##
* *Reflection:
Letters & Postcards, Day 2 of 2 - Section 1: Student Presentations

I am totally committed to class discussions. Students need to learn how to make conjectures and how to critically examine them. They learn confidence as well as humility by putting their ideas before their peers to be either accepted or rejected on their merits. They learn to listen to one another and to learn from one another. Once everyone has had a chance to ask questions, propose explanations, the truth of the matter should be visible for all to see.

*Should be.*

Like any teaching method, class discussion and Socratic questioning don't always work. Learning is an incremental process, and I have to remind myself that while every student will learn something from the discussion, none of them can be expected to learn everything. The attached student work is a good example of the kind of finished product I'm thinking of. In many ways it's very good, but it still reveals some misunderstanding on the part of the student.

***

Today, I had an opportunity to work one-on-one with a handful of students who were seriously struggling. These students were simply stuck and had no way to move forward without some very direct intervention. With these students, I focused entirely on making sense of the graphical solution. They needed help understanding how verbal expressions were turned into algebraic inequalities; they needed help graphing these inequalities; they needed help understanding what their graph meant. At this point, I wasn’t as concerned with finding the *optimum* solution as I was with understanding what was different about the various feasible solutions. At times, it's important to scaffold your instruction by focusing on the most important concepts, rather than the flashy or "neat" ones. In this case, that meant interpreting the model in context.

*The limits of discussion.*

# Letters & Postcards, Day 2 of 2

Lesson 5 of 15

## Objective: SWBAT write a system of linear inequalities and use the system to answer questions about balancing time and cost in a real world context. SWBAT explain their solutions to a modeling problem to their peers and respond to the explanations given by others.

## Big Idea: Systems are useful mathematical models for situations with a several of constraints. Time is money!

*45 minutes*

#### Choose Your Own Adventure

*15 min*

For the final 15 minutes of class, students will be assigned new groups of about 3 students each and given the following assignment:

*Write a real-world problem that may be solved with linear programming. Be creative, but keep it realistic, too! Your problem must have at least three constraints on two variables and require us to optimize a third variable in some way.*

*We'll begin today, but this will be finished as an in-class assignment tomorrow. Have fun!*

Please see the next lesson: **Choose Your Own Adventure**!

Be prepared to help students narrow the number of variables down to two, and a third that can be expressed as a function of the other two. Also, encourage them to be fun and creative, and remind them that the solution set doesn't have to be restricted to the first quadrant. It's interesting to see what sorts of variables students come up with that may be either positive or negative!

[For the record, the Music Shop Problem was originally written by a student named Jake Garcia!]

*expand content*

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- UNIT 1: Modeling with Algebra
- UNIT 2: The Complex Number System
- UNIT 3: Cubic Functions
- UNIT 4: Higher-Degree Polynomials
- UNIT 5: Quarter 1 Review & Exam
- UNIT 6: Exponents & Logarithms
- UNIT 7: Rational Functions
- UNIT 8: Radical Functions - It's a sideways Parabola!
- UNIT 9: Trigonometric Functions
- UNIT 10: End of the Year

- LESSON 1: What is Algebra?
- LESSON 2: The Music Shop Model, Day 1 of 2
- LESSON 3: The Music Shop Model, Day 2 of 2
- LESSON 4: Letters & Postcards, Day 1 of 2
- LESSON 5: Letters & Postcards, Day 2 of 2
- LESSON 6: Choose Your Own Adventure
- LESSON 7: What Goes Up, Day 1 of 3
- LESSON 8: What Goes Up, Day 2 of 3
- LESSON 9: What Goes Up, Day 3 of 3
- LESSON 10: The Constant Area Model, Day 1 of 3
- LESSON 11: The Constant Area Model, Day 2 of 3
- LESSON 12: The Constant Area Model, Day 3 of 3
- LESSON 13: Practice & Review, Day 1 of 2
- LESSON 14: Practice & Review, Day 2 of 2
- LESSON 15: Unit Test