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20 Math Critical Thinking Questions to Ask in Class Tomorrow

• November 20, 2023

The level of apathy towards math is only increasing as each year passes and it’s up to us as teachers to make math class more meaningful . This list of math critical thinking questions will give you a quick starting point for getting your students to think deeper about any concept or problem. 

Since artificial intelligence has basically changed schooling as we once knew it, I’ve seen a lot of districts and teachers looking for ways to lean into AI rather than run from it.

The idea of memorizing formulas and regurgitating information for a test is becoming more obsolete. We can now teach our students how to use their resources to make educated decisions and solve more complex problems.

With that in mind, teachers have more opportunities to get their students thinking about the why rather than the how.

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Looking for more about critical thinking skills? Check out these blog posts:

• Why You Need to Be Teaching Writing in Math Class Today
• How to Teach Problem Solving for Mathematics
• Turn the Bloom’s Taxonomy Verbs into Engaging Math Activities

What skills do we actually want to teach our students?

As professionals, we talk a lot about transferable skills that can be valuable in multiple jobs, such as leadership, event planning, or effective communication. The same can be said for high school students. 

It’s important to think about the skills that we want them to have before they are catapulted into the adult world. 

Do you want them to be able to collaborate and communicate effectively with their peers? Maybe you would prefer that they can articulate their thoughts in a way that makes sense to someone who knows nothing about the topic.

Whatever you decide are the most essential skills your students should learn, make sure to add them into your lesson objectives.

When should I ask these math critical thinking questions?

Critical thinking doesn’t have to be complex or fill an entire lesson. There are simple ways that you can start adding these types of questions into your lessons daily!

Start small

Add specific math critical thinking questions to your warm up or exit ticket routine. This is a great way to start or end your class because your students will be able to quickly show you what they understand. 

Asking deeper questions at the beginning of your class can end up leading to really great discussions and get your students talking about math.

Add critical thinking questions to word problems

Word problems and real-life applications are the perfect place to add in critical thinking questions. Real-world applications offer a more choose-your-own-adventure style assignment where your students can expand on their thought processes. 

They also allow your students to get creative and think outside of the box. These problem-solving skills play a critical role in helping your students develop critical thinking abilities.

Keep reading for math critical thinking questions that can be applied to any subject or topic!

When you want your students to defend their answers.

• Explain the steps you took to solve this problem
• How do you know that your answer is correct?
• Draw a diagram to prove your solution.
• Is there a different way to solve this problem besides the one you used?
• How would you explain _______________ to a student in the grade below you?
• Why does this strategy work?
• Use evidence from the problem/data to defend your answer in complete sentences.

When you want your students to justify their opinions

• What do you think will happen when ______?
• Do you agree/disagree with _______?
• What are the similarities and differences between ________ and __________?
• What suggestions would you give to this student?
• What is the most efficient way to solve this problem?
• How did you decide on your first step for solving this problem?

When you want your students to think outside of the box

• How can ______________ be used in the real world?
• What might be a common error that a student could make when solving this problem?
• How is _____________ topic similar to _______________ (previous topic)?
• What examples can you think of that would not work with this problem solving method?
• What would happen if __________ changed?
• Create your own problem that would give a solution of ______________.
• What other math skills did you need to use to solve this problem?

Let’s Recap:

• Rather than running from AI, help your students use it as a tool to expand their thinking.
• Identify a few transferable skills that you want your students to learn and make a goal for how you can help them develop these skills.
• Add critical thinking questions to your daily warm ups or exit tickets.
• Ask your students to explain their thinking when solving a word problem.
• Get a free sample of my Algebra 1 critical thinking questions ↓

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Elementary Assessments

101 Great Higher-Order Thinking Questions for Math

If you’re looking to improve students’ critical thinking skills in mathematics, science, or technology classes, it is beneficial to utilize higher-order thinking questions for math. 

While it’s important that students know their basic math facts and the steps for how to solve a math word problem, what’s even more important is their ability to use higher-order thinking skills.

That is what separates weak math students from strong ones, the ability to think deeply about math concepts beyond the literal.

But how can we get students to that level? The answer is by utilizing higher-order thinking questions for math. 

Higher-order thinking questions are critical thinking questions that require students to infer, apply, predict, connect, evaluate, and judge knowledge in new ways. 

