Met a math teacher today. After some lighthearted discussion, we found some mutual interests. I need to know people like him to solve those periodic geometry questions that come up. He wants someone like me to walk into the classroom for an hour and talk about why even us hammer swingers need math skills. So I agreed.
This fall, I’m going to go talk to high school kids. But I’d love ammunition. So this is a call, a BEG, for those worksite generated math issues of “how the heck do I figure that one?”
Jerrald better drop in.
I can think of a couple. How to define (and cut) an accurate oval. The difference, and how to cut, an elliptical vs parabolic arch. Or I want to put an arch between point A and B with a height of C. Whats the radius of the circle?
What have you run into?
“If you pick up a starving dog and make him prosperous, he will not bite you. This is the principal difference between a dog and a man.” – Mark Twain
Replies
3/4/5 triangle. Numerous applications.
Calculating roof area for ordering shingles.
Calculating rafter length and cuts. Then tell them about rafter squares.
Calculating stair treads and risers.
I've got lots of ideas. What level math class(es) will you be addressing? Will you be speaking to students who aren't especially turned on to math?
Stairs are a biggie -- takes a fair amount of figuring if you want them to come out even and finish off nicely.
Calculating areas for siding/drywall/painting.
Calculating the volume of a footing -- lots of folks seem to have a mental block on this one, though it's quite simple for the typical round footing.
Showing them framing square with stair stops is good. Showing them something like a rotary laser level would be good too. Or a transit/contractor's level. And a water level would bring a little physics into it.
The one that I use most is x - x - radical 2 for a 45 degree triangle. Essentially, the two legs of the triangle represent x and for a 45 degree right triangle, the hypotenuse is then equal to x times radical 2 (radical 2 is the square root of 2). Radical 2 is roughly equal to 1.41. So I go around all the time checking myself by multiplying my leg dimensions by 1.5.
Try it out.... for a 45 degree rectangle with leg dimension of 27 what do you get for the hypotenuse? Roughly 40 or so... maybe a little lighter than that so maybe close to 38.5.
The real answer is 38.183766184073566317645595553662......... or so.
There's also one for a 30 degree right triangle.
Rob Kress
"I can think of a couple. How to define (and cut) an accurate oval. The difference, and how to cut, an elliptical vs parabolic arch. Or I want to put an arch between point A and B with a height of C. Whats the radius of the circle?"
Uhhhh......if yer gonna be covering this stuff, can you ask if they've got an extra seat in there for me? Could use it.
Kidding about the extra seat part.
Not kidding about the "could use it" part.
Maybe you should just bring me in with you. You'd only have to stand there and point..."See! This is what happens when you don't pay attention in math class! Watch this idiot screw up this pile of stock trying to figure out how to trim that arch." :)
memorize .03937..mm to .000 it helps in all things. Cuz soon we'll all be metric..{GD&R}
Spheramid Enterprises Architectural Woodworks
Repairs, Remodeling, Restorations.
how to figure cubic yard too.
Man I hope your wrong!
about which part? it really IS .03937x MM= our way in thousandths..
Or ya mean the impending mathematical takeover? The one where a gallon of gas will be listed in Imperial gallons per Euro..so it seems the price is not going sideways up the wazoo?
It's a bushy tactic..soon the signs will be back to a reasonable number..like 98.2..."see gas is cheaper"
ooops, I waxed political..maybe thats cuz my F350 now takes a c note to fill.
Spheramid Enterprises Architectural Woodworks
Repairs, Remodeling, Restorations.
impending mathematical takeover
That part!!!
I cant make the change. Too old, set in my ways, I dont know what excuse but I'm sure I can come up with one.
My boss is French(man I probably shouldnt say that in here) he's always telling us that we'd be better off with metric, then he goes off on a half hearted tangent about those damn Brit's screwing it all up!
Doug
Well, first of all, you're HIRED. I need all the help I can get not to look too silly. And second, man, why do you think I'm asking this all now. I need to have the summer months just to figure it all out so I can present it. Some things I use. Some things I'm reading and saying . . . uhh. Ok. How DO you do that? Yeah. We all could use some of it, I suspect."If you pick up a starving dog and make him prosperous, he will not bite you. This is the principal difference between a dog and a man." - Mark Twain
Another one I thought of (and have no answer to)
You're building the house, you're putting slate on some of the floors. Mfr says you need a floor with no more than L720 deflection. You know your Ijoists are L360.
Maybe Boss being a truss guy knows something about deflections. So how do you know that you need to add 1/2 or 5/8 or 3/4 ply . . . moreover, is that process something that can be extrapolated into a mathematical process, or in laymans terms, can I make an essay question out of it?
