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Home < Work and Study Tips << G. Written work formats for developing and showing skill
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Written Formats for Developing and Showing skill
Skill and written work has to be seen to be credible. The show work formats below require you to do and record given data, formulas and figuring steps, etc, one at a time, one after another, so that you and others have a story or path to see and check, as done or later. How to Show Work in Evaluation of Arithmetic ExpressionsThe calculation of arithmetic and algebraic expressions may employ a vertical alignment of equal signs as follows.
The equal sign here means has the same value as. The repeated use of the equal sign above and below gives the mathematical version of a sentence that goes on and on, with clauses and subclauses. In the following sentence a verb is missing. The missing verb here is chased. That being said, evaluating an arithmetic or algebraic expression without using equal signs to relate them is like writing a sentence with a verb. How to Show Work when using a Geometric FormulaSteps
Rectangle Area Example:Find the area of a 12 cm by 5 cm rectangle
Solution:
\begin{eqnarray*} \def\cm{\mbox{ cm}} \mbox{Area } A &=& W \times L \qquad \quad \mbox{Write formula} \\ &=& (12 \cm)\times(5 \cm)\quad \mbox{Substitute}\\ &=& (12 \times 5) \cm^2 \quad \mbox{Simplify} \\ &=& 60 \cm^2 \end{eqnarray*} The evaluation does and records steps in an in observable and verifiable manner. Here again equal signs are present and vertically aligned. How to Show Work in Using a formula indirectlyProblem: Find the length of the hypotenuse in a right triangle with legs (two other sides) of length 5 and 12. In the solution below, the three dots means therefore or thus. The Pythagorean formula $c^2+ a^2+b^2$ is a direct formula for $c^2$ not $c$. Finding the value of c from it steps slightly away from the direct use of the formula. See Chapter 14 in Volume 2 for insights - we hope - into the direct and indirect use of formulas. Solution:
Observe how the solution leaves a trail of steps to follow.
The above solution could be improved by using a geometric symbol to indicate the location of the right angle; and using the phrase like the Pythagorean theorem says. Those improvements follow.
Departing from the verticalThe vertical alignment of equals signs becomes difficult at the bottom of a page or blackboard. In that case, use an arrow to indicate the location of the next step in a solution.
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Home < Work and Study Tips << G. Written work formats for developing and showing skill
[1] [2] [3] [4] [5] [6] [7] [8][9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23]
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Logic-Reason for all Careful Thinking Chains of Reason Mathematical Induction Responsibility Bodies-of-Knowledge |
Arithmetic - Ages 10+ |
Geometry 1 Maps + Plans Use 2 Euclidean Geometry 3 Rct +Polr Coordinates 4 Lines-Slopes [I] 5. What is Similarity |
Algebra Starters - the base 1. Better Work Format 2. Solve Linear Eqns 3. Computation Rules 4. Axioms, Item 3 Viewpnt 5. Formulas Backwards |
More Algebra Logarithms-ax & m/nth roots Five Polynomial Operations Quadratics Geometrically Functions || Vectors too Arith. Skill Check+Answers |
Calculus Prep/Preview What is a Variable Why study slopes Why factor polynomials Complex Numbers Limits + Continuity |
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