The answers to these questions require prior knowledge and an expansive schema so that readers can see beyond the facts and information in front of them.

What’s more, these questions encourage the consideration of alternative explanations.

Possessing this type of critical thinking skill is essential not only in math class but in all subjects. 

Here you will find a collection of H.O.T.S higher-order thinking questions for math. Used consistently, these questions will improve students’ test scores and their confidence in math.

What’s more, students will begin to think deeper about math concepts without much prompting, become better problem-solvers, and be able to articulate their math processes more clearly.

101 Higher-Order Thinking Questions for Math

Following you will find various levels of math higher-order thinking questions categorized from “easiest” to “hardest”.

• How would you define this word?
• What do you remember about this math word problem?
• Can you name_____?
• How would you rephrase the question?
• What is _____?
• Who or what is this story problem about?
• What have you heard about_____?
• Can you list the steps for _____?
• How would you define the term_____?
• What is the setting of the math story problem?
• Will you please explain why you think this?
• How would you state this problem in your own words?
• What problem are you trying to solve?
• So what do you know so far?
• What information or clues are presented in the word problem?
• What strategy do you plan to use to solve the problem? Why?
• How would you outline the steps of _____?
• What is the difference between these two ideas or concepts?
• What can be inferred from_____?
• How would you explain this to someone?
• What knowledge do you have that is not stated in the problem?
• How would you summarize the main idea of this chapter?
• What is the main idea of this part?
• What else do you understand now?

Related Content:

80+ More Higher-Order Thinking Questions (All Subjects)

• How can you restate what the problem is asking?
• What can be said about_____?
• How would you describe this shape?
• What unanswered questions do you have?
• How would you compare and contrast _____ and _____?
• Could you elaborate on the steps you used to solve this problem?
• What would happen if _____?
• How would you differentiate between _____ and _____?
• What illustrations, diagrams, or other visuals would aid understanding?
• Could you clarify the part about_____?
• What have you learned today?
• How have you tackled similar problems in the past?
• What information is needed to solve the problem?
• Are you able to tell the main idea of this lesson/activity?
• What parts confused you?
• What can you infer from reading this part of the math textbook?

• How would you illustrate_____?
• What examples can you provide to prove this?
• Why does this strategy work?
• How would you classify these numbers?
• How could this problem be presented so that it is understood by others?
• What would be the result if _____?
• What action steps do you need to take in order to perform this math word problem?
• How could this be modified _____?
• How can this math word problem be demonstrated?
• How would you solve this problem?
• What other way could you have solved this problem?
• How would doing ___ change the final results?
• What are the advantages and disadvantages of _____?
• Are you able to provide an example of _____?
• How would you classify these things?
• Will you explain what you have done so far?
• Which evidence from the math word problem supports your claim?
• How would you order_____? 
• What are the pros and cons of solving the problem this way?
• How can these two concepts be compared?
• What are the pros and cons of using_____?
• Do you notice a pattern here?
• Will you explain the method you used to solve the problem?
• How would you explain_____?
• What explanation do you have for_____?
• How did you use prior knowledge to help you solve this problem?
• How is _____ similar to_____?
• What do you predict will be the solution?
• How does this relate to_____?
• Can you tell me how you came up with that answer?
• How is math all around us?
• Does your answer seem reasonable? Why or why not?
• How can you justify your answer?
• What changes could be made to revise_____?
• What would happen if we changed this part?
• How did you come to that conclusion?
• What strategy could you come up with to solve_____?
• How would you elaborate upon this?
• What do you predict will be the final outcome?
• Why is this strategy better to use in this situation than that one?
• How could you disapprove this answer?
• What prompted you to solve the problem this way?
• How would changing this number affect the outcome?
• What if you had executed this strategy? How would that have affected the outcome?
• Why did you choose to use this particular strategy?
• What made you organize your data like this?
• Do you think there’s a better way to solve this? 
• Have all possibilities been considered?
• Do you agree with this? Why or why not?
• What would have happened if _____?
• How would you grade_____?
• What suggestion do you have for_____?
• Which part is the most important and why?
• How can you determine which facts _____?
• What is your opinion about_____?
• How could you prove that_____?
• What criteria would you use to assess_____?
• How would you rank the importance of _____?
• What information was used to evaluate the outcome?
• Did you agree with the outcome? Why or why not?
• What data could you use to prove your answer?

