How to Check Your Work on a Math Test (4 Strategies That Save Points)

What should your child do when they finish a math test with a few minutes to spare? That time is a good opportunity to review their answers, since a small calculation error or a missed detail in the question can easily lead to a wrong answer.

Although students can hear the advice to “check their work,” they may not know what to look for or how to approach the review. A few specific strategies can make this final step more useful.

Today, our education specialists share four practical ways your learner can use to check their math answers beyond simply rereading their work.

1. Substitute the Answer Back Into the Original Problem

One simple way to check an answer is to put it back into the original problem and see if everything adds up. For an equation, both sides should be equal. For a word problem, the answer should make sense with all the details in the question.

Let's say your child is solving 3x + 4 = 19 and gets x = 4. They can check their answer in a few simple steps:

• Substitute the answer: Replace x with 4 in the original equation: 3 × 4 + 4 = 19.

• Calculate: 12 + 4 = 16.

• Check the result: Since 16 doesn't equal 19, the answer must be incorrect.

• Try again: Your child solves the equation again and gets x = 5. Substituting 5 gives 3 × 5 + 4 = 19, so the answer checks out.

It's important to use the original problem for this check, not just the last line of your child's work. If a mistake crept in earlier, going back to that same step won't necessarily help them catch it.

Word problems work the same way. Let’s say your child reads, “26 students are going on a field trip, and each van holds 8 students. How many vans do they need?” They divide 26 by 8, get 3.25, and write 3 vans.

• Put the answer back into the story: 3 vans carry 3 × 8 = 24 students.

• Compare it to the details: The question says 26 students are going, so 2 students would be left behind.

• Rethink the answer: Part of a van doesn’t work either, so your child rounds up to 4 vans.

• Check again: 4 vans carry 4 × 8 = 32 students. That’s enough room for all 26, so the answer makes sense.

A simple question like “Does your answer make the original problem true?” can help them build the habit of checking their reasoning, not just rereading their calculations.

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2. Estimate to See If the Answer Makes Sense

Would you trust a GPS that said a 10-kilometer drive would take five hours? Probably not. You’d know something was off before checking a single turn. Estimation works the same way in math.

Your child rounds the numbers to get a quick estimate, then compares it to their answer. When the two are far apart, there’s likely a mistake to find, and they don't need to redo the whole problem to find it. 

Take 48 × 21. Say your learner forgets to change the second partial product and gets 144. Rounding to 50 × 20 gives an estimate of 1,000. An answer of 144 is far too small, which points to the partial products. The correct answer, 1,008, sits close to the estimate.

Estimation is especially helpful for catching misplaced decimal points. If 4 notebooks cost $3.95 each, an answer of $158.00 looks wrong next to an estimate of 4 × $4 = $16. The correct total is $15.80. 

One limitation to keep in mind is that estimation catches large errors, not small ones. An answer of 1,018 for 48 × 21 would still look reasonable next to an estimate of 1,000. 

3. Decide Which Problems to Check First

Students get the most out of leftover test time when they check the problems most likely to contain mistakes first, instead of rereading the whole test from the top. 

Your learner can start this process during the first pass. If an answer feels uncertain, a small mark next to the problem creates a ready-made checking list for later, as long as the test rules allow marks on the page. 

Once the last question is done, they can work through the test in this order:

1. Blank or skipped questions

2. Flagged answers

3. Problems with several calculation steps

4. Questions worth more points

If the test rules don’t allow marks on the page, learners can use a blank sheet of paper instead. They can note question numbers and jot down what confused them, with the added benefit of creating a clear list to return to during the review. 

Research on answer changes supports going back to flagged problems. In a study of more than 1,500 college students’ exams, changes from wrong to right outnumbered changes from right to wrong 2-to-1. 

At home, have your learner rate each answer in a practice set as “sure,” “kind of sure,” or “not sure.” Check the answers together and compare them to the ratings. 

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4. Work Backward to Check Answer

If you’ve ever rewound a video to find where something started, you’re already familiar with the idea behind working backward in math. Your child starts with the answer and reverses each step in the opposite order. If they return to the original number, the calculation checks out.

Keep in mind that each operation has an opposite that can help verify the result. Addition checks subtraction, and multiplication checks division. Learners can use these inverse operations to check an answer without repeating the original calculation.

Let's say your child solves 85 - 37 and gets 52. How can they check their answer without doing the subtraction all over again? They can use addition to work backward:

• Start with their answer: 52

• Add back the number they subtracted: 52 + 37 = 89

• Compare with the original number: The result is 89, not 85, so the answer must be incorrect.

• Try again: The correct answer is 48. Checking it gives 48 + 37 = 85, which matches the original number.

This simple check helps your child catch small errors without repeating the original calculation. 

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Mathnasium helps students build the math skills and understanding they need to approach tests with greater confidence. 

How Mathnasium Helps Students Prepare for Tests with Confidence

Mathnasium is a math-only learning center dedicated to helping K–12 students of all skill levels learn and master math.

We’ve helped many students prepare for math tests, whether they’re working to keep up in class or are ready for an additional challenge. 

We support our students not with a one-size-fits-all curriculum but with the Mathnasium Method™, our proprietary teaching approach designed around each student's individual needs and learning style.

When a learner joins us, we start with a diagnostic assessment that identifies their strengths and areas for improvement. With those insights, we create a personalized learning plan tailored to their needs and goals.

With the plan in place, our specially trained tutors follow it closely, teaching math face-to-face in a supportive and engaging group environment. We use clear, everyday language and a mix of verbal, visual, mental, tactile, and written techniques so each concept lands in a way that makes sense.

When a concept is tricky, we break it down into manageable steps and work through both the how and the why. Over time, students build real problem-solving skills and critical thinking tools they can carry into math and beyond.

Fun is built into how we work. We use game-based activities, let students earn rewards, and celebrate every bit of progress, keeping them engaged and growing in confidence with each session.

The results speak for themselves:

• 94% of parents report an improvement in their child’s math skills and understanding

• 93% of parents report an improved attitude toward math after attending Mathnasium

• 90% of students saw an improvement in their school grades

With over 1,200 learning centers across North America, there is likely a Mathnasium near you. 

Families across Round Rock, Pflugerville, Hutto, Georgetown, and surrounding communities trust Mathnasium of Round Rock East to help their children build solid foundations for math mastery. 

If your child keeps losing points to mistakes on math tests, or needs more targeted support with any other math challenge, our team is ready to help. 

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