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© 2014 Pacific Crest
35
Examples
Long Division and Decimals
Consider that long division of decimal numbers is exactly like
long division of whole numbers, but with a decimal point included. How different are these two?
2.34 254.12
and
234 25412
Will the arithmetic be different, other than needing
to address the placement of the decimal point?
How does converting a fraction to a percentage differ from performing long division?
The Practice
3. Start Simple
& make quick, easy-to-validate connections
Description
When/How to Apply
When starting or when confused, 1) Use small numbers 2) Use simple situations
When exploring a new mathematical idea, start simple. Pick a situation you are comfortable or familiar
with so that you can use this experience to help increase your understanding. When exploring, use
simple numbers and make the computation and contextual factors as uncomplicated as possible. When
creating your own example, just think simple and familiar.
Examples
Multiplication and Division of Fractions
Explore situations that you have experienced in your
life. For example, dividing pizza among a group of people. Start with simple numbers: half a pizza
and two people. How much pizza do I get when I get half of a half of a pizza? We all know from
experience it would be 1/4 of a pizza.
Now figure out the relationship between half of half and
1 1 1
2 2 4
=
The context is simple because it is very familiar, but we also have simple computation involving
the number 2.
If we know that a teenager will average one third (1/3) of a pizza per
meal, how many teenagers will 2 pizzas feed? 2 divided by thirds gives
us an answer of 6 teenagers:
2
3 2
6
1
1
3
=
=
Creating a Table of Values
If you’re graphing an equation, using a table of values is an easy way
to start. And it makes sense to use simple and straightforward values, in most cases.
Let’s say you’re trying to graph the following function:
3
1
( ) 3
7
2
f x x
x
= − +
It makes sense to try using 1,
–
1, and 0: simple values. Of course, you could use 56.39 as a value,
but why put yourself through the unnecessary frustration and time that would require? Though
this example may seem extreme, it demonstrates how thinking simple can make a big difference.
3
1
3(56.39)
(56.39) 7
2
3(179310.732119) (28.195) 7
(537932.196357) (28.195) 7 537911.001357
−
+ =
−
+ =
−
+ =
x
f
(
x
)
56.39 537911.001357
versus
3
1
3(0)
(0) 7 7
2
− + =
x
f
(
x
)
0
7
1.4 Best Practices for Learning Mathematics