Final Thoughts On Higher-Order Thinking Questions for Math

Create confident mathematicians in your classroom by utilizing these helpful higher-order thinking questions for math. 

Using these higher-level questions, students will become better thinkers, better problem-solvers, and more self-assured in their math abilities. 

A solid math foundation is one of the keys to success in school and life beyond the classroom.

If you found these higher-order thinking questions for math helpful, you might be interested in math sentence stems .

Related: Practice math higher-order thinking using these math word problems.

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• Critical Thinking

How To Encourage Critical Thinking in Math

By Mary Montero

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Critical thinking is more than just a buzzword… It’s an essential skill that helps students develop problem-solving abilities and make logical connections between different concepts. By encouraging critical thinking in math, students learn to approach problems more thoughtfully, they learn to analyze and evaluate math concepts, identify patterns and relationships, and explore different strategies for finding the solution. Critical thinking also involves a great deal of persistence. Those are critical life skills!

When you think about it, students are typically asked to solve math problems and find the answer. Showing their work is frequently stressed too, which is important, but not the end. Instead, students need to be able to look at math in different ways in order to truly grasp a complete understanding of math concepts. Mathematics requires logical reasoning, problem-solving, and abstract thinking.

What Does Critical Thinking in Math Look Like?

When I think about critical thinking in math, I focus on:

• Solving problems through logical thinking . Students learn how to break down complex problems, analyze the different parts, and understand how they fit together logically.
• Identifying patterns and making connections. Students learn how to identify patterns across different math concepts, make connections between seemingly unrelated topics, and develop a more in-depth understanding of how math works.
• Evaluating and comparing solutions. Students learn to evaluate which solution is best for a given problem and identify any flaws in their reasoning or others’ reasoning when looking at different solutions

Mathematician Posters

These FREE Marvelous Mathematician posters have been a staple in my classroom for the last 8+ years! I first started using a version from MissMathDork and adapted them for my classroom over the years. 

I print, laminate, and add magnetic stickers on the back. At the beginning of the year, I only put one or two up at a time depending on our area of focus. Now, they are all hanging on my board, and I’ll pull out different ones depending on our area of focus. They are so empowering to my mathematicians and help them stay on track!

A Marvelous Mathematician:

• knows that quicker doesn’t mean better
• looks for patterns
• knows mistakes happen and keeps going
• makes sense of the most important details
• embraces challenges and works through frustrations
• uses proper math vocabulary to explain their thinking
• shows their work and models their thinking
• discusses solutions and evaluates reasonableness
• gives context by labeling answers
• applies mathematical knowledge to similar situations
• checks for errors (computational and conceptual)

Critical Thinking Math Activities

Here are a few of my favorite critical thinking activities. 

Square Of Numbers

I love to incorporate challenge problems (use Nrich and Openmiddle to get started) because they teach my students so much more than how to solve a math problem. They learn important lessons in teamwork, persistence, resiliency, and growth mindset. We talk about strategies for tackling difficult problems and the importance of not giving up when things get hard.

This square of numbers challenge was a hit!

ALL kids need to feel and learn to embrace challenge. Oftentimes, kids I see have rarely faced an academic challenge. Things have just come easy to them, so when it doesn’t, they can lack strategies that will help them. In fact, they will often give up before they even get started.

I tell them it’s my job to make sure I’m helping them stretch and grow their brain by giving them challenges. They don’t love it at first, but they eventually do! 

This domino challenge was another one from Nrich . I’m always on the hunt for problems like this!!  How would you guide students toward an answer??

Fifteen Cards

This is a well-loved math puzzle with my students, and it’s amazing for encouraging students to consider all options when solving a math problem.

We have number cards 1-15 (one of each number) and only seven are laid out. With the given clues, students need to figure out which seven cards should be put out and in what order. My students love these, and after they’ve done a few, they enjoy creating their own, too! Use products, differences, and quotients to increase the challenge.

This is also adapted from Nrich, which is an AMAZING resource for math enrichment!

This is one of my favorite fraction lessons that I’ve done for years! Huge shout out to Meg from The Teacher Studio for this one. I give each child a slip of paper with this figure and they have to silently write their answer and justification. Then I tally up the answers and have students take a side and DEBATE with their reasoning! It’s an AMAZING conversation, and I highly recommend trying it with your students. 

