How to Study Math

Co-authored by Grace Imson, MA and Amy Bobinger

Last Updated: April 15, 2024 Approved

There’s no denying it--math can be tricky! Even if you don't feel like it's your strongest subject, though, you can get better at math if you're willing to put in the work. The best way to do well in math is to practice every day, so set aside plenty of time to study on your own or with a group. With a little determination, you can make real strides in math and it will benefit you in every way.

1

Do your homework, but don't stop there.

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Work through some extra practice problems, as well. Your teacher assigns a certain number of problems for homework, but if you don’t feel like you can fully understand, you might need to try a few extra problems. Look for extra practice sets in your textbook or online, and try some of those until you feel more confident. Oftentimes, the answers to all the odd-numbered problems are in the back of the book. Do the odd-numbered problem, check your answer, then try the even-numbered problem next to it.^{[1]
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- Solving problems over and over is the best way to get good at math, which is why doing your homework is so important.
- If you're looking for practice questions online, you might check out popular math sites like Khan Academy, Math-Aids, and Corbettmaths.^{[2]
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2

Read your textbook actively.

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Take your time to make sure you understand what you're reading. Read each section slowly, making sure you fully understand it before you move on to the next one. Take note of any definitions and examples that are mentioned in the book. Also, pay attention to any learning goals that are mentioned at the beginning of the chapter, as well as the summary at the end.^{[3]
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- Reading your math book might not sound like a lot of fun, but it can really help you understand a difficult concept you're struggling with. In addition, your textbook can help you understand why things are done a certain way, helping you go beyond simply memorizing the steps.
- Each night when you're studying, read a few pages ahead of what you've already been assigned. That can make it easier to keep up during class because you'll already be familiar with what the teacher is talking about.

3

Spend a few minutes studying each day.

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Don't try to cram for tests at the last minute. In math, everything new you learn builds on something else, so you have to really nail down each concept before you can move on to the next one. If you try to study it all at once, it can get really confusing, so set aside a few minutes every day to study and do your homework.^{[4]
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- If you spend even 30 minutes a day studying math, you'll be less stressed when it's exam time because you'll already be familiar with the material you're being tested on.^{[5]
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- When you're studying, read through the notes you took in class, go over any formulas you're using in class, and re-read your textbook.
- Try making flashcards—you might write a problem on one side and the answer on the other, or you might write down a formula on one side and its name on the other.

4

Show your work on every problem.

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Write out complete solutions, even for practice and homework. Your teacher will usually require you to show your work—or write out every step—when you're taking a math test. Get in the habit of doing that every time you work a problem, even if it's just something you're doing to practice.^{[6]
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- In addition to helping you on exams, showing your work makes it easier to go back and see where you made a mistake if you get the wrong answer.
- For instance, if you're solving "2x = 3+1," don't just skip to "x = 2." Write out "2x = 4," then "2x/2 = 4/2," then "x = 2."

5

Give extra attention to word problems.

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Use these to test your math comprehension. Word problems are especially tricky because you have to take a sentence and convert it into math. However, they're a really great way to train your brain to think about math in real-world terms, so any time you're assigned a word problem, work through it carefully. Read through the entire problem before you begin to solve it. Make sure you understand the situation and what math techniques you’ll need to use. If there are any graphs, charts, or tables included with the problem, read those carefully, too.
- It can help to draw a picture or diagram illustrating the problem. Include any quantities that are listed in the problem. If the quantities aren't named, use a variable like "x" (or you could make up your own, like using "a" if you're solving a problem about apples).

6

Check your work once you’re finished.

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Look up the answer or put the solution back into the problem. Sometimes, your textbook will have the answers to homework problems listed in the back of the book. If that's the case, try looking up the answer once you've finished the problem. If you got a different answer, work back through the problem to see if you can find where you made a mistake. If you still don't get the right answer, ask your teacher about it during your next class.^{[7]
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- Some problems—like equations with variables—can be checked by substituting the solution in place of the variable. For instance, if you solved "2x = 3+1" earlier and got "x = 2," you could check that by working through "2*2 = 3+1," or "4 = 4." Since the answer is true, you know you have the correct answer.^{[8]
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EXPERT TIP

Joseph Meyer
Math Teacher
Joseph Meyer is a High School Math Teacher based in Pittsburgh, Pennsylvania. He is an educator at City Charter High School, where he has been teaching for over 7 years. Joseph is also the founder of Sandbox Math, an online learning community dedicated to helping students succeed in Algebra. His site is set apart by its focus on fostering genuine comprehension through step-by-step understanding (instead of just getting the correct final answer), enabling learners to identify and overcome misunderstandings and confidently take on any test they face. He received his MA in Physics from Case Western Reserve University and his BA in Physics from Baldwin Wallace University.

Joseph Meyer
Math Teacher

When doing practice problems, promptly check to see if your answers are correct. Use worksheets that provide answer keys for instant feedback. Discuss answers with a classmate or find explanations online. Immediate feedback will help you correct your mistakes, avoid bad habits, and advance your learning more quickly.

7

Refresh your memory by going through older problems.

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Keep practicing old skills while you learn new ones. Math builds on itself—every new skill you come across is built on something you've already learned. That's why if you find yourself struggling in math, it can feel hard to get caught up. Stay on top of the game by going back through concepts you've already learned. For instance, each day after you finish your homework, you might do one problem each from 3-4 previous chapters.^{[9]
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- Do this even if it seems like what you're studying isn't related to those previous chapters. Chances are, something you learn later will help tie everything together.

