Students will be able to write and solve equations from a profit model.

Extend writing expressions into solving equations through modeling a student run business. Linear modeling as entry point to build students' algebra confidence.

10 minutes

I include **Warm ups **with a **Rubric **as part of my daily routine. My goal is to allow students to work on **Math Practice 3 **each day. Grouping students into homogeneous pairs provides an opportunity for appropriately differentiated math conversations. The resource Video Narrative explains this lesson’s Warm Up- Selling Cake Pops Day 3 which asks students to evaluate an expression modeling a lawn care business.

I also use this time to correct and record the previous day's **Homework**.

15 minutes

Finding the solution to equations has been shifted in the Common Core as a goal in earlier years. With that being said, I am teaching this lesson to ensure that all of my students are on the same page and prepared for many of the concepts important to Algebra 2.

We are going to start with a quick review of solving equations. I have a list of steps that I give my students as a guide. For proficient students, this is only a loose guide. For struggling students, I encourage them to follow this more closely. My goal here is not to TEACH solving equations, they have already studied this many times. My goal is just to refresh their memory so they feel confident in the algebraic modeling portion of today's lesson.

There are four examples to be solved (shown in PowerPoint- Selling Cake Pops Day 3) which progress in difficulty.

22 minutes

Introduction

The first step is to make a list of the important expressions from the previous lesson. In the last lesson, pairs of students would write their work on a note card and bring it up to the me. Unlike the first lesson, I need all students to have the same expression(s) which we’ll build on. I write all the variations on the board and the instructional method I use, one of my favorites, leads the class to a common solution. I present a problem and then walk around checking solutions. I give feedback as needed but mainly I call out as I see correct solutions. This method works well motivating students both in effort and striving to get the solution. I view myself as a cheerleader in a way.

Breaking Even

The first thing the students do is to write three equations finding the number of cake pops that need to be sold at each market to break even (**Math Practice 4**). Breaking even is a term some students may need clarified. Once the students have found the equations, I ask for volunteers to come and write their steps on the board. Please watch my short video for more information on this process.

As a side note, calculators are an important resource for these problems. Our goal is not that the students review basic operations with decimals, therefore calculators will save time.

Profit

In the next problem, the students set the profit expressions for the Boise and the Caldwell markets equal to each other and solve the resulting equation. I try not to just tell students how to solve problems (**Math Practice 1**). In this instance, I remind them what same means in mathematics and ask guiding questions until they can solve it themselves. A student who has yet to share puts their solution on the board. It is important to watch the clock. I ask the students to explain the meaning of each step - constructing meaning in the context of the algebraic model (**Math Practice 2**), a process which will be used over the year.

The students will then compare Nampa to Boise, and Nampa to Caldwell (Math Practice 8). These should go fairly quickly since they now have the pattern. The Nampa/Caldwell problem is sneaky. The answer to this problem is a negative number. This is in IMPORTANT discussion. Once this is solved, I have the students do a think-pair-share to discuss how this answer relates to our cake pop business.

The final task asks the students to figure out how many cake pops need to be sold at each market to get a profit of $100. If there is time, I have the students explain what each step means to the problem.

Please see Section 2 for the PowerPoint.

2 minutes

I use an exit ticket each day to provide a quick formative assessment to judge the success of the lesson.

This Exit Ticket checks that the students can successfully solve a multi-step equation similar to those modeled in the lesson.

1 minutes

The first six problems are equation practice problems. The next problems asks the students to figure out how many cake pops need to be sold at each market to make $150. This is similar to what was done during the lesson. Next, they are asked to figure out, for each market, how many cake pops need to be sold from one batch (since they are baked in batches) to break even. Finally, they are asked to compare the different markets and decide which market they would choose to attend.

A note here, the Caldwell market has the smallest fees but it is also gets significantly less traffic and therefore the chances of selling of cake pops is smaller. The Nampa market is quite a bit bigger but not nearly as large as the Boise one. My mother's main market is the Nampa market. This is where she makes her highest profit. She also works the Caldwell market. She has chosen not to do the Boise market as the fees are so large and so much has to be sold just to break even.

This homework was created with Kuta Software, an amazing resource for mathematics teachers.