Speaking of Boss. Live loads and dead loads on roof framing members."If you pick up a starving dog and make him prosperous, he will not bite you. This is the principal difference between a dog and a man." - Mark Twain
Baluster spacing with code max 4" space between.
Volume of piers and footings
Conversions. They should be able to convert square inches to square feet, etc., volume conversion from cubic inches to cubic yards. They should have gotten this during a chemistry class, if they took chemistry.
The eighths, .125, .375, etc. Faster than dividing on your calculator
Figure drop of waste line over a stated length of run
Figure slope of porch for a given length
Angles for other than a square, such as bevels for an octagon column constructed of separate boards
Compound angles, such as for crown molding
Ratios, such as 1 part water for 3 parts leveling compound, when the only known identity is the weight of the compound in pounds. (More conversions, gallons into pounds, and although this is a well known number, it might be good to derive where it comes from.)
and the drag on a pendulum..like plum , bob..lol
Spheramid Enterprises Architectural Woodworks
Repairs, Remodeling, Restorations.
The Golden Mean - 1:1.618
If you're good, you can teach them three different ways to derive it.
Edited 5/26/2004 9:45 pm ET by Uncle Dunc
If you're willing to refresh our collective memories as to how to derive it . . . by all means. I know it's in a book somewhere around here."If you pick up a starving dog and make him prosperous, he will not bite you. This is the principal difference between a dog and a man." - Mark Twain
Derivation #1. No algebra.
The Fibonacci series starts with two numbers, 0 and 1. Each subsequent term is the sum of the two previous terms. So the first 13 terms of the series are
0 1 1 2 3 5 8 13 21 34 55 89 144
Any two adjacent Fibonacci numbers are an approximation of the Golden Mean. The farther you go in the series, the more accurate the approximation. 89/144 = .618055..., which is correct to four decimal places.
Derivation #2. Some algebra, but you don't have to understand it.
1. Enter any number greater than 1 in your calculator.
2. Press the invert key, 1/x.
3. Add 1 to the result.
4. Repeat steps 2 and 3 until you have as many decimal places as you need.
Example #1:
1.6
1.625
1.615384615 - 2 correct decimal places after 2 iterations
1.619047619
1.617647059
1.618181818
1.617977528
1.618055556 - 4 correct decimal places after 7 iterations
The closer your initial value is to the correct value, the faster the process will converge, but it can be entertaining to watch it converge from very extreme values. (May not work if you start with a value very near the calculator's limit.)
Example #2:
11
1.090909091
1.916666667
1.52173913
1.657142857 - 1 correct decimal places after 4 iterations
1.603448276
1.623655914
1.61589404 - 2 correct decimal places after 7 iterations
1.618852459
1.618153365
1.617988395
1.618051405 - 4 correct decimal places after 11 iterations
Derivation #3. Real algebra.
The definition of the Golden Rectangle is that the ratio of the short side to the long side is equal to the ratio of the long side to sum of the short and long sides. S/L = L/(S+L). Set the short side to 1 and do a few algebraic manipulations. (I use ^ as the power of operator.)
1/L = L/(1+L)
1 + L = L^2
0 = L^2 - L - 1
This is a quadratic equation of the form
ax^2 + bx + c = 0,
which can be solved by the quadratic formula
x = (-b +- sqrt (b^2 - 4ac)) / 2a
See http://mathworld.wolfram.com/QuadraticEquation.html for the more familiar algebraic notation.
In our quadritic equation, a = 1, b = -1, and c = -1. So
L = (-(-1) +- sqrt (-1^2 - 4(1)(-1))) / 2(1)
L = (1 +- sqrt (1 + 4)) / 2
L = (1 +- sqrt (5)) / 2
Two cases, 1 + sqrt (5) and 1 - sqrt (5)
case 1 L = (1 + 2.23607) / 2 = 3.23607 / 2 = 1.61803
case 2 L = (1 - 2.23607) / 2 = -1.23607 / 2 = -0.61803
A negative length doesn't makes sense in this context, so we discard the second solution and keep the first.
GEOMETRIC GOLDEN MEAN
I consider my math skills to be very weak. For awhile I was good in math but that all went south in 10th grade.
Consider the following case:
Putting up soffit. The first piece must be cut to fit the angle created by the soffit running down onto another roof.
It is almost second nature to me to hold the uncut piece at the point that the angle begins. One corner needs to move (for example) six inches to get to where it should be.
Mark six inches back from the other corner and draw the line from that mark to the first corner. There's your cut. Perfect fit.
(Maybe there's other, easier ways).
My helper is completely unable to do this. I went through it several times and he still can't manage it. He's got several years in the trades (he's hung a ton of drywall and installed a lot of EIFS) and he seems to be of at least average intelligence, but he is simply incapable of seeing how to determine the angle to cut.
