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39
The Practice
8. Apply a Methodology
to help learn a process
Description
When/How
to Apply
When learning a new process, 1) Review the steps 2) Study the example 3) Read and understand
the discussion using the example(s) 4) Try your own example
Methodologies are a generalization of process knowledge (how experts perform with this knowledge)
that shows the learner how the process should look when applied and how it works. Each key step
is identified, modeled, and discussed so the learner can truly appreciate the value, mathematical
reasoning, and nuances of each step. With this degree of understanding, the learner can transfer the
use of the methodology to new situations.
Examples
Methodology for Adding Fractions
Step
Explanation
Example
1
Set up the problem
Set up the problem vertically.
2 3
Find the sum of and .
3 4
2
Determine the LCD
Determine the LCD of the fractions and
identify the multipliers needed to build up
equivalent fractions with the LCD.
LCD = 12 by inspection
Multiplier for 3 is 4
Multiplier for 4 is 3
3
Build equivalent
fractions
Build equivalent fractions using the LCD
and set up the problem with the equivalent
fractions.
2 4
8
3 4
12
3 3
9
4 3
12
× =
+ × = +
4
Add or subtract the
numerators
Add (or subtract) the numerators and
place the sum (or difference) over the
common denominator.
2 4
8
3 4
12
17
12
3 3
9
4 3
12
× =
+ × = +
5
Convert to a
mixed number if
necessary
Convert an improper fraction answer to a
mixed number.
17 5
12 12
1
=
6
Reduce
Reduce the fraction to lowest terms.
5
12
1 is reduced.
7
Present the answer
Present your answer.
5
12
1
8
Validate your
answer
Validate your answer with the opposite
operation. Begin with your answer and
match the result to the original addend or
minuend.
5
5
17
12
12
12
8
12
1 1
3 3
9
9
4 3 12
12
=
=
− × = − = −
2
3
8 4
12 4
÷
=
÷
1.4 Best Practices for Learning Mathematics