LARN 15.5

LARN Unit Conversions

Start the following in class:

1.  Connect to the internet and log into your class section for which your registered at www.visionlearning.com .  If you do not log into your class and section but choose to ignore these instructions and take the quiz by accessing the Library menu at the right side of some of the Visionlearning pages, your quiz scores will not be recorded and your teacher will not be able to credit your work!

a. Select the module on the left about unit conversion by dimensional analysis.

b. Use your Learning Log to record Cornell notes or a study guide.  For the price of gas conversion problem, write down each factor including its units and divide out identical units that appear in the numerator of one factor and the denominator of another factor.

c. For the price of velocity conversion problem, write down each factor including its units and divide out identical units that appear in the numerator of one factor and the denominator of another factor.  (Without Flash software installed on your computer, the velocity conversion hyperlink does not work, so you needn’t bother to click on it.) Circle or box in the number and unit of the calculated result.

d. Note that each quantity has both a numerical part and a unit of measure.  Write down each factor including its units and divide out (cross or “cancel” out) identical units that appear in the numerator of one factor and the denominator of another factor.

[Although the author and our textbook authors in different places express fractions with both a solidus ( /) and a horizontal line ( _____), using only the horizontal line ( _____) makes for a clearer presentation in which units above and units below in the various factors are arranged in such a way that only one numerator or one denominator or both does not cancel out.  We will want to be strict with ourselves in writing each conversion ratio with a numerator quantity above the horizontal line and the denominator quantity below the horizontal line.  When we use the horizontal line ( _____) to express fractions, we can easily and clearly divide out (cross out) units that are the same.]

e. Circle or box in the number and unit of the calculated result.  What you have recorded on your paper on the left and right side of the equal sign is the problem’s “setup” and “answer“.

        f. As an example, in your learning log record the setup for this question:

              Word problem: How many nickels are in $6.70?

Translate the problem

into a setup:                      ?      nickels            =         $6.70 x   100 pennies   x    1 nickel___  =  134 nickels

                                                                                                           $1.00                   5 pennies

Note that the setup is the solution to the problem.  What is typically called the answer to the problem is simply the outcome of renaming our result by carrying out the indicated mathematical operations.

g. If you are a registered user of www.visionlearning.com, double check that you have logged into your class and section, and then click on the Questions and Quizzes tab and answer the online questions.  At present there are errors in two questions which each ask about setups that have not been given in the problem, so you should skip those questions.

h. When you are finished taking the quiz, click on Score Quiz button at the bottom of the page.

i. Take or retake the quiz until you understand the quizzed material at a 100% proficiency.  Since there are errors in two questions that are nevertheless scored automatically, at present 5 out of 7 questions correct or 71% represents 100% proficiency.

2. The required journal focus topic, JUC, for today is:

When doing a word problem that can be solved by using one or more conversion ratios or comparison rations in science, what is meant by the instruction to “show your work or show your setup”?

[Hints:

a. How did you show the setups in the Visionlearning activity that you just finished?

b. This manner of exhibiting the work was first shown to you in Step 2 (labeled Calculate Solve for the Unknown) of Sample Problem 1.1 on page 30 of your text.]

3.  In your Learning Log, record a similar setup, but first label the units of what we are looking for with a ? followed by the unit of what we are looking for on the left side of the equal sign.  Also for simplicity, show the setup on one line with all the needed conversion factors shown being multiplied there in such a way that units that are not needed (as shown on the left side of the equal sign) divide out to give the units of the product on the far right.  The numerical result for the product shown in red below is then just the product of the numerical values of all of the factors, shown in black ink below. 

? minutes = 8 blocks  1 mile___ 20 minutes  = 16 minutes

                                             10 blocks              1 mile

Note that when all the units have canceled on the right side of the first equal sign, what remains is our answer.  What you have recorded on your paper on the left and right side of the first equal sign will, from here on out, be termed the problem’s “setup” and “answer”.

Recommended for those who have time left in their 45 minute study period, but not required of all:

1. If you need more assistance on understanding this method of showing how a problem is solved, please refer to Appendix C in your text, pages R66 through R68 where you will find an article entitled Conversion Problems and Dimensional Analysis. There are six problems given on page R66.  On pages R66 and R67 study how the conversion factors were selected and set up such that the units in the problem divided out to yield the units of the sought for quantity.  For each problem, except that the ? followed by the unit of what we are looking for on the left side of an equal sign is missing, the given quantity times the labeled factors shown make clear how each problem was solved with unneeded units being divided out and with the resulting quantity being given to the right of the equal sign that follows the factors. If you take notes on any of these problems, include a ? followed by the unit of what is being sought on the left side of an equal sign for each problem. The result for each problem is the problem’s setup and resulting answer.  Please encircle or draw a box around each answer.