I haven't asked him, but I bet geometry was not a class into which he put a lot of effort.
I would have never considered my ability to find the proper cut even worth mentioning until I watched him struggle with it. Maybe I can do it because I loved geometry up until 10th grade.....
Long story short, maybe geometry helps one learn how to visualize shapes and mentally manipulate them.
Rich Beckman
Another day, another tool.
>> ... maybe geometry helps one learn how to visualize shapes and mentally manipulate them.
Maybe. Maybe not. I aced geometry. 100% on all the tests. Got a B for the class only because I never turned in any homework. But it's not helping me visualize the soffit cut you're describing.
".. it's not helping me visualize the soffit cut you're describing."
Yeah, but that is more likely the fault of my poor writing. Using my even poorer computer "CAD" skills, I created this...
Perhaps it will clarify.
Rich Beckman
Another day, another tool.
Sorry, I can't read .doc files.
try this....
Very nice! I hadn't heard of that one before.
TenPenney: Thanks for the conversion.
I once got a commission to make a geometry cart for a museum. They wanted sight impaired folks to be able to get it, too. Here's how we generated the golden section. The pyramid is Cheops',and red building is the Parthenon. Took me 3 tries to make it through high school geometry, but after I made this stuff, even I got it. Don't worry, we can fix that later!
Dang, I shoulda learned how to post pics<G> Don't worry, we can fix that later!
One thing to remember is THE UNITS!
Keep them in the equations! If they're not the same and need to be, multiply by a factor of one. We all know factors of one: 12" per 1 ft, 16 ounces per 1 pound, 25.4 mm per 1 inch, 16 fluid oz. per pint, 2 pints/qt, 4 qts/gallon, etc.
The word "per" in mathematics means divided by. For the factors of one, they can be flipped with either number (keep its unit with it) as the numerator (top) or denominator(bottom). It's 1. Anything x 1 = that same anything.
that is whay I have to remember so few conversion factors. I can usually derive what I need from what I have.
Convert MPH (miles per hour) to furlongs per fornight, if you have too much time on your hands.
I tutored my neighbor in algebra one time. Before she even had her first class, I told her to memorize y=mx + b.
Before long, during our tutoring sessions, every question she asked me, I could answer with y=mx + b. Every single one. About the 3rd session, it sank in.
For physics, F = ma. and you can't push a string.Pete Duffy, Handyman
Of course you should talk about all the practical applications of math: trig, geometry, adding and subtracting........
But math is more than those practical applications. It's a discipline and a way of thinking. Its an accumulation of known rules that work together in order to solve new problems. I'm sorry, but I can't explain this very well here. I've got a math background that came with my engineering degree many years ago. The "structured" thinking that are part and parcel of math and engineering have enabled me to enter the construction/speciality fabrication trade with little extra training. I suggest that you get into a conversation with the teacher.....talk about what you do, and ask him about his math. Don't talk about the applications or actual problem solving.....talk about how the work each of you do affects your thinking, your reasoning.
I don't know if any of this makes any sense to you. I'm talking about drawing parallels between math and construction. You use boards and nails, he uses theorums and laws. But you both build things. Talk about the philosophy and the beauty of building.
If you want me to ramble some more, let me know. Maybe some other folks can chime in along this vein.
No, I totally get what you're saying. I'm not sure that the invitation to talk to the class was to discuss philosophy, but I still know what you're saying. He is pretty much looking for someone like me who is in a trade that most high schoolers probably don't assume requires a lot of math skills - to show that it really doesn't matter where you go. All this stuff has it's applications.
To be blunt and self deprecating - hey, construction is viewed as blue collar. Some kids say hey, I can swing a hammer. I don't need no education. And if all they ever want to do is be the guy that just does laborer work, they're right. But not many really set their aspirations there. We all dream of doing, becoming more. So a remodeler, a guy who yeah, he still swings a hammer, but he's not a dummy and he's not the stereotype in the head of a 17 YO. . .
My degree is criminal justice, and I spent time as a military cop. You want to talk about things that change your thinking and reasoning . . .heh heh. I'm not too forgiving about people who break rules, for example. But that's waaaaaaaaay off topic."If you pick up a starving dog and make him prosperous, he will not bite you. This is the principal difference between a dog and a man." - Mark Twain
Sounds like you're going to do these kids some good. You're to be commended.
But about this rule breaking thing........laws I don't break, rules I break all the time!
