July 12, 2011

Lesson Materials
-n-spire
-Chart paper (with graph)
-Student Activity Sheet
-Markers/tape
-

Make Changes on Lesson Plan

Notes

Opening activity
-How to make connections between the activities (flow)
-Moving from ti activity into graphing?
-Teacher will push students into finding equations, tables and graphs if they do not find it themselves (before they solve systems)
- Push students to represent their problem in as many ways as possible.
-How are our students sharing their ideas with each other? When they pair their constraints?
- How are students going to use the posters? Can they add to them? Have students give feedback on other posters?
-After jigsaw one partner adds their information to the other partners poster. (add missing constraint)
- Have students add a column to the table and new line to the graph on the posters. What problems may arise?
-Share out after
-What are we looking for in their presentations to know if students understand the concepts?

Nspire
-If students only come up with tables and equations go straight to ti inspire, or if they are missing any representation.
-Include the nspire activity if we have no constraints on time.
- Have students work on nspire worksheet and ask quick poll questions
- Is there a way to anonymously submit their solutions to the quick polls? (white boards, post its)


Another task/Exit Ticket
-How can we push students to solve systems using equations?
-Keep a running list of possible methods to solving systems
- Give students an ordered pair and ask them to check and see if it is a solution
- Have students individually represent a word problem with a table, graph and equation
- Have students identify a solution to the systems, a point that is a solution to one of the constraints and a point that is not a solution to any constraint
- Give students another task if we have time left over. It could roll over into homework. (possible-population problem)

Lesson Run through
Possible Student Responses/differences
ProblemA
-Not considering zero
-Using only multiples of 5
- Graphing mistakes-inceasing graph and not thinking about slope being negative
- FInding something that represents all of the possibilities
- is the graph an exact representation (discrete)

Problem B
-Reverse ski and snowboarders in the equation
-Reverse axis on the graph. There is no dependent or independent variable
-Scaling of the axis, how will the match with the other constraints
-Not going high on the table
- How the skip numbers, 3s, 5s, 10s?
- Not using variables (writing out the names)
-Discrete vs continuous

Problem C
-Having (0,20) a point. Can you have negative ski or snowboarders?
- labeling axis
- no dependent or independent variable


Teacher Responses A, B,C,
- What will the teacher's reaction be if these differences come up?
-Have student narrate their posters in the order in which they set it up (how did they get different scaling and axis, etc)
-Why did you all decided on this? Discuss similarities and differences between each group
-allow students to have differences until the share out
-Bill wants these kids to be crying afterwards. (WITH JOY OF COURSE!)
-Does your graph agree with your table, equation or visa versa. Ex. Does the point in the table correspond to your graph?
- Give a point 20 boards 40 ski, whose constraint does this work for?
- Bring out vocab: Solution, constraint.
-Both of these constraints have infinite number of solutions but only one unique solution that satisfies both constraints

Creating Systems-misconceptions
A/B
-No solution by table (decimal answers)
-overlaying the graphs wrong, scales, axis
-overlaying the correct solution but it is difficult to see the solution
- Asking them to point things out from the total column on the graph. Adding L1 and L2 and finding 100 instead of creating 3rd column from other partner's data

B/C
-write snowboarders in terms of skiers, add another column for skiers
-What is the prompt for this exchange?
-In each of these situations, we still don't know the exact number of skiers and snowboarders. Is there a number of snowboarders and skiers that is an answer to both?
-If we put both of your situations together can you find the number of skiers and snowboarders?
-Do you have enough information to confidently determine the number of skiers and snowboarders?
- Ask these questions while they are still in A,B, C group. (hopefully they say no)
- Then pose the same question when they switch groups and after they have looked at each others different representations.

A/C
-How are the variables going to be defined?
-if they use an algebraic technique, only finding one unknown
- can you use graphs to solve this problem? What would a solution look like on a graph?