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## Objective

SWBAT combine standard function types using arithmetic operations.

#### Big Idea

Combine functions to help determine which mode of travel is cheapest.

## Set the Stage

5 minutes

In yesterday's lesson we looked at college expenses, so today we're going to compare the costs of different ways of getting to college.  My students will again be using chromebooks so if you don't have access to computers/internet you will want to print out information from these websites.  I begin class with a map of the US projected on the front board and explain to my students that one of my children went to school in Vermont (This is clear across the country from where we live, in Idaho!  You may want to change this just a bit to fit your students and situation, for instance making this an end-of-high-school trip to see both coasts.)  I ask if any of them have applied or will apply to schools out-of-state and allow a moment or two for discussion of where they hope to be after high school.  I tell them that today's challenge will be to figure out whether it will be cheaper to travel across the country by car and hotel, car and camper or by plane and ship all the extra luggage.

## Put It Into Action

40 minutes

The goal of this assignment is to have students create equations to answer their questions, but this can be tough for some students and analogies as I discuss in my video can help.  I let my students choose their partner for today's assignment and distribute the Road Trip Challenge.  I give them a moment to read through the paper and ask if there are any questions, then tell them they have until the last five minutes of class to complete the challenge. (MP1, MP2, MP4) While my students are working on this challenge I walk around giving assistance and redirection as needed.  For example I might ask a struggling team "What do you need to know to calculate the fuel costs for the trip?" or "How many nights will you need to stop along the way if you can only go 500 miles each day?"  This is a fairly open assignment with several possible "correct" answers, so I also have to reassure some teams that it's okay to have different answers than the other teams.   I expect that this activity will take most of the class period as students encounter different roadblocks (no pun intended) and figure out how to solve them.

## Wrap It Up

5 minutes

For the last few minutes of class I ask my students to turn in whatever they've completed of the challenge.  I hand out notecards and ask them to briefly describe the most difficult part of today's lesson, which part they found the easiest, and why. (MP2) This gives them a chance to reflect on the lesson as a whole and also lets them discuss their personal strengths and weaknesses. I use activities like this to help my students build their own sense of how well they understand and apply mathematical concepts and skills.