8

Take practice tests to check your skills.

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Treat the practice test like it's a real test. If you’re anxious about taking an exam, do one or more practice ones ahead of time. Try to recreate the test environment--keep your study room quiet, time the test, and avoid interruptions. Check your work after taking the practice test, and study more if you need it.
- Ask your teacher if there are practice versions of the test that you can use for study.
- You may also be able to find practice tests online. Just search for something along the lines of "geometry + free practice tests" or "ACT math practice tests."

9

Think about math as a language.

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Study the symbols like they're words. Math uses its own vocabulary, including symbols you don't see anywhere else—and that can be a little confusing at times. However, it can help if you think of it like learning a language. Practice reading symbols like they're words—you might read "divided by" when you see a fraction line, for instance, or you might say "square root" whenever you see "√."^{[10]
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- If you're struggling to remember what the different symbols and terms mean, keep a vocabulary log where you write down any words or terms you learn, along with the definition.
- You can also use flashcards to help you remember the definitions of different words and symbols.

10

Focus on comprehension more than memorization.

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Learn the meaning behind what you're doing. Don't just try to memorize everything your teacher writes down. Instead, focus on understanding why you need to do a certain process at a certain time, or where a formula comes from. When you can do that, it will be a lot easier to memorize it. If you can't visualize that, it's going to be harder to memorize it.^{[11]
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Expert Source

Grace Imson, MA
Math Instructor, City College of San Francisco

Expert Interview. 25 November 2019.}
- If you're really struggling with a certain concept, try asking your teacher to explain it again, re-read that chapter in your textbook, ask a friend for help, or find a math tutor.
- Sometimes, teachers and professors might allow you to bring a list of formulas with you to a test. If you don't understand how and when to use them, though, this won't be much help.^{[12]
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11

Use repetition to help you nail down formulas.

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Write down formulas over and over until you remember them. Even once you understand when and why to use a certain formula, you may still need to commit it to memory for a test. Spend a few minutes every day copying the formula down several times so you'll be able to remember it at test-time.^{[13]
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- At the same time, say them to yourself over and over. The combination of hearing the formula, seeing it, and writing it may help make it easier to remember.
- You can also use mnemonics, or memory devices, to help you remember concepts or formulas. For instance, you might remember the order of operations (parentheses, exponents, multiplication, division, addition, subtraction) by setting the acronym PEMDAS to a phrase like "Please excuse my dear Aunt Sally."

12

Participate in class.

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Listen, take notes, and join in discussions. Any time your teacher is explaining something, follow along carefully. Write down any formulas or concepts that your teacher talks about in detail, since they'll probably be used in your homework and on tests. Also, make sure to ask your teacher if you have any questions or need more explanation.^{[14]
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- If your teacher asks a question, try to come up with the answer, even if you don't raise your hand—it will be good practice for later.
- Focus on key information when you're taking notes. Write down things like formulas, definitions, and sample problems—but spend more time listening than writing. For instance, if your teacher is explaining why it's important to show your work, you might just write, "Show all steps" instead of copying what they say word-for-word.^{[15]
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13

Join a study group.

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Work with others to help you get through tricky concepts. Study groups can be great for learning math since you can take turns quizzing each other and checking each other’s work. Studying with others also means that you can help each other out if anyone’s having trouble understanding a concept or how to do a problem. Just make sure that you find a group with people who are serious about doing the work.
- Be active in your study group—explaining things to other people can actually help you understand the subject better.^{[16]
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EXPERT TIP

Joseph Meyer
Math Teacher
Joseph Meyer is a High School Math Teacher based in Pittsburgh, Pennsylvania. He is an educator at City Charter High School, where he has been teaching for over 7 years. Joseph is also the founder of Sandbox Math, an online learning community dedicated to helping students succeed in Algebra. His site is set apart by its focus on fostering genuine comprehension through step-by-step understanding (instead of just getting the correct final answer), enabling learners to identify and overcome misunderstandings and confidently take on any test they face. He received his MA in Physics from Case Western Reserve University and his BA in Physics from Baldwin Wallace University.

Joseph Meyer
Math Teacher

Develop your mental math skills. Mental math is when you perform mathematical calculations without using calculators, paper, or counting aids. Use your mind, memory, lessons, and discussions with your classmates to refine your math skills and build strong problem-solving strategies.

14

Get more help if you need it.

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Reach out to your teacher or get a tutor. If there’s something you don’t understand or a math concept you’re struggling with, reach out to your teacher. If there are tutoring programs at your school, your local library, or somewhere else, take advantage of those, too.^{[17]
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- Don’t be embarrassed to ask for help. Math can be difficult, and there’s a lot of information to keep up with. The most important thing is to make sure you understand how to do the work, and anything that helps you do that is a good thing.

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How do I concentrate in math or any other subject?

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You can remove any distractions around you, like cell phones, your laptop, video games etc. Then, set up goals, like studying in 20-minute intervals, then increasing as you go on. Keep your room organized, which helps your mind to relax. Before you begin, go through everything you plan over covering.

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How can I study in a particular way so that I'm always certain of my answer? On a test, I usually doubt myself and worry that my answer is wrong.

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The only solution to this problem is studying more. The better you know the material, the more confident you will be. If you're feeling anxious during the test, just take a couple of slow, deep breaths and try to clear your mind. Then read the question again and make your most educated guess as to the answer.

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How do I study harder for math?

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Practice as much as you can. Teach others the math concepts that you are studying .

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