Math class is going to look and feel a little different. You will still learn important math skills, solve problems, and explain your answers—but you will also spend more time thinking, discussing, testing ideas, and learning with others.
This approach is called Thinking Math.
In Thinking Math, your goal is not to finish first or immediately know the correct answer. Your goal is to become a stronger problem solver by asking questions, trying different strategies, and explaining your thinking.
What Will Thinking Math Look Like?
During a Thinking Math lesson, you may:
- Work with a randomly selected group.
- Stand and solve problems on a whiteboard or another shared workspace.
- Discuss possible strategies before writing an answer.
- Study another group’s approach.
- Make mistakes and revise your work.
- Explain why a strategy works.
- Complete an individual problem to show what you understand.
Some problems may feel unfamiliar when you first see them. That is intentional. You are learning how to begin a problem even when the complete solution is not obvious.
Our Thinking Math Routine
1. Enter Ready to Learn
Come inside quietly, sit in the correct spot, and follow the directions on the board. Have your materials ready and listen when the main speaker is talking.
2. Understand the Challenge
The teacher will introduce a problem or challenge. Listen carefully and identify:
- What information is provided?
- What are you trying to determine?
- What questions do you have?
- What could you try first?
You may not receive every direction at once. Part of the challenge is learning how to make sense of the problem.
3. Think With Your Group
Your group should discuss the problem before rushing to calculate. Every person should contribute ideas, questions, or observations.
A strong group does not allow one student to do all the work.
4. Show Your Thinking
Record enough work that another person can understand your strategy. Your work might include:
- Calculations
- Tables
- Graphs
- Diagrams
- Labels
- Equations
- Written explanations
An answer without supporting work does not show your complete mathematical thinking.
5. Check and Revise
Ask whether your answer is reasonable. Test it, use another strategy, or compare it with the original problem.
If you discover a mistake, do not erase all evidence of it. Correct the mistake and explain what changed. Revising your thinking is part of learning mathematics.
6. Share and Learn
You may be asked to explain your group’s strategy or study another group’s work. Listen for similarities and differences between approaches.
You should be prepared to explain:
- What your group tried
- Why you selected the strategy
- Where your group became stuck
- How you know the answer makes sense
7. Finish Independently
At the end of the lesson, you may complete a short problem or reflection independently. This helps you and your teacher see what you understand and what you still need to practice.
What Is Expected of You?
Participate
You do not need to have every answer, but you must join the thinking. Ask a question, share an observation, test an idea, record the group’s work, or explain a step.
Explain Your Reasoning
Do not stop with “I just knew it” or “I did it in my head.” Explain how you arrived at your answer and why your strategy makes sense.
Listen to Understand
Give classmates time to finish their ideas. Ask questions before deciding that someone’s strategy is incorrect.
Useful responses include:
- “Can you explain that step?”
- “Why did you choose that operation?”
- “I agree because…”
- “I see it differently because…”
- “Can we test that idea?”
- “What information from the problem supports that?”
Make Space and Take Space
If you usually speak first, pause and invite someone else into the conversation. If you usually remain quiet, challenge yourself to contribute. Everyone deserves an opportunity to think and speak.
Use Resources Responsibly
You may use tools such as whiteboards, manipulatives, rulers, calculators, or Chromebooks when directed. Use each resource to support your thinking—not to avoid it.
Respect Productive Struggle
Feeling confused does not mean you are bad at math. It means you have reached a point where learning can happen.
Before saying, “I can’t do this,” try:
- Restating the problem.
- Drawing a picture or diagram.
- Organizing the information.
- Testing a simple example.
- Asking a group member a specific question.
- Trying a different strategy.
Follow the Cougar Code
Thinking Math depends on a classroom where students feel safe sharing unfinished ideas. Be safe, kind, respectful, and responsible. Disagree with an idea without disrespecting the person who shared it.
What Should You Do When You Are Stuck?
Do not immediately ask, “Is this right?” First, explain what you understand and where you became stuck.
Try asking:
- “We noticed ______. What should we examine next?”
- “We tried ______, but then ______ happened.”
- “We understand the first step, but we need help with ______.”
- “Could you ask us a question that will help us continue?”
These questions allow your teacher to support your thinking without solving the entire problem for you.
Mistakes Are Useful Information
In Thinking Math, mistakes are not something to hide. A mistake can reveal:
- A misunderstood direction
- A missing piece of information
- A calculation that needs to be checked
- A strategy that works only in certain situations
- A new question worth investigating
Strong mathematicians do not avoid mistakes. They notice them, learn from them, and revise their work.
Before You Begin
Remember:
You are not expected to know everything immediately. You are expected to think, participate, and keep working.
Your ideas matter. Your questions matter. Your mistakes can help the class learn. The more you explain, listen, test, and revise, the stronger your mathematical thinking will become.
Thinking Math Written Responses
For each prompt, write a complete five-sentence response. Include specific details from the reading and explain your thinking.
- Explain what a successful student does during a Thinking Math lesson. Include how the student participates, works with a group, and shows mathematical thinking.
