July 8 Notes

Determine a Lesson Goal:
Everyone wrote a lesson goal on the board and we discussed the goals.

Similarities in Goals
  • Use multiple representations (graphs, tables, equations) to represent and solve systems
  • Identifying solutions to systems
  • Using only 2 variables

Difference in Goals
  • Some goals have a very broad scope and others are more narrow
  • Some seem more like overall goals and others are more like objectives

Goal: Students will develop strategies to solve problems with 2 unknowns.
Students will develop the concept of a solution to a system of equations.

Objectives:
Determine the students' prior knowledge of solving systems of equations.
Students will be able to solve a problem with 2 unknowns systematically.
Students will identify solutions and nonsolutions to a system of equations using graphs,
tables and equations and be able to justify why a particular set of values is a solution.

Group-Worthy Tasks
5 Design Features:
  1. open-ended and require complex problem solving
  2. provide multiple entry points adn multiple opportunities to show competence
  3. deal with dicipline-based, intellectually important content
  4. require positive interdependence and individual accountability
  5. include clear criteria for evaluation

Reations: What are some example of group work that works and examples that don't?
Looked at "Crossing the River" problem


Task:

Eight adults and two children need to cross a river, and they have one small boat available to help them. The boat can hold either one adult, or one or two children. Everyone in the group is able to row the boat. How many one-way trips does it take for the eight adults and two children to cross the river?



Final Product:

On a separate sheet of paper, show how you get all eight adults and two children across the river. Using this method or another method, find how many trips it would take to get the following groups across the river:

  • 6 adults and 2 children
  • 15 adults and 2 children
  • 3 adults and 2 children
  • 100 adults and 2 children



Generalize these results in order to write a rule for finding the number of trips needed to get any number of adults (A) and two children across the river.

Gail came to talk at 2:
Cautions us about having students work in groups. Pairs may be more effective because of the students' lack of group experience.

Presents results from high stakes tests - students have a poor concept of what makes something a solution

Showed N-spire document "What is a Solution?", "The Elimination Method" and "Balanced Equations"

Brainstorm: Components we want in our lesson:
poll (perhaps to determine prior knowledge, as pretest)
simple question (like chicken problem)
Exit task/slip
N-spire file "What is a Solution?"
Push them to come up with as many ways to solve the problem as we can (graph, table, equation)
Use a problem with rich context
hands-on/moving around
Represent one constraint in many different ways and then combine constraints into one system
Have different pairs work with diffferent representations of systems
Include short story or history (Brelin Airlift problem?)
Why should students care/know how to solve systems
Write or share "What is a solution to an equation?"
Homework?
Motivate students to learn the rest of the unit
In pre-test "How do you know whether or not a point is on a graph?"

This weekend:
Read lesson template (wiki: click on plant)
Read TTOP (wiki: click on plant)
Think about lesson flow and tasks