## December 3, 2017

### Budgeting with Matrices

I've been trying to weave some big conversations about life and social justice into math class. I wanted to use matrices to analyze some complex data but it just wasn't falling into place nicely. Instead we did a fairly simple word problem about budgeting for young adults and had a decently nuanced discussion about it.

The point of using matrices is to organize data and reduce the repetitive nature of computation by having the calculator do the calculating. This was the first assignment where I allowed students to use a calculator so I had them do out all the computations for one person first to make sure they were using the calculator properly.

The Assignment. The Calculator Instructions.

They had a hard time with the "5 days a week, 3 miles each way" part, mostly due to a lack of reading that sentence. Many kids left the three values separate at first (income, meal spending and travel spending) which was fine because #4 has them go back and compare. So the front of this handout is a decently scaffolded matrix word problem. Standard fare. The back is where we move beyond matrices into real world application.

It turns out poor Sarah doesn't have enough money to cover rent, let alone groceries or fun. Jose has just enough for his essentials and Ana has what seems like plenty of money to spare. It was interesting to see what recommendations students made for each person to save money. Here's the first round of suggestions:

We discussed which of those options were reasonable. Is someone going to walk 3 miles to work? Moving or getting a different job makes more sense. I heard students talking about living at home or in the dorms though interestingly no one wrote that as a suggestion. Fixing the car (Jose) and buying a car (Ana) are good ideas in theory, but if someone is living in poverty and barely has enough money to pay rent they won't be able to save up the money needed to make a smart long term investment.

In Massachusetts the minimum wage is \$11 an hour, so there are lots of higher paying jobs out there, but these are kids who just graduated high school so they don't really have many better options. This is where we talked about why anyone would want to be like Sarah (going to school full time and in debt) when they could be like Ana (working full time). Yes, it looks like Ana is doing fine right now, but we haven't factored in any of her other expenses and she doesn't have much potential for getting a better job. We talked about how training (not necessarily college - we have several certificate programs at our school for automotive, child development, culinary and other trades) is necessary to get a well paying job.

This conversation gets us all the way through the beginning of #8 (who would you be and why). Students didn't write much for their "detailed budget" so the next class their opener was to list things people spend money on. Here are the results from my three classes:

We had a good discussion about what people absolutely need and what they feel like they need. I still didn't get great detailed budgets on the resubmitted assignments but I did get a bit more thought than the first round. I wonder what the cost/benefit would be for spending the time to have them research and make a complete budget. I think it would take more time than I want to spend in Algebra 2. All of the seniors go to a reality fair where they're given a salary (based on the job they choose) and have to go to a variety of booths to spend money - some are choice (pick your car) and some are random (get invited to a destination wedding, spend lots of money!). It's a cool day.

Overall I'm happy with this assignment, it shows the benefit of using matrices to avoid repetitive computation, asks student to do some thinking about their own futures and hopefully develops a bit of empathy for people in poverty for the kids who aren't already keenly aware of how difficult choices can be when money is tight.