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Can You See the Mathematics Hiding in Plain Sight?
The other day, I found myself trying to answer a simple question: Which Costco membership should I buy for my household?
There are only two choices: the Gold Star Membership and the Executive Membership, so not too complicated, right?
Like most people, I started by comparing prices and benefits. The Executive Membership costs $65 more than the Gold Star membership each year, but it also returns an annual 2% Reward on qualifying purchases. So I asked myself: At what point does the higher membership fee pay for itself?
I wanted to know how much I needed to spend in a year to break even; essentially to get my additional $65 back. I realized I did not need to invent an equation. Costco had already provided every piece of it. Everything I needed was right there in front of me.
I yanked a piece of paper from my waste basket and started thinking on paper. I came up with this…
Not very eloquent I agree and nothing I would expect anyone reading these scribbles to follow. But sometimes, that’s math.
The question becomes, two percent of what amount of annual purchases equals $65?
Translating words into math symbols:
“two percent”….2
“of”….tells me to multiply
“what amount of annual purchases”…this is the unknown, what I am trying to find. Let’s call it “p” for purchases
Now the equation starts to form…
2% x annual purchases = $65
One last pass and we have an equation that produces our break-even amount…
0.02p = 65
I sat with this equation a moment and realized what started as an example of math use in daily life, uncovered something deeper:
The break-even equation was already hiding in plain sight. I simply had to recognize it.
The mathematics was not something I had created. It was something I had recognized. That realization stayed with me.
And then I started to think…
Perhaps That’s What Mathematical Literacy Really Is
We often think mathematics begins when someone writes an equation on a whiteboard.
x + 3 = 7
But that is not where mathematics begins.
That is where the mathematical representation begins.
Long before anyone writes a symbol, someone has already noticed a relationship worth describing. Someone has decided what matters, what can be ignored, and how the situation might be represented. The equation is not the beginning of the thinking. It is the record of the thinking.
That distinction matters.
Reading is recognizing words on a page.
Mathematical literacy is recognizing relationships in the world.
Once we recognize those relationships, mathematics gives us a language for representing them in ways we can understand, communicate, and reason about.
Learning to See
Perhaps that is why mathematics seems invisible to so many people.
It is not because the mathematics is not there. It is because we have not always been taught how to see it.
Michelangelo wrote:
“I saw the angel in the marble and carved until I set him free.”
The metaphor is beautiful.
Michelangelo did not believe the sculptor created the figure from nothing. The figure was already there, waiting to be uncovered.
Good mathematics often feels the same way.
We do not invent the relationships between quantities. We discover them. The mathematics already exists within the situation. Our task is to recognize it and represent it.
The Mathematics of Everyday Life
The Costco membership problem was not really about memberships at all.
It was about seeing relationships.
And once I began thinking that way, examples seemed to appear everywhere.
- Mortgage payments
- Interest rates
- Insurance deductibles
- Fuel economy
- Election polling
- Medical risks
- Retirement planning
Modern life is filled with relationships waiting to be recognized. Rarely does someone hand us a neatly written equation. Instead, we are given information and asked to make decisions.
That is why mathematical literacy matters.
Not because everyone needs advanced mathematics. They do not.
But everyone needs the ability to recognize the mathematical structure hidden inside everyday life.
Why It Matters Even More Today
As intelligent systems become increasingly capable of performing calculations and analyses, this distinction becomes even more important. Computers can manipulate equations at extraordinary speed. They cannot decide which relationships deserve our attention or whether the answer they produce is the answer we actually needed.
Those remain questions of judgment.
Are We Starting in the Middle of the Story?
Which brings me back to the classroom.
Most students believe mathematics begins when the teacher writes an equation on the board.
I wonder if we have been starting in the middle of the story.
What if mathematics really begins much earlier—with learning to notice relationships, ask better questions, and recognize the patterns already present in the world around us?
Perhaps the greatest lesson mathematics offers is not how to solve equations.
Perhaps it is learning to see the mathematics before it is written.