Sometimes we leave it hanging overnight and work on visual models to make some proofs. 

Logic Puzzles

Logic puzzles are always a hit too! You can enrich and extend your math lessons with these ‘Math Mystery’ logic puzzles that are the perfect challenge for 4th, 5th, and 6th grades. The puzzles are skills-based, so they integrate well with almost ANY math lesson. You can use them to supplement instruction or challenge your fast-finishers and gifted students… all while encouraging critical thinking about important math skills!

Three levels are included, so they’re perfect to use for differentiation.

• Introductory logic puzzles are great for beginners (4th grade and up!)
• Advanced logic puzzles are great for students needing an extra challenge
• Extra Advanced logic puzzles are perfect for expert solvers… we dare you to figure these puzzles out! 

Do you have a group of students who are ready for more of a fraction challenge? My well-loved fraction puzzlers are absolutely perfect for fraction enrichment. They’ll motivate your students to excel at even the most challenging tasks! 

Math Projects

Math projects are another way to differentiation while building critical thinking skills. Math projects hold so much learning power with their real-world connections, differentiation options, collaborative learning opportunities, and numerous avenues for cross curricular learning too. 

If you’re new to math projects, I shared my best tips and tricks for using math projects in this blog post . They’re perfect for cumulative review, seasonal practice, centers, early finisher work, and more.

I use both concept-based math projects to focus on specific standards and seasonal math projects that integrate several skills.

Error Analysis

Finally, error analysis is always a challenging way to encourage critical thinking. When we use error analysis, we encourage students to analyze their own mistakes to prevent making the same mistakes in the future.

For my gifted students, I use error analysis tasks as an assessment when they have shown mastery of a unit during other tasks. For students in the regular classroom needing enrichment, I usually have them complete the tasks in a center or with a partner.

For students needing extra support, we complete error analysis in small groups.  We go step-by-step through the concept and they are always able to eventually identify what the error is. It is so empowering to students when they finally figure out the error AND it helps prevent them from making the same error in the future!

My FREE addition error analysis is a good place to start, no matter the grade level. I show them the process of walking through the problem and how best to complete an error analysis task.

When you’re ready for more, this bundle of error analysis tasks contains more than 240 tasks to engage and enrich your students in critical thinking practice.

If you want to dig even deeper, visit this conceptual vs computational error analysis post to learn more about using error analysis in the classroom. 

Related Critical Thinking Posts

• How to Increase Critical Thinking and Creativity in Your “Spare” Time
• More Tips to Increase Critical Thinking

Critical thinking is essential for students to develop a deeper understanding of math concepts, problem-solving skills, and a stronger ability to reason logically. When you learn how to encourage critical thinking in math, you’re setting your students up for success not only in more advanced math subjects they’ll encounter, but also in life. 

How do you integrate critical thinking in your classroom? Come share your ideas with us in our FREE Inspired In Upper Elementary Facebook group .

Mary Montero

I’m so glad you are here. I’m a current gifted and talented teacher in a small town in Colorado, and I’ve been in education since 2009. My passion (other than my family and cookies) is for making teachers’ lives easier and classrooms more engaging.

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Mary Thankyou for your inspirational activities. I have just read and loved the morning talk activities. I do have meetings with my students but usually at end of day. What time do you

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Using Questioning to Stimulate Mathematical Thinking

Types of questions, levels of mathematical thinking, combining the categories.

Engaging Maths

Dr catherine attard, promoting creative and critical thinking in mathematics and numeracy.

• by cattard2017
• Posted on June 25, 2017

What is critical and creative thinking, and why is it so important in mathematics and numeracy education?

Numeracy is often defined as the ability to apply mathematics in the context of day to day life. However, the term ‘critical numeracy’ implies much more. One of the most basic reasons for learning mathematics is to be able to apply mathematical skills and knowledge to solve both simple and complex problems, and, more than just allowing us to navigate our lives through a mathematical lens, being numerate allows us to make our world a better place.

