Our first Real Trades Math (“RTM”) Question
Moving things around in your head so you can figure out the fastest, safest way to get the job done is a common skill journeymen apply on a daily basis in their careers. But it’s not a skill often developed in academic math classes, outside of geometry. What we are about to explore is our first Real Trades Math problem that I talked about in the Overview for this Trades Math class.
RTMs use multiple parts of the brain, which is why they’re often simple to say, like an “Are You Smarter Than a Fifth Grader” question, but deceptively difficult to do. How to communicate something that requires multiple parts of your brain, remotely online, will be very challenging, so here’s some advice.
How to Take Notes on a RTM problem
Finding the best way to learn how to solve a feet & inch missing side problem will require you to find a notetaking technique that works for you. Color highlighting, writing down a list of numbered steps, translating, writing down and summarizing what you read here, and during our Zoom meetings, into your words, that’s how you solve an RTM. You can’t just scroll down and believe you now understand and can apply the information in the paragraph. You have to take something in your brain and make your body create a physical expression of what you know. And that’s what construction trades apprentices do all of the time, getting closer to becoming journeymen. So let’s take a step.
Finding Missing Sides of a L Shape
One of the missing sides is a horizontal side (left-right), the other a vertical side (up-down). Also notice that two of the sides, the ones that touch in the bottom right corner, are bigger than the other four sides. Knowing these two things allows us to apply a couple of rules when solving a missing side problem:
- To find out an unknown left/right (horizontal) side, you can only use other left/right sides.
- To find out an unknown up/down (vertical) side, you can only use other up/down sides.
- If you’re finding the big side, ADD the small sides.
- If you’re finding a small side, SUBTRACT the small side from the big side.
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Let’s apply the rules above to the L shape diagram to the left.
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TRICK: L shapes can apply the rectangle perimeter formula: add the two big sides, and double the sum.
It doesn’t matter which side is the length or width, mathematically speaking. The convention is the Length is the Longer side.
We’ll look at two more shapes in class, a C shape and a T shape, so I won’t sketch out each detail here for them.
C Shape
C Shapes are the most difficult of the missing side problems, because you need to find an intermediate length in order to find the missing side. There are two paths to find an intermediate side to a C shape: the interior and envelope methods.
- To find the missing horizontal side, either ADD 10’10“ and 12’3“ and then SUBTRACT the sum from 49’2“, or SUBTRACT both 10’10“ and 12’3“ from 49’2“.
- To find the missing vertical side, either SUBTRACT 11’9“ from 24’3“, and take that difference away from 21’2“, (interior method) or, SUBTRACT 21’2“ from 24’3“, and take that difference away from 11’9“ (envelope method).
TRICK: There is no trick for a C Shape.
T Shape
- To find the missing vertical side, either ADD 15’6“ and 14’10“ and SUBTRACT the sum from 44’2“, or SUBTRACT both 15’6“ and 14’10“ from from 44’2“.
- To find the missing horizontal side, ADD 17’9“ and 18’5“, and then SUBTRACT 23’3“ from that sum.
TRICK: T shapes can use the rectangle perimeter formula, just like the L shapes. To find the missing big side, add the two small sides (s → B).
To the Learnbox!