OBECTIVES:  After today's lesson students should be able to...

• demonstrate proficiency in factoring numbers to prime factors
• reduce fractions using prime factor and common factor technique
• recall specific, required unit comparisons (see handouts)
• perform one and multiple-step dimensional analsysis problems by constructing and solving dimensional analysis problems according to demonstrated algorithm

CLASS LESSON

1. Read Mars orbital article (demonstrating why recording units is important)
2. Steps to building understanding in this lesson:
   1. Remind students what prime numbers are:
      1. Numbers which each have only one pair of factors which are one and itself (by this definition, 1 is NOT a prime number)
      2. Ex:  2, 3, 5, 11, 13, 29, 53... [this is necessary background knowledge for today]
   2. Remind students how to factor a number into prime factors [this is necessary background knowledge for today]
   3. Demonstrate method of using prime factors of complex numbers to reduce fractions (ex.  24/72 = 2•2•2•3/ 2•2•2•3•3 = 1/3 [this is necessary skill and understanding for following exercises in dimensional analysis]
   4. We will use this "eliminate common factors" method with units in order to solve problems.  This method of problem solving based on carefully tracking units is called "dimensional analysis" or sometimes the "factor label method."  The name is unimportant but the technique is powerful...
   5. Lastly:  Student must understand that "equivalencys," like 60 minutes = 1 hour, can be inverted without changing their value:  since 60 min=1 hour; this can also be written as a fraction, so that 1 hour/60 min is the same value as 60 min/1 hr.  Therefore if we write this as a fraction as 60 min/1 hour or as 1 hour/60 min; either way it equals "1" since the "value" of the numerator and the denominator are the same. 
      • This is a more complex issue than writing 4/4 = 1, but it means the same thing. 
      • Try to help students understand this
      • Therefore; 2 hours (60 min/1 hour) is really saying "1 hour times 1..." in other words we are not changing the value of the original expression by multiplying it.  We are not being sneaky and making the number bigger or smaller.  Instead we are keeping the value but only changing the units.  By using this technique to do it, we are preserving the original value and through careful bookkeeping are appropriately changing the units (...but NOT the value).
   6. Introduce Imperial and American units according to those on "Unit Practice" worksheet.  [The reason for using these "weird" units, like teaspoons, is to force students to depend on the "dimensional analysis technique for problem solving instead of a (possibly) intuitive grasp of metric units.  These strange units force them to learn good technique.  These strange units will be used in todays assignment.]

1. Solve using at least two steps in class:
   1. How many hours in 3 years?
   2. How many kilograms in 13 teaspoons?
   3. How many calories in 1 pound of protein?
   4. How many grams in 13 stones?
   5. How many Joules in 1 pound of fat?
   6. How many hours in 2.7 centuries?
   7. How many mg does 23 pounds of paper weight?
   8. How many Joules in 79 grams of fat (lipid)?
2. Following questions require more than 2 steps:
   1. How many ounces are there in 321 teaspoons?
   2. 51 kilograms are how many stones?
   3. If I run 12 miles, how many pounds of fat will I use up (ie. burn)?
3. Use at least 3 steps for the following questions:
   1. How many seconds are in 0.7 centuries?
   2. How many Joules in 2 pounds of fat?
   3. How many ounces in 7 tablespoons (T)?

ASSIGNMENT:  Complete assignment as describe above in purple text.  Please pay special attention to text in orange if any is found above.