one part where you need to find the area and one part where you need to approximate a derivative. Be creative.

19. Challenge Problem

20. Challenge Question