Aside from all the ideas already mentioned, I've got a beam sizing example. Relates length depth thickness and the load a beam can support. Don't know how super accurate it is, but it demonstrates that blue collar carpenters need to know a thing or two about algebra. Would be appropriate for an Algebra I or Algebra II classroom. (I use it in both my Alg I and Alg II classes)
The example doesn't differentiate for species or anything but it just gives a good general idea that the math concepts we learn in school are important. Maybe get some ADA info too. I use ADA info when we discuss slope. Set up a scenarios where a business owner needs to build a ramp in x feet, what will the slope be, does it meet ADA specs, etc.
I cut equilateral triangles out of plywood to screw to the floor and ceiling to secure hollow columns. I needed to know the length of the triangle sides relative to the diameter of the column. Turned out to be square root of 3 times the radius. Had someone smarter than me figure that out, so I can't tell you how he did it, but it worked perfectly. Bill.
And don't forget that to make a circle into a hexagon, or divide it into 6 equal sections (which will allow you to go to 3 sections, or 12....) use a compass set at the radius of the circle, and "flip" your way around the circle......
and the distance from a corner to the center of a square is what ya need to make an octagon, walk off the steps, from a corner.
Spheramid Enterprises Architectural Woodworks
Repairs, Remodeling, Restorations.
What about the algebra involved in figuring whether I will make any money on this job given costs of materials, transportation, labor, ect? Clearly not the fun magic tricks you get from geometry and such, but a really useful and everyday calculation.
dc
a standard equation for my guesstimates is materials times three..then 20% and then 20% more to that, for guesstimating it mostly comes out close to what all crunchin turns into..for me, maybe not someone else...
Spheramid Enterprises Architectural Woodworks
Repairs, Remodeling, Restorations.
Even before math skills, to be a contractor, you need arithmatic skills to count boards and do estimates and billing or to track same for the records. This arithmatic skill is spelled M O N E Y and it gets their attention that way.
Welcome to the Taunton University of Knowledge FHB Campus at Breaktime. where ... Excellence is its own reward!
A friend of mine called me recently because he needed new bases for his porch columns. I said I need the column diameter. he said how do I measure that? I told him to wrap a tape measure around the column then divide that number by Pi (3.1416). Circumference / Pi = diameter
wanna really have fun with math,,use two framing squares and a set of gauges..make a big caliper..then slide em around easc other and look at all the number alignments ya can create..
oh, that's how I woulda measured the colum base..too.
Spheramid Enterprises Architectural Woodworks
Repairs, Remodeling, Restorations.
Yeah, thats one way. But try to explain that to a guy who's lucky he has a tape measure
I think the two most common calculations are areas and volumes.
Areas for sheathing, flooring, roofing, wallpaper, paint, lawns, asphalt, pavers, siding, housewrap, concrete block, brick, etc.
Volumes for concrete (including round forms, like sonotube), gravel, fill dirt, etc., especially irregular volumes, such as calculating enough fill to bring a driveway to a certain level.
Conversions, such as measuring stone and soil in cubic feet but ordering by tons, converting feet to inches, square feet to roofing squares, cubic feet to cubic yards.
Proportions, such as when you need 2 quarts of water for a 50 lb bag of grout, how many ounces of water for 10 pounds of grout? Applying fertilizer, when the soil test says to add 13 pounds of nitrogen per 1000 square feet, how many pounds of 10-5-6 fertilizer is that? Mixing two part paints, when you add 1 quart hardener per gallon of resin, how much hardener to mix with a quart of resin? Or how much of each if you need a quart total after it's mixed?
Business calculations. Borrow $2000 at 15% for two years, what are the payments? If offered terms of 2%/10 net 30, is it better to pay in 10 and save 2% or leave your money in the bank for the extra 20 days and pay full price? Which is better, 0% financing for 4 years or $1000 rebate? How do you add up all your costs, overhead, and profit to decide on what your charge out rate should be? If you have $2000 on a credit card at 1½% per month and you pay only the minimum payment of $50 per month, how long will it take to pay it off and how much total interest does it cost you?
5 milkbones to whoever can answer all of those <G>..um, correctly.
Spheramid Enterprises Architectural Woodworks
Repairs, Remodeling, Restorations.
You missed one of the basic conversions/ ratios,
Hours to dollars!
;)
Welcome to the Taunton University of Knowledge FHB Campus at Breaktime. where ... Excellence is its own reward!
Make metric easy to visualize:
One liter = about one quart
One meter = about a yard
One kilometer = about a half mile
One kilogram = about two pounds
One cubic centimeter = the size of a sugar cube
~Peter
"When having a wedding celebration in an occupied country, do not allow your guests to shoot guns in the air." -- Jerry Pournelle
Bidding, overhead, markup, down payment, draws....contractor business math.
MES
never leave out the Golden Ratio/rectangle and how it applies in art, nature, and design.
Welcome to the
Taunton University of Knowledge FHB Campus at Breaktime.
where ...
Excellence is its own reward!