##
* *Reflection:
Letters & Postcards, Day 2 of 2 - Section 3: Choose Your Own Adventure

When students are given a condition like “There may be at most three widgets for every grommet.” they almost universally write the inequality incorrectly as 3*w* < *g*. I've found that it's very difficult to help them see the error in this. I suggest thinking about it without the equation; for instance, if you make 5 grommets, how many widgets can you make? Remember, you can have up to 3 widgets for every grommet.

When the student answers, “15 widgets”, I then say, “Okay, that means that 5 grommets and 15 widgets should satisfy the condition. But 3*w* < *g* is false if *w* = 15 and *g* = 5. What’s wrong?”

I also try asking them which is the smaller quantity, *g* or *w*. It would make sense to multiply the *smaller* number by 3 to obtain an equality. This is hard to understand because in this context we're really dealing with an *in*equality.

I'll have to think about this misconception some more, because at this point I'm not sure how else to explain it!

*The most persistent error*

*The most persistent error*

# 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