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. (possiblepopulation problem)
Lesson Run through Possible Student Responses/differences ProblemA Not considering zero
Using only multiples of 5
 Graphing mistakesinceasing 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 Systemsmisconceptions 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?
Lesson Materials
nspire
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. (possiblepopulation problem)
Lesson Run through
Possible Student Responses/differences
ProblemA
Not considering zero
Using only multiples of 5
 Graphing mistakesinceasing 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 Systemsmisconceptions
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?