Stuck on a Math Problem? Use These Five Thinking Steps

Being stuck on a math problem does not mean you are bad at math or unable to solve it. It means you have reached a point where you need to slow down, study the information, and choose a useful next step.

During a Thinking Math lesson, you may not immediately know which operation to use or how to reach the answer. That is intentional. The goal is to practice making decisions, testing ideas, learning from mistakes, and explaining your reasoning.

Strong problem solvers do not wait for someone to show them every step. They use a process to move their thinking forward:

Notice → Wonder → Try → Test → Explain

You can use these five steps with almost any math challenge, including patterns, proportions, equations, graphs, geometry, puzzles, and real-world problems.

Step 1: Notice What You Know

Before calculating, slow down and examine the problem.

Look for:

• Important numbers
• Labels and units
• Rules or restrictions
• Pictures and diagrams
• Information that repeats
• Values that change
• Values that remain the same
• Relationships between quantities

Start your group discussion with statements such as:

• “I notice that…”
• “The problem tells us…”
• “This number represents…”
• “One rule we must follow is…”
• “This part changes, but this part stays the same.”

Noticing helps you understand the situation before choosing a strategy. It also prevents you from grabbing numbers and performing a random operation.

Make Your First Move

Write or circle at least three things you notice. Then explain why one of those details might be important.

You do not have to understand the entire problem yet. Your first goal is simply to identify what you already know.

Step 2: Wonder About the Problem

Once you have identified the available information, determine what you need to find.

Ask:

• What is the problem asking us to determine?
• What information seems most useful?
• What information have we not used?
• What could change?
• What must stay the same?
• Could there be more than one answer?
• What would a reasonable answer look like?
• Which part is still confusing?

Instead of saying, “I don’t get it,” identify the exact point of confusion.

Try saying:

“I understand ______, but I am trying to figure out ______.”

A specific question gives your group something to investigate. A general statement such as “This is too hard” does not tell your group what to do next.

Turn Confusion Into a Question

If you are stuck on a math problem, turn the confusing part into a question your group can discuss or test.

For example:

• “How are these two quantities connected?”
• “Which value should we change first?”
• “How can we represent this information?”
• “How will we know whether an answer works?”

A useful question can become the beginning of a strategy.

Step 3: Try a Reasonable Strategy

You do not need to know whether an idea will work before trying it.

Select one strategy that fits the information you noticed. You might:

• Draw a picture.
• Create a diagram.
• Make a table.
• Write an organized list.
• Act out the situation.
• Use objects or manipulatives.
• Test a smaller or simpler case.
• Estimate a reasonable result.
• Search for a pattern.
• Write an equation.
• Work backward from the goal.
• Try one possible example.

When you are stuck on a math problem, trying one reasonable strategy is more useful than waiting for the perfect idea.

Your group could say:

• “Let’s test this idea.”
• “We can begin with a simpler case.”
• “Let’s organize the information in a table.”
• “Could we draw what is happening?”
• “We are not sure this will work, but it may help us notice something.”

Your first strategy does not have to become your final strategy. Its purpose is to help you gather information and understand the problem more clearly.

Step 4: Test What Happened

After trying a strategy, stop and examine the result.

Ask:

• Did we follow every condition?
• Does our answer make sense?
• Did we use the correct units?
• Does our model match our calculations?
• Can we substitute the answer into the original problem?
• Does the strategy work more than once?
• Could we check it another way?
• Did we find one solution or every solution?
• What did this attempt teach us?

Testing your work helps when you are stuck on a math problem because even an unsuccessful attempt can provide useful information.

If the strategy did not work, do not immediately erase everything. Find the exact point where the reasoning stopped making sense.

You may need to:

• Correct a calculation.
• Add a missing label.
• Use a different operation.
• Reorganize the information.
• Change an assumption.
• Test another example.
• Revise the strategy.

A strategy that does not produce the correct answer can still help your group eliminate an idea, recognize a pattern, or decide what to try next.

Step 5: Explain Your Reasoning

A correct answer does not show your complete mathematical understanding.

A strong explanation tells others:

• What you did
• Why you selected the strategy
• What you discovered
• How your thinking changed
• Why the answer makes sense
• How you checked the result
• Whether the strategy could work in another situation

Connect your ideas using words such as:

• Because
• Therefore
• If
• Then
• Since
• As a result
• This shows

Instead of saying:

“We just multiplied.”

Explain the mathematical reason:

“We multiplied because the situation contained equal groups of the same amount.”

Instead of saying:

“We found a pattern.”

Describe the actual pattern:

“Each time the first value increased by two, the second value increased by six.”

Your explanation should be clear enough that someone who was absent could follow your reasoning.