- Describe what you should do when you become stuck on a challenging math problem. Include at least three strategies you can try before asking the teacher for help.
- Explain how students should work together during a Thinking Math activity. Describe what it means to listen, contribute, and make sure everyone is included.
- Respond to this statement: “Making mistakes can help you become better at math.” Explain whether you agree and describe what a student should do after discovering a mistake.
- Describe how you will be a successful member of our Thinking Math classroom. Identify one expectation that will be easy for you, one that may be challenging, and how you will improve.
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!
22 Responses
A successful student works the whole time and tries different solutions.They participate by listening to others ideas.What you can do when you become stuck is ask your teammates if their stuck to or ask the teacher for help.Students should work together during the math thinking activity by reading what the question is asking working together to think of ways to solve the problems.Making a mistake can help you become better at math I agree with because the more you make a mistake you learn from it and learn how to do something.After discovering a mistake students can ask for help or try another way.I will be a successful member of the math classroom by asking for help when I need it and trying to think and find different solutions,I will improve by staying on task and listening to what is being asked.
When you are answering fast sometimes you don’t answer it correctly because your worried about answering fast instead of understanding the prompt or equation that’s given so focusing on the idea is better than answering fast .
During a Thinking Math lesson, students should work academically together. They should learn from their mistakes and learn to accept failure not make things a big deal. The term, ¨Making mistakes can help you become better at math.” indicates that sometimes failing is for the best. From my experience with being stuck on challenging problems, I learn to not panic and take things slow, not everything has to be solved in less than 20 seconds. Its also important to have patience. I would be a successful member of the Thinking Math classroom because one of the most important expectations is working together and having patience, and lucky for me I do both of those somewhat good.
When doing a Thinking Math lesson, a good and successful student communicates with their peers and explains everything carefully. If a student does not explain things carefully then their classmates cant follow along and understand what they are doing. A good student also lets others work with them and listens to what they are saying. If a student doesn’t communicate with their peers then they will get less work done because they cant share each other’s ideas with each other. When you are doing a group project its important to communicate with your peers so you can get as much ideas as you can to expand your knowledge.
1. A successful student is a student that Shares ideas openly, asks questions, and engages in math talk rather than waiting passively for answers.
2. A strategy to use when stuck is reading the text two or three times to find hidden clues or numbers.
3.Working Together in a group is to pay close attention when a teammate shares a different way to solve a step.
4.Learning from Mistakes is Making mistakes helps you grow because your brain builds new connections when you fix an error.
5.Being a Classroom Member is Sharing ideas out loud with a partner.
Communication, listening, and sharing ideas are the secrets to success in both math and group projects.
What a successful student dose during a math lesson if your working with a group you get to know the people your working with you take some of the plans and put it down on you notes so you can keep It. and when you by your self when teacher talking take what he talking about put it in your notes and when he done take what you got of the notes and put it down to help you get a A
A successful student does work and they include their team in the work instead of working independently. A good group will not make one student do all the work then the rest of the group takes all the credit.When you are stuck on a problem try to use the method that works best for you, and if you make a mistake it will be okay but figure out the mistake then fix it.”Making mistakes makes you better at math” if you don’t try you will never figure out the answer.
1. A successful student in a Thinking Math lesson actively engages with the task by sharing ideas and asking clarifying questions. They collaborate closely with their small group, ensuring that everyone discusses the problem rather than just rushing to find a single answer. To show mathematical thinking, the student explains their reasoning using pictures, numbers, and words instead of just writing down a final solution. They remain open to different problem-solving methods and carefully analyze how their peers approach the same challenge. Ultimately, their focus is on understanding the deeper mathematical concepts rather than simply completing the worksheet first. 2. When you get stuck on a challenging math problem, you should pause, breathe, and use structured problem-solving strategies rather than staring blankly at the page or immediately giving up. 3.During a Thinking Math activity (often part of a “Building Thinking Classrooms” model using vertical non-permanent surfaces or group-worthy tasks), students share the brainpower of the whole team rather than working alone. 4.Redo a fresh problem: Try a similar problem from the beginning to prove to yourself that you know the method now. 5.I will be a successful member of the Thinking Math classroom by actively sharing ideas, standing up and working on vertical whiteboards with my group, and viewing mistakes as important steps for learning.
A successful student does work and they include their team in the work instead of working independently. A good group will not make one student do all the work then the rest of the group takes all the credit.When you are stuck on a problem try to use the method that works best for you, and if you make a mistake it will be okay but figure out the mistake then fix it.”Making mistakes makes you better at math” if you don’t try you will never figure out the answer.
To be a successful member of our Thinking Math classroom, I will share my ideas, draw models, and actively contribute instead of letting one person do all the work. I agree that making mistakes helps you learn, so if I get an answer wrong, I’ll find my error instead of just erasing it. When stuck, I promise to try three things before asking the teacher: reread to mark key details, sketch a diagram, or try the problem with simpler numbers. In groups, I will listen to my partners, give my input even if I’m unsure, and include quieter teammates. While explaining my own thinking will be easy, being patient when someone explains a slower method will be a challenge. To improve, I will pause and ask them a question to understand their strategy.