The mathematics curriculum in Australia provides teachers with the perfect opportunity to teach mathematics through critical and creative thinking. In fact, it’s mandated. Consider the core processes of the curriculum. The Australian Curriculum (ACARA, 2017), requires teachers to address four proficiencies : Problem Solving, Reasoning, Fluency, and Understanding. Problem solving and reasoning require critical and creative thinking (). This requirement is emphasised more heavily in New South wales, through the graphical representation of the mathematics syllabus content , which strategically places Working Mathematically (the proficiencies in NSW) and problem solving, at its core. Alongside the mathematics curriculum, we also have the General Capabilities , one of which is Critical and Creative Thinking – there’s no excuse!

Critical and creative thinking need to be embedded in every mathematics lesson . Why? When we embed critical and creative thinking, we transform learning from disjointed, memorisation of facts, to sense-making mathematics. Learning becomes more meaningful and purposeful for students.

How and when do we embed critical and creative thinking?

There are many tools and many methods of promoting thinking. Using a range of problem solving activities is a good place to start, but you might want to also use some shorter activities and some extended activities. Open-ended tasks are easy to implement, allow all learners the opportunity to achieve success, and allow for critical thinking and creativity. Tools such as Bloom’s Taxonomy and Thinkers Keys  are also very worthwhile tasks. For good mathematical problems go to the nrich website . For more extended mathematical investigations and a wonderful array of rich tasks, my favourite resource is Maths300   (this is subscription based, but well worth the money). All of the above activities can be used in class and/or for homework, as lesson starters or within the body of a lesson.

Will critical and creative thinking take time away from teaching basic concepts?

No, we need to teach mathematics in a way that has meaning and relevance, rather than through isolated topics. Therefore, teaching through problem-solving rather than for problem-solving. A classroom that promotes and critical and creative thinking provides opportunities for:

• higher-level thinking within authentic and meaningful contexts;
• complex problem solving;
• open-ended responses; and
• substantive dialogue and interaction.

Who should be engaging in critical and creative thinking?

Is it just for students? No! There are lots of reasons that teachers should be engaged with critical and creative thinking. First, it’s important that we model this type of thinking for our students. Often students see mathematics as black or white, right or wrong. They need to learn to question, to be critical, and to be creative. They need to feel they have permission to engage in exploration and investigation. They need to move from consumers to producers of mathematics.

Secondly, teachers need to think critically and creatively about their practice as teachers of mathematics. We need to be reflective practitioners who constantly evaluate our work, questioning curriculum and practice, including assessment, student grouping, the use of technology, and our beliefs of how children best learn mathematics.

Critical and creative thinking is something we cannot ignore if we want our students to be prepared for a workforce and world that is constantly changing. Not only does it equip then for the future, it promotes higher levels of student engagement, and makes mathematics more relevant and meaningful.

How will you and your students engage in critical and creative thinking?

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Course Contents

What is critical thinking, critical thinking.

Thinking comes naturally. You don’t have to make it happen—it just does. But you can make it happen in different ways. For example, you can think positively or negatively. You can think with “heart” and you can think with rational judgment. You can also think strategically and analytically, and mathematically and scientifically. These are a few of multiple ways in which the mind can process thought.

What are some forms of thinking you use? When do you use them, and why?

As a college student, you are tasked with engaging and expanding your thinking skills. One of the most important of these skills is critical thinking. Critical thinking is important because it relates to nearly all tasks, situations, topics, careers, environments, challenges, and opportunities. It’s a “domain-general” thinking skill—not a thinking skill that’s reserved for a one subject alone or restricted to a particular subject area.

Great leaders have highly attuned critical thinking skills, and you can, too. In fact, you probably have a lot of these skills already. Of all your thinking skills, critical thinking may have the greatest value.

What Is Critical Thinking?

Critical thinking is clear, reasonable, reflective thinking focused on deciding what to believe or do. It means asking probing questions like, “How do we know?” or “Is this true in every case or just in this instance?” It involves being skeptical and challenging assumptions, rather than simply memorizing facts or blindly accepting what you hear or read.

Who are critical thinkers, and what characteristics do they have in common? Critical thinkers are usually curious and reflective people. They like to explore and probe new areas and seek knowledge, clarification, and new solutions. They ask pertinent questions, evaluate statements and arguments, and they distinguish between facts and opinion. They are also willing to examine their own beliefs, possessing a manner of humility that allows them to admit lack of knowledge or understanding when needed. They are open to changing their mind. Perhaps most of all, they actively enjoy learning, and seeking new knowledge is a lifelong pursuit.

This may well be you!

The following video, from Lawrence Bland, presents the major concepts and benefits of critical thinking.