The Process Is a Cycle

The five steps will not always happen once or in a perfect order.

You might try an idea, test it, notice something new, and then revise your original strategy.

Your process may look like this:

Notice → Wonder → Try → Test → Notice Again → Revise → Explain

This is normal.

Mathematical thinking is a cycle. Each attempt should help you understand something that you did not understand before.

Changing your strategy does not mean you failed. It means you used new information to make a better decision.

What Productive Struggle Looks Like

Productive struggle means continuing to think when the answer is not immediate.

It does not mean:

• Sitting silently
• Repeating random guesses
• Copying another group
• Waiting for the teacher
• Allowing one student to do everything
• Saying, “I can’t do it,” and stopping

Productive struggle does mean:

• Rereading the problem
• Asking a specific question
• Drawing a representation
• Testing a simpler case
• Comparing strategies
• Searching for a pattern
• Finding and correcting an error
• Explaining an unfinished idea
• Revising your work

Confusion becomes productive when you take an action that moves your thinking forward.

What to Say When You Are Stuck on a Math Problem

The words you use can help your group continue working.

Instead of saying, “I don’t know,” try one of these statements:

• “I notice ______, but I am unsure about ______.”
• “One idea we could test is ______.”
• “Could we represent this with a picture or table?”
• “Which rule or condition have we not used?”
• “What happened in the example we already tried?”
• “Our strategy stopped working when ______.”
• “Can someone explain why this step makes sense?”
• “What could we change while keeping everything else the same?”
• “How can we check this result?”
• “What should we try next?”

These statements ask for support without asking someone else to solve the entire problem.

How to Help Without Taking Over

Helping a classmate does not mean giving that person the answer.

Help your classmates continue their own thinking by asking:

• “What do you notice?”
• “What have you tried?”
• “What does this number represent?”
• “Where did you become stuck?”
• “Which condition are you using?”
• “How could we test that idea?”
• “Does the result match the original problem?”
• “Could you represent it another way?”

A strong group shares ideas, but every group member still thinks.

Before moving to a new step, make sure everyone can explain what the group is doing and why it makes sense.

Make Your Thinking Visible

Your group’s workspace should tell the story of your thinking.

Depending on the problem, include:

• Important information
• Questions
• Pictures or diagrams
• Tables
• Organized lists
• Calculations
• Equations
• Labels
• Patterns
• Corrections
• Written explanations

Do not erase every unsuccessful attempt. Cross it out neatly, draw an arrow, or add a note explaining why your group changed directions.

Someone looking at your work should be able to determine:

1. Where your group began
2. What your group tried
3. What your group discovered
4. How your strategy changed
5. Why your conclusion makes sense

Visible thinking makes it easier for your group to discuss ideas, locate mistakes, compare strategies, and explain its reasoning.

Before You Ask the Teacher

When your group is stuck on a math problem, complete this check before asking the teacher for help.

Notice

What important information, rule, relationship, or pattern have we identified?

Wonder

Can we clearly explain what we are trying to determine?

Try

Have we tested at least one reasonable strategy?

Test

Have we checked what worked and identified exactly where we became stuck?

Explain

Can every group member describe what we have done so far?

After completing the check, ask a specific question.

Instead of asking:

“Is this right?”

Try asking:

“We noticed ______ and tried ______. Our strategy worked until ______. Could you ask us a question that will help us decide what to try next?”

Your teacher may respond with another question instead of giving you a step. That question is intended to help your group continue thinking independently.

Your Five-Step Thinking Tool

Use this process during every Thinking Math lesson:

1. Notice

Identify the important information, rules, and relationships.

2. Wonder

Decide what you need to find and name what is confusing.

3. Try

Choose a reasonable strategy and take action.

4. Test

Check the result and learn from what happened.

5. Explain

Use evidence to show why your reasoning makes sense.

The next time you are stuck on a math problem, do not wait for the entire solution to appear. Choose one action that can move your thinking forward.

Strong mathematicians are not people who immediately know every answer. They are people who know what to do when they do not know.

Student Response

Write one paragraph of at least five complete sentences explaining how you will use the Notice → Wonder → Try → Test → Explain process during future Thinking Math lessons.

Your response must:

• Identify the step that will help you the most.
• Describe one useful action you can take when you become stuck.
• Explain how a classmate can help you without giving you the answer.
• Describe how you will make your thinking visible.
• Explain how this process can help you become a more independent problem solver.

When you’re finished, check out the rest of our blog for more tips, ideas, and activities to help you learn and grow. Be sure to follow our classroom Instagram page for behind-the-scenes moments, project highlights, and fun updates. Let’s work together to make learning fun, exciting, and something you look forward to every day!