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 just can’t type “real-life” without quotes because I’m yet to resolve what “real-life” means in a math class. But for this post it means – “Math someone needed to do at their job”. And in this post that someone is my wife – who much to her distain and my joy – does a lot of geometry as a project manager at a construction firm.
So here’s what we need to know: How much cement is needed to make that border? We need the answer in cubic yards because you buy cement in cubic yards.
The image below provides some of the context for the problem – The cement border is being used to circle an existing tree.
I was actually surprised how open the middle was on this problem. Yet students used two main strategies. The first was the standard subtract the areas and multiply by the height, or they subtracted the volumes of both cylinders directly. The second was the find the perimeter, think of the wall as a rectangle (dimensions of 2*pi*r X 1′), find the area of that rectangle and then multiply by the height.
One student using the second strategy used a radius of 14ft and got a solution of 16.2 cubic yards. He told me he knew the answer would be a little too small because of only using the inner radius. Another students used 14.5 and got the same solution as the area subtracting syndicate.
Converting from cubic feet to cubic yards is a great time to practice your perplexed I wonder why you divide by 27? face.
By the way the wall ended up costing around $35000. I can’t believe how long I would have to work to put a wall around a tree 🙁
Posted in #industry, #technology, geometry
Tagged annulus, area, cylinders, geometry, industry, IndustryMath, math1, math2, open middle, real-world, volume
When I first started this blog the idea was to categorize assignments based on a series of twitter style hashtags, which would ultimately allow a teacher to quantify how differentiated their lessons had been – in a macro sense at least. I have not really stuck to that idea, but one of the original hashtags I had was #industry. The purpose of #industry was pretty simple – someone had to do this in their job.
I was hoping that #industry would end up as a collection of problems that come directly from people’s work experiences. These experiences would be served to student’s unedited from the workplace to the classroom. Inherent in this hashtag would be the answer to the question “why?” because presumably anybody doing something for their job would have a clear reason as to why they were doing it. (presumably?)
So here’s the problem: My fiance is a project manager and she had one site that was 3/4 an acre and a price from that site for $54,000 for some work. Then she had another site that was 2.5 acres and needed to know how much that same work would be for the larger site. That was the first thing she needed to calculate, but she ended up just wanting to know how much 1 acre was worth, so she could scale it to all her other jobs.
Here’s an error analysis angle to this question – To scale the cost for 1 acre she had initially multiplied 54,000 by 1.25 and she was genuinely curious about why that did not work. Hhhhmmmmm…