Entrepreneurs dream about building the next big billion-dollar company. You're constantly told to think big. And it's easy to get caught up in envisioning your business going viral and getting to millions of users even before it has made a single dollar.

But all the hopes and visions in the world won't get you any closer to your billion-dollar exit. In fact, it turns out that setting out to build a billion-dollar startup is one of the biggest mistakes that you can make.

At the School of Visual Arts in New York City and his side project boot camp, instructor Gary Chou teaches his students how to launch a startup by taking the opposite approach. His course in entrepreneurial design has a surprising syllabus for a business class: Don't write up a business plan or create a pitch deck for an imaginary billion-dollar company. Instead, go out and create an actual, $1,000 company.

Chou tasks his students with creating a project that will produce $1,000 in monthly profit in a way that's repeatable and sustainable. The results include profitable, ongoing businesses and funded Kickstarter projects. But beyond the money that's been made and the companies that have been created, it's the experience and knowledge taken away that's most important.

That's because if you take on the challenge of building a $1,000 startup, you'll learn three invaluable lessons.

1. Your $1,000 Startup Will Give You Self-Sufficiency and Independence

Individuals and startups need to be self-sufficient and that's why getting your project to ramen profitability is such a vital and game-changing milestone. When you require a salary to make a living, or your company needs investor money to continue to exist, your autonomy and creativity become severely limited.

Deciding to raise investor funding and swing for the fences often means chasing someone else's dream, not your own. When you set out to build a billion-dollar startup, you're often implicitly following another's path to success rather than thinking independently.

For Zingerman's, an Ann Arbor, Michigan-based deli that was doing $5 million in annual revenue, going big meant taking a local operation national and becoming a chain restaurant, replicating the same formula in city after city. That's what everyone advised them to do.

But instead of listening to the experts and chasing more revenue and growth, they decided on their own definition of success. They stayed small and local--rather than replicate the deli over and over, they created the opportunity for their employees to start distinct local businesses, like a bakery and a creamery and more, based on the Zingerman's culture and brand.

Their self-sufficiency empowered them to think independently and in the following years they multiplied their annual revenue 10-fold by blazing their own path.

Get your company to make $1,000 per month, and you begin to be able to cover your rent. Your self-sufficiency will lead you to a dawning sense of limitless possibilities. Product manager Ailian Gan calls it "creating a sense of self-propulsion," that feeling that you can take charge of your own destiny. You have the means, the autonomy, and the creativity to do something totally original.

2. Your $1,000 Startup Will Teach You How to Actually Build a Business

Treading the path of idea to high-flying startup accelerator to funding to operating often results in a rude awakening. I've talked to a number of founders who have attended top accelerator programs, raised glitzy million-dollar seed rounds, and then fell flat when it came time to actually build the business. They'd never made a single dollar online and didn't know how.

In short, building a business is a lot different from fundraising.

By the time my startup, iDoneThis, had grown past 5,000 users and hit $1,000 in recurring revenue, I had learned how to lay the groundwork and grow from there--from how to build a product, to how bring it to market, to how to get people to pay for it, to how to hire and build a team.

Most important, if you focus on building a $1,000 startup rather than a billion-dollar one, you'll get the order of operations right: validate and learn first, then scale.

I've seen first-hand how successful startup founders initially gained real, paying customers before talking to investors. By the time they did raise money, they were ready to use the cash to drive serious growth, not continuing to sputter about in search of product-market fit.

Zirtual, a virtual-assistant service, grew its business for a year and a half without any funding. They weren't able to build any real technology, but that didn't stop co-founder and CEO Maren Kate Donovan.

The new customer-signup form on its website just sent an email to Donovan to alert her that someone was trying to sign up. She had to add that customer to the new customer spreadsheet and email the new customer manually, and then scan through her pool of virtual assistants to find the best fit. Signing up a new customer took an amazing 45 minutes.

Donovan and her co-founders went through this pain to make Zirtual happen in spite of their lack of funding to be absolutely sure they were building something that people wanted before they scaled up. When they did finally raise a $2 million seed round, it was fuel for their rocket ship, not a runway for a plane trying to take off.

If you focus on building a $1,000 startup instead of trying your hand at building a business for the first time as a funded company, you'll learn how to actually build a business first without millions of dollars of investor cash and your employees' livelihoods at stake. You'll save yourself a lot of pain and time that way.

Your $1,000 Startup Might Be Bigger Than You Think

In the biggest twist of all, it turns out that one of the best ways to build something big is to build something small.

The paradox is that limiting yourself to "big" ideas tends to produce bad ones, according to famed investor and founder of Y Combinator Paul Graham. The best ideas are often what Graham calls "toys," or ideas you wouldn't recognize as touching on a billion-dollar opportunity.

The major mistake is to focus on opportunities that seem big within the realm of ideas or go after big markets, but whose products no one would pay for or use.

ZeroCater, a Y Combinator-funded company started by founder Arram Sabbeti, was born from the humble ambition Arram had when he wanted to quit his job and needed enough income to pay for his rent and ramen. He wasn't thinking about the $9 billion catering market; his only worry was helping his own company cater their company lunches.

After he noticed that he'd solved a pain point for his company, he started to expand to other companies in the area. What started as a $1,000 startup soon became a much bigger opportunity and then a full-fledged startup as Arram added more paying clients. Within a year, Arram had turned his rent and ramen side project into a startup backed by the best investors in Silicon Valley.

To Graham, it's far better to build a product that has customers who "really need what [you're] making." This will be a small number of people at first, and that's okay. When your product has $1,000 worth of passionate customers, you have concrete evidence that you're on to something with the potential to be huge. That's why Peter Thiel's number one piece of advice for first-time entrepreneurs is to "start with focusing on a small market and dominate that market first."

Thinking about the $1,000 startup strips the distorting force of market opportunity out of the idea equation. It properly focuses you on the question of whether you're building something that some significant number of people want enough that they're willing to pay you for it.

Meanwhile, you get out there with a seed, you do the work to grow it, and you learn to put one foot in front of the other.