Download Algebraic activities In this chapter, students will solve

Chapter 4 Systems of Measurement and Conversions
Algebraic activities
In this chapter, students will solve conversion
problems using SI and imperial measurements.
When solving measurement problems algebraically,
the underlying mathematical concept that students
will understand is the ability to solve a problem by
multiplying by 1.
Dimensional analysis
Dimensional Analysis (also called the FactorLabel Method or the Unit Factor Method) is a
problem-solving method that uses the fact that
any number or expression can be multiplied by 1
without changing its value. It is especially useful
when working with conversion problems involving
different units. Unit factors (conversion ratios)
may be made from any two terms that describe
the same or equivalent amounts of what you are
interested in.
Example
You know that 1 inch equals 2.54 centimetres.
How many inches are there in 12 cm?
SOLUTION
You can write the conversion factor as follows.
2.54 cm
1 inch
2.54 cm or 1 inch
The unit to which you want to convert is
placed in the numerator of the fraction.
Students who normally have difficulty
understanding when to divide versus multiply
by a conversion ratio may find this system easy
to use.
Once the conversion factor is decided, show
your students that the units also cancel, leaving
only the units that you are interested in.
12 cm × _______
​  1 inch 
 ​ = 4.72
 
inches
2.54 cm
The unit centimetres cancels, leaving only
inches in the answer.
Therefore, 12 cm is equal to 4.72 in.
Proportional reasoning
Conversion questions can also be solved using
proportional reasoning.
Example
We know that 1 inch = 2.54 centimetres. How
many inches are there in 12 cm?
SOLUTION
Set up the proportion.
x in  ​ 
1 in  ​ = ​ 
​ _______
 ______
2.54 cm 12 cm
Multiply each side of the equation by 12 cm to
isolate x.
12
1 = 12 x
( 2.54
) ( 12 )
Note that on both sides of the equation, the
centimetres cancel, leaving only inches.
12  ​ = x
​ ____
2.54
4.72 = x
Therefore, 12 cm is equal to 4.72 in.
The original proportion could have been set up
in a few ways and still yield the same result.
2.54 cm ​ = ​ 
1 in
​ _______
 
  ____
  
​ 
12 cm
x
2.54 cm
12 cm
​ _______
 ​ = ​ 
 
  ______
   
​ 
1 in
x
Students tend to find it easier to have the
unknown variable in the numerator.
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