Critical Thinking and Logic

Critical thinking is fundamentally a process of questioning information and data. You may question the information you read in a textbook, or you may question what a politician or a professor or a classmate says. You can also question a commonly-held belief or a new idea. With critical thinking, anything and everything is subject to question and examination for the purpose of logically constructing reasoned perspectives.

Questions of Logic in Critical Thinking

Let’s use a simple example of applying logic to a critical-thinking situation. In this hypothetical scenario, a man has a PhD in political science, and he works as a professor at a local college. His wife works at the college, too. They have three young children in the local school system, and their family is well known in the community. The man is now running for political office. Are his credentials and experience sufficient for entering public office? Will he be effective in the political office? Some voters might believe that his personal life and current job, on the surface, suggest he will do well in the position, and they will vote for him. In truth, the characteristics described don’t guarantee that the man will do a good job. The information is somewhat irrelevant. What else might you want to know? How about whether the man had already held a political office and done a good job? In this case, we want to ask, How much information is adequate in order to make a decision based on logic instead of assumptions?

The following questions are ones you may apply to formulating a logical, reasoned perspective in the above scenario or any other situation:

• What’s happening? Gather the basic information and begin to think of questions.
• Why is it important? Ask yourself why it’s significant and whether or not you agree.
• What don’t I see? Is there anything important missing?
• How do I know? Ask yourself where the information came from and how it was constructed.
• Who is saying it? What’s the position of the speaker and what is influencing them?
• What else? What if? What other ideas exist and are there other possibilities?

Problem-Solving with Critical Thinking

For most people, a typical day is filled with critical thinking and problem-solving challenges. In fact, critical thinking and problem-solving go hand-in-hand. They both refer to using knowledge, facts, and data to solve problems effectively. But with problem-solving, you are specifically identifying, selecting, and defending your solution.

Problem-Solving Action Checklist

Problem-solving can be an efficient and rewarding process, especially if you are organized and mindful of critical steps and strategies. Remember, too, to assume the attributes of a good critical thinker. If you are curious, reflective, knowledge-seeking, open to change, probing, organized, and ethical, your challenge or problem will be less of a hurdle, and you’ll be in a good position to find intelligent solutions.

Critical Thinking, Problem Solving, and Math

In previous math courses, you’ve no doubt run into the infamous “word problems.” Unfortunately, these problems rarely resemble the type of problems we actually encounter in everyday life. In math books, you usually are told exactly which formula or procedure to use, and are given exactly the information you need to answer the question. In real life, problem solving requires identifying an appropriate formula or procedure, and determining what information you will need (and won’t need) to answer the question.

• "Student Success-Thinking Critically In Class and Online."  Critical Thinking Gateway . St Petersburg College, n.d. Web. 16 Feb 2016. ↵
• Critical Thinking Skills. Authored by : Linda Bruce. Provided by : Lumen Learning. Located at : https://courses.lumenlearning.com/collegesuccess-lumen/chapter/critical-thinking-skills/ . Project : College Success. License : CC BY: Attribution
• Critical Thinking. Authored by : Critical and Creative Thinking Program. Located at : http://cct.wikispaces.umb.edu/Critical+Thinking . License : CC BY: Attribution
• Thinking Critically. Authored by : UBC Learning Commons. Provided by : The University of British Columbia, Vancouver Campus. Located at : http://www.oercommons.org/courses/learning-toolkit-critical-thinking/view . License : CC BY: Attribution
• Problem Solving. Authored by : David Lippman. Located at : http://www.opentextbookstore.com/mathinsociety/ . Project : Math in Society. License : CC BY-SA: Attribution-ShareAlike
• Critical Thinking.wmv. . Authored by : Lawrence Bland. Located at : https://youtu.be/WiSklIGUblo . License : All Rights Reserved . License Terms : Standard YouTube License

Critical Thinking Questions for 6th Grade Math

Activities to help students answer inferential questions.

Sixth grade students have mastered the four operations of mathematics -- addition, subtraction, division and multiplication. By the end of the year, these middle school students have used these operations with decimals, fractions and negative numbers. At this point, math also involves reasoning, building on knowledge and observing; these skills are encouraged by higher level questions and participation from the students in a collaborative setting.

