Trade mathematics and unit conversions
Exact conversion factors and what a rounded one costs, fractions of an inch, pitch and true length, girth, weight, pieces and thermal movement worked with units and rounding written down, and the common take-off errors with how to catch them.
4 lessons · about 49 min · 13 diagrams · 4 videos
Version 1.0.0
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0 of 4 complete
Lesson 1 · 11 min · 10 slides · 10 questions
Trade mathematics and unit conversions: principles and terminology
Why units travel with every number, which factors are exact by definition, what a rounded factor costs, how an inch divides to sixty-fourths, how pitch, slope and the right triangle relate, and the safety rules that rest on slope and setback.
You will be able to: Define exact and rounded conversion factors, read fractions of an inch as decimals and millimetres, state pitch in its four forms, and name the roof-slope and ladder rules that depend on the arithmetic.
Not startedStart →Lesson 2 · 14 min · 11 slides · 12 questions
Trade mathematics and unit conversions: materials, standards and design constraints
NIST, ASTM and manufacturer sources behind the numbers, why a table can print a rounded factor, rounding down to fit and up to order, AFS limits in inches and millimetres, 24 ga weight, and metal expansion coefficients with their units.
You will be able to: Name who defines the unit factors and the rounding rules, choose a rounding direction by purpose, write AFS limits in inches and millimetres, and match a material coefficient to its temperature unit.
Not startedStart →Lesson 3 · 12 min · 11 slides · 9 questions
Trade mathematics and unit conversions: methods and worked application
A seven-step method, then worked examples from decimal feet to the tape, a coping blank width, the 48 in sheet check, area and weight, a sloped edge, a 64 ft cut plan and thermal movement, each with its units and rounding written down.
You will be able to: Apply a seven-step documented method to tape readings, girth and Blank Width, sheet fit, weight, true length, pieces and billed length, and thermal movement, with units and rounding stated.
Not startedStart →Lesson 4 · 12 min · 11 slides · 9 questions
Trade mathematics and unit conversions: defects, verification and case study
The common math defects in a flashing take-off, how computers round, a constructed L-shaped coping take-off with four planted errors and their corrections, the estimate-and-reverse check, the record to keep, and the limits of calculator results.
You will be able to: Diagnose plan-length, rounded-factor, early-rounding, wrong-direction, temperature-change and girth-convention errors, correct a constructed take-off, and record the evidence of a calculation.
Not startedStart →
Practical task
Build a documented calculation packet for one coping of your own design: convert a metric drawing to inches with exact factors, find its Blank Width, weight, true length, pieces and billed length, then check it by estimate and by reversing it.
Hand in
- A decision rationale: the units you worked in, the factors you used, and the rounding direction you chose for each result and why
- A marked-up sketch of the coping section with every leg, the hem types and the Blank Width written in fractions and in millimetres
- An assumptions sheet with units: material and thickness, leg lengths, piece length, run length, pitch and temperature range, each marked as from the drawing or assumed
- A quality checklist: the eight-line math check card, filled in with your numbers
- A defect analysis: one error planted in a friend's take-off (plan length, rounded factor, early rounding, wrong direction, temperature change or girth convention) and the correction, with the size of the error
Rubric
| Criterion | Meets the standard when |
|---|---|
| Units and factors | Every number carries a unit, and every conversion uses 25.4 mm per inch, 0.3048 m per foot or 0.45359237 kg per pound. |
| Rounding | Nothing is rounded until the end, and each rounded result states its direction: down to fit a limit, up to order, nearest 1/16 in for a shop mark. |
| Blank Width | The legs and the hem allowances are both shown, the hem types are named, and the blank is checked against the 48 in limit. |
| Sloped runs | A sloped edge uses its true length, found with the slope factor, and the plan length is not used as an installed length. |
| Verification | An estimate was made first and the answer was reversed to the starting number, with the check written down. |
| Safety | The packet states that calculator results are informational, and sends slope classes and ladder setbacks back to the CFR. |