“But they never taught this! How can it be on the test?”
This is a common complaint in higher-level math classes. The student is not referring to a Calculus question on an Algebra 2 exam. They’re referring to what’s known as an extension question.
What are extension questions?
Oftentimes, extension questions ask you to use what you’ve been learning in a novel way. The type of problem hasn’t shown up in class or on homework assignments, but the math skills you need have. So you technically have all the knowledge you need to solve the question, but you’re being asked to use that knowledge in a way you’re not used to.
This makes extension questions excellent training for the SAT, which is loaded with weird math problems: questions that ask you to use familiar Algebra 2 knowledge in an unfamiliar way. Flip that around, and one of the benefits of prepping for the SAT is getting better at extension questions.
Other times, extension questions take what you’ve learned and ask you to stretch just beyond your current understanding. They ask you to take the logical next step in the progression of your math knowledge. In this way, they’re training you to teach yourself, to be your own guide on the mastery path.
Extension questions are about mastery.
If you haven’t progressed beyond the “I get it!” milestone of the mastery path, you have no hope of answering an extension question. But if you’ve done enough practice to truly master the content, then you’re ready to handle the challenge.
Putting your knowledge to use in an unfamiliar way requires that you have that knowledge solidly under your belt. Stretching just beyond your current knowledge requires that you’ve already reached the outer limits of the topic. You can’t do something strange and difficult with quadratics if you don’t already know how to use quadratics for basic problems.
So to handle extension questions, you have to put in the practice required to master the math. This means doing more than what you’re asked to do. Find extra worksheets online. (Kuta Software is great for that.) Work through Khan Academy problem sets. Do additional textbook problems. (If the class doesn’t have a textbook, buy one.)
By the way, textbooks usually have a few extension questions in the problem sets they offer; it’s just that teachers rarely assign those questions. So you can practice extension questions at home, building up your comfort with them before the test.
Extension questions are a form of guessing.
You’d think that after more than a decade of tutoring full time, I would have encountered every type of question imaginable, but I haven’t. I run into extension questions every week. Problems that make me think, Hmm… That’s weird. I can handle them because I’ve mastered the content, and because I’m comfortable guessing.
What makes something an extension question is that you’ve never seen it before, so you’re not sure how to solve it. You should think carefully about it and apply what you know, but in the end, you’ll have to guess.
It’s not a random guess, but an educated one. And the more educated you are (the more you’ve mastered the topic), the better.
Remember, guessing is a skill you have to practice. Extension questions are a great opportunity to practice guessing.
Extension questions earn good money.
Most working professionals spend their time on extension questions: solving problems that aren’t easily solved with past knowledge alone. They use the knowledge they gained in trade school or college, along with their on-the-job experience, but they also have to exercise judgment. They have to make difficult choices in the face of novelty and uncertainty.
- An engineer tackling the latest technical challenge for their company
- A therapist deciding how to advise each of their unique clients
- An electrician troubleshooting in a mid-century house
- A marketer designing an ad campaign in our ever-changing media landscape
Life is full of extension questions.
Day-to-day life involves lots of routine. In this, it’s like a repetitive math assignment. But the most meaningful parts of life – the parts of life that make the routine worthwhile – are extension questions: situations where you have to stretch beyond your current skill level, leave your comfort zone, and take a leap of faith.
- At each transition growing up – from middle school to high school, from high school to college, from college to career – you have to stretch and adapt. People can give you advice, but in the end, you have to figure it out for yourself.
- You’ve learned how to interact with your partner so far, but you’re not sure how to support them in the next chapter of your life together. That’s a big extension question.
- Just when you’ve figured out how to raise your child, they turn into a teenager, and you’re forced to rethink your strategies.
Life rarely lets you get too comfortable before it throws you out of your comfort zone. And that’s a good thing because life’s extension questions are how we progress.
You could complain, “They never taught me how to do this!” but playing the victim won’t get you anywhere. Instead, you can choose to be proactive and embrace uncertainty as you get to work figuring out how to move forward.
Chris Loper has been working as a tutor and academic coach since 2014, racking up over 13,000 hours of experience supporting students.
Along with Greg Smith, Chris is the co-creator of Parenting for Academic Success, a series of classes that create empowered parents, confident students, and harmonious families.
Chris writes the popular self-improvement blog Becoming Better, where he also offers habit coaching, helping busy adults with habit formation and productivity.
Chris’s most recent endeavor combines his academic and habit-formation expertise to help students thrive in college. Visit SmartCollegeHabits.com to learn more.
In 2021, he published a humorous memoir titled Wood Floats and Other Brilliant Observations, a book that blends crazy stories with practical life lessons.
He lives in Issaquah, WA, where he is the owner of South Cove Tutoring.