Open Questions

Asking open questions is a way to provide an opportunity for your students to think critically. For example, asking the sixth grade students how many polygons they can make with an area of 24 units is an open question. A closed question with the same objective is to have a polygon drawn and ask them the area of that polygon. Open questions can have more than one answer, and differentiation occurs automatically with this type of question. The more advanced students search for many ways to construct the polygon and answer the question. Other students also try to find a polygon to meet the criteria, realize that finding the many answers is valued, and continue working. Discussion of the different ways to answer the open question adds value to the question in the sixth grade classroom.

Questioning Words

In Bloom's Taxonomy, a collection of verbs is divided into levels of thinking. Appraise, compare, contrast, criticize, differentiate, discriminate, distinguish, examine and question are verbs from Bloom's "analyzing" level, which encourages critical thinking. For example, having your sixth graders compare the distances around various circles' circumferences to their diameter measurements is a great introduction to pi and the formula for the circumference of a circle. It is also a critical thinking question which promotes exploration.

Great questions are wasted if wait time is not given for the answers. Too often teachers don't allow the students time to think and answer, blurting out the answer themselves or calling on another student. Some sixth grade students need more time to formulate their answers. Teachers should provide a few seconds of wait time for students to process the question and their answer.

Make Connections

Math builds on prior lessons. Critical thinking questions should help the sixth grade students see those relationships and connections. Teachers should ask students how the problem they are working on is connected to something they learned previously. For example, when your sixth graders are learning about ratios, you can remind them of their study of similar triangles. By asking them to think of how ratio and similar triangles are connected, the students are led to review what they have already learned about similar shapes and apply it to the study of ratios. The teacher helps the students to see the relationship between the two concepts and to deepen their understanding through the connections.

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Susan Rickey started writing in 1994 with a technology feature article for the "Pioneer Press." She was the writer of the Klamath Forest Alliance newsletter, an environmental organization. Rickey obtained her teaching credential from California State University and acquired her Bachelor of Science from the University of Arkansas.

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Critical thinking questions math

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100+ Critical Thinking Questions for Students To Ask About Anything

Critical thinkers question everything.

In an age of “fake news” claims and constant argument about pretty much any issue, critical thinking skills are key. Teach your students that it’s vital to ask questions about everything, but that it’s also important to ask the right sorts of questions. Students can use these critical thinking questions with fiction or nonfiction texts. They’re also useful when discussing important issues or trying to understand others’ motivations in general.

“Who” Critical Thinking Questions

Questions like these help students ponder who’s involved in a story and how the actions affect them. They’ll also consider who’s telling the tale and how reliable that narrator might be.

• Is the protagonist?
• Is the antagonist?
• Caused harm?
• Is harmed as a result?
• Was the most important character?

• Is responsible?
• Is most directly affected?
• Should have won?
• Will benefit?
• Would be affected by this?

• Makes the decisions?

“What” Critical Thinking Questions

Ask questions that explore issues more deeply, including those that might not be directly answered in the text.

• Background information do I know or need to know?
• Is the main message?
• Are the defining characteristics?

• Questions or concerns do I have?
• Don’t I understand?
• Evidence supports the author’s conclusion?
• Would it be like if … ?
• Could happen if … ?
• Other outcomes might have happened?
• Questions would you have asked?
• Would you ask the author about … ?
• Was the point of … ?
• Should have happened instead?
• Is that character’s motive?
• Else could have changed the whole story?

• Can you conclude?
• Would your position have been in that situation?
• Would happen if … ?
• Makes your position stronger?
• Was the turning point?
• Is the point of the question?
• Did it mean when … ?
• Is the other side of this argument?
• Was the purpose of … ?
• Does ______ mean?
• Is the problem you are trying to solve?
• Does the evidence say?
• Assumptions are you making?
• Is a better alternative?
• Are the strengths of the argument?

• Are the weaknesses of the argument?
• Is the difference between _______ and _______?

“Where” Critical Thinking Questions

Think about where the story is set and how it affects the actions. Plus, consider where and how you can learn more.

• Would this issue be a major problem?
• Are areas for improvement?
• Did the story change?
• Would you most often find this problem?

• Are there similar situations?
• Would you go to get answers to this problem?
• Can this be improved?
• Can you get more information?
• Will this idea take us?

“When” Critical Thinking Questions

Think about timing and the effect it has on the characters or people involved.

