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© 2014 Pacific Crest
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1.5
Number Sense
P
urpose
The role this topic plays in quantitative reasoning
We use words to make and receive meaning in daily life whether we’re thinking, writing, or speaking.
We use numbers to do the same when we engage in quantitative reasoning. But numbers only give us
meaning when they are in context.
Consider the following numbers: 3.7 100,000 80 –20 45 325 Without context, they really don’t have
much meaning. Let’s add some context:
Jeremy’s high school GPA was 3.7. His Uncle Al earns an annual salary of $100,000 and will be 80
years old on his next birthday. You dress differently when it is 20 degrees below zero outside than you
do when it is warm. A car that gets an average of 45 miles/gallon is relatively fuel-efficient. 325 degrees
(Fahrenheit) is arguably the optimal temperature for baking chocolate chip cookies. Thanks to context,
those numbers now mean something much more than just their digits.
When you come across a number, knowing how to make quick sense of it and what it represents is at the
heart of quantitative literacy. It is important that you have a way to visualize or reference concepts such as a
$10 trillion dollar debt, a flow rate of 1,000 gallons per minute, the relative earning power of $15 per hour,
the existence of 1023 molecules in a mole of a substance, the speed of sound (767 mph), and an annual
percentage rate of 4.5%. These are just a few examples of numbers that we encounter on a daily basis.
Numeracy is the ability to make sense of numbers in context — to understand what numbers mean,
represent, and symbolize. If you have some level of facility with numeracy and can think skeptically,
advertizers and politicians (among others) will find it that much more difficult to use numbers to fool
and manipulate you. Additionally, number sense is critical to quantitative reasoning and problem solving
in almost every discipline as well as across disciplines. Most fields use numbers as a kind of common
communication tool.
L
earning Goals
What you should learn while completing this activity
1.
Understand numbers on the basis of their meaning and implications in context.
2. Validate the degree to which numbers and computations are reasonable in a new context by comparing
them with numbers in familiar and similar contexts.
3. Strengthen your ability to perform mental math through strategies such as taking short cuts, making
predictions, and estimating results.
D
iscovery
Finding out for yourself
Read enough content in a daily newspaper or news website to identify five numbers used that don’t
trigger ready or clear images in your head. Try to determine what it is about these numbers that makes
them unclear or confusing. Share your findings with someone who can answer your questions and help
you achieve clarity and understanding of the numbers and their meaning. For each of the numbers that
initially gave you difficulty, provide an explanation, in your own words, of what the number means as
well as
why
you initially had difficulty understanding that meaning.
Measure some aspect of number sense with the interactive quiz available at the companion website.