A successful student does work and they include their team in the work instead of working independently. A good group will not make one student do all the work then the rest of the group takes all the credit.When you are stuck on a problem try to use the method that works best for you, and if you make a mistake it will be okay but figure out the mistake then fix it.”Making mistakes makes you better at math” if you don’t try you will never figure out the answer and thats it.
Instead of working alone, a successful student collaborates with their team. A good group won’t assign all of the work to one kid and then claim all the credit.Try to adopt the approach that works best for you when you are stuck on a subject. If you make a mistake, it’s alright as long as you identify it and correct it.You get better at arithmetic by making mistakes. If you don’t attempt, you won’t be able to solve the problem.
A Thinking Math lesson, students should actually do work together, and not goof around. Students should see that making mistakes is a crucial part of learning and growing. Not doubting yourself. The quote, “Making mistakes can help you become better at math.” shows that sometimes failing is for the best. It’s also important to not doubt yourself. I would be good member of the Thinking Math classroom because I’m good at math and I work with groups well.
A successful student listens to what the teacher has to say and actually tries to learn so they can be successful in the future. Also when you have to work in a group a successful student actually tries to communicate with the people in their group, and actually does they’re part to do the work so they get good grades.
When you answer quickly, your mind doesn’t have time to overthink or get distracted by other problems. The strategies I use to solve things faster and ensure good results involve simply focusing on the task at hand and ignoring gossip or comments from others. I also focus on one thing at a time because I struggle to multitask; trying to do two things at once can slow your mind down. Many students get so caught up in learning strategies that they fail to solve actual problems, focusing instead on a single approach that may not even work. One way to complete your work with better understanding is to ask others or the teacher for help. Working in teams that actually provide support—rather than just chatting—makes the job easier; however, things don’t have to be perfect, and running into problems is fine, since we learn from our mistakes.
focuses on reasoning through the process and understanding how numbers work rather than just A successful student in a Thinking Math lesson actively engages with the task by sharing ideas and asking questions. They collaborate closely with their small group, ensuring that everyone discusses them by just rushing to find a single answer. To show mathematical thinking, the student explains their reasoning using pictures, numbers, and words instead of just writing down a final solution. They remain open to different problem-solving methods and carefully show their peers the same challenge. Ultimately, their focus is on understanding the deeper mathematical concepts rather than simply completing the first. When you get stuck on a challenging math problem, you should pause, breathe, and use structured problem solving strategies rather than staring blankly at the page or immediately giving up.During a Thinking Math activity (often part of a “Building Thinking Classrooms” model using vertical non-permanent surfaces or group-worthy tasks, students share the brainpower of the whole team rather than working alone. a fresh problem: Try a similar problem from the beginning to prove to yourself that you know the method .
When doing a Thinking Math lesson, a good and successful student communicates with their peers and explains everything carefully. If a student does not explain things carefully then their classmates cant follow along and understand what they’re doing. A good student also lets others work with them and listens to what they’re saying. If a student doesn’t communicate with their peers then they will get less work done because they cant share each other’s ideas with each other. When you are doing a group project its important to communicate with your peers so you can get as much ideas as you can to expand your knowledge.
Thinking mathematically is less about calculating numbers and more about a disciplined, curious mindset that seeks out the underlying order of the world. It is a creative, cyclical process where you investigate confusing problems by searching for patterns, visualizing abstract relationships, and breaking complex structures into simpler pieces. Instead of relying on memorized rules, a mathematical thinker experiments with specific examples to form hypotheses, generalizes those findings into universal principles, and logically proves why they must be true. Ultimately, it shifts your perspective from asking “What is the answer to asking “Why does this pattern work turning frustration and mistakes into valuable data points along the way.
A successful student in thinking math works and thinks with their group. When they are stuck they first explain what they understand and where they got stuck.Students should work together and have a strong group. They do that by having every person contribute to the conversation. The statement “Making mistakes can help you become better at math.” is correct because mistakes are important to getting better. I will be a successful member of our Thinking Math classroom by contributing to my group, understanding where I get stuck, and coming back from my mistakes.
To be a successful member of Thinking Math classroom is to share your ideas with your group, and to participate with the group. When you are stuck on a math question you can either ask your partners or if they don’t know what to do then you can ask the teacher for help. If i get something wrong with a math question then I’ll fix my mistakes and work on it. Mistakes can help you learn certain things, so if I get an answer wrong, I will try again and work on it so that I can get a good grade. A good group will not make one student do all the work, then the group has to participate so that they can earn credit.
A successful student engages and does the work the teacher told them to do and listens to the teacher.They also help their team understand the tasks and helps them when they do not understand the assignment.They stay on task and participate with there group and have ideas not help them.When stuck on a challenge you should raise your hand and ask the teacher or someone from your table.They should help each other figure out the problem,listen to the instructions the teacher says, and contribute something to what they are doing. I agree with the statement “Making mistakes can help you become better at math.” Because if you make mistakes you can learn from them and get it right.I will be a successful member of our Thinking Math classroom, by using the tools I have, asking people for help, and listening to the teacher.