• Is this acceptable?
• Is this unacceptable?

• Does this become a problem?
• Is the best time to take action?
• Will we be able to tell if it worked?
• Is it time to reassess?
• Should we ask for help?
• Is the best time to start?
• Is it time to stop?
• Would this benefit society?

• Has this happened before?

“Why” Critical Thinking Questions

Asking “why” might be one of the most important parts of critical thinking. Exploring and understanding motivation helps develop empathy and make sense of difficult situations.

• Is _________ happening?
• Have we allowed this to happen?
• Should people care about this issue?

• Is this a problem?
• Did the character say … ?
• Did the character do … ?
• Is this relevant?
• Did the author write this?
• Did the author decide to … ?
• Is this important?

• Did that happen?
• Is it necessary?
• Do you think I (he, she, they) asked that question?
• Is that answer the best one?
• Do we need this today?

“How” Critical Thinking Questions

Use these questions to consider how things happen and whether change is possible.

• Do we know this is true?
• Does the language used affect the story?
• Would you solve … ?
• Is this different from other situations?

• Is this similar to … ?
• Would you use … ?
• Does the location affect the story?
• Could the story have ended differently?
• Does this work?
• Could this be harmful?
• Does this connect with what I already know?
• Else could this have been handled?
• Should they have responded?

• Would you feel about … ?
• Does this change the outcome?
• Did you make that decision?
• Does this benefit you/others?
• Does this hurt you/others?
• Could this problem be avoided?

More Critical Thinking Questions

Here are more questions to help probe further and deepen understanding.

• Can you give me an example?

• Do you agree with … ?
• Can you compare this with … ?
• Can you defend the actions of … ?
• Could this be interpreted differently?
• Is the narrator reliable?
• Does it seem too good to be true?

• Is ______ a fact or an opinion?

What are your favorite critical thinking questions? Come exchange ideas on the WeAreTeachers HELPLINE group on Facebook .

Plus, check out 10 tips for teaching kids to be awesome critical thinkers ., you might also like.

5 Critical Thinking Skills Every Kid Needs To Learn (And How To Teach Them)

Teach them to thoughtfully question the world around them. Continue Reading

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Critical thinking definition

Critical thinking, as described by Oxford Languages, is the objective analysis and evaluation of an issue in order to form a judgement.

Active and skillful approach, evaluation, assessment, synthesis, and/or evaluation of information obtained from, or made by, observation, knowledge, reflection, acumen or conversation, as a guide to belief and action, requires the critical thinking process, which is why it's often used in education and academics.

Some even may view it as a backbone of modern thought.

However, it's a skill, and skills must be trained and encouraged to be used at its full potential.

People turn up to various approaches in improving their critical thinking, like:

• Developing technical and problem-solving skills
• Engaging in more active listening
• Actively questioning their assumptions and beliefs
• Seeking out more diversity of thought
• Opening up their curiosity in an intellectual way etc.

Is critical thinking useful in writing?

Critical thinking can help in planning your paper and making it more concise, but it's not obvious at first. We carefully pinpointed some the questions you should ask yourself when boosting critical thinking in writing:

• What information should be included?
• Which information resources should the author look to?
• What degree of technical knowledge should the report assume its audience has?
• What is the most effective way to show information?
• How should the report be organized?
• How should it be designed?
• What tone and level of language difficulty should the document have?

Usage of critical thinking comes down not only to the outline of your paper, it also begs the question: How can we use critical thinking solving problems in our writing's topic?

Let's say, you have a Powerpoint on how critical thinking can reduce poverty in the United States. You'll primarily have to define critical thinking for the viewers, as well as use a lot of critical thinking questions and synonyms to get them to be familiar with your methods and start the thinking process behind it.

Are there any services that can help me use more critical thinking?

We understand that it's difficult to learn how to use critical thinking more effectively in just one article, but our service is here to help.

We are a team specializing in writing essays and other assignments for college students and all other types of customers who need a helping hand in its making. We cover a great range of topics, offer perfect quality work, always deliver on time and aim to leave our customers completely satisfied with what they ordered.

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Building a Thinking Classroom in Math

Over more than a decade, the author has developed a 14-point plan for encouraging students to engage deeply with math content.

One day in 2003, I was invited to help June implement problem solving in her grade 8 classroom. She had never done problem solving with her students before, but with its prