This application isn’t real world but it’s real enough world. It’s not real world in the sense that nobody needed to figure out this exact question at their job. But it’s real enough world because a financial advisor at a well known wealth management firm told me he does calculations like this a lot. He simply invented the following scenario because he thought young kids could relate to it. I’m not sure if they can – but I’m damn sure they can learn from it. Since he’s the expert I’ll just leave it all in his words:
Additionally, here are some well- known abbreviations that I’ll reference in two scenarios:
PV = present value
FV = future value
N = years to goal
i = assumed annual growth rate
PMT = annual payment
Scenario 1 – When his son is age 18, a dad opens a Roth IRA for the boy with a $1000 investment (PV). The dad tells the boy “I’m giving you this money under one condition…and that is, you must contribute $600 per year (PMT) and leave it alone until you turn age 65, which is 47 years from now (N). We’re going to invest the money in an aggressive growth stock mutual fund that over time, I expect, should grow 9% per year on average (i). At age 65, I expect your account value will be in the neighborhood of $433,535 (FV).” Pretty amazing what time and compounding will do, huh?
Scenario 2 – A 13 year-old girl wants to purchase a used car at age 18, 5 years out (N). She expects the car to cost $8000 (FV). So far, she has saved $3000 (PV) and wants to know how much she must save annually (PMT) if her money is invested at a 4% annual rate (i). Solving for PMT:
PV = $3000
FV = $8000
i = 4%
N = 5 years
PMT = $803.13
I only ended up using scenario 1 and my teacher move was to block out the $433,535 and have students go through the estimation process about that account value after 47 years. What’s it going to be? Give me a couple dollar amounts it definitely won’t be because they are too high or low. Brave guesses only. (I heard Dan use the term “brave” after prompting for an estimation and it works well).
I will categorize this post as “sometimes you just need a worksheet”. #SYJNAW for my twitter peeps.
I have always kind of disliked teaching the circles unit in geometry because of all the different rules – tangent / secant angles, chord-chord sides, chord-chord angles, blah blah. This year I put together a learning segment on circles that involved satellites in geostationary orbit. It was based on my experiences working at Lockheed Martin and my engineering background. I will write about it when I have time. But for now I will just attach a couple worksheets I made of problems that I put on a homework, or threw in a test. I figured I would just share these, because you know… some times you just need a worksheet.
These problems themselves involve tangents, central angles, and trig functions. The actual learning unit is very similar, but requires the students to contextualize and decontextualize. So without further comment – here’s some of the practice problems I used:
The Goods: (sorry I only have pdf’s, I create things with Adobe Illustrator)
I decided to remix the Math Hospital. All the steps are the same that I outline in my original post about the activity, which can be found here. The only difference is the handout, where I now embed the problem that we are fixing into the worksheet. This allows students to circle and point to the things that they like, or believe are right or wrong. I also have them fix the patient (correct the problem) right there on the worksheet.
Sell the hospital. To have them quite down, tell them the patient is sleeping. If correcting the problem becomes homework, say “I want to have this patient looking healthy by tomorrow”. And so forth…
I’ve done this in groups of four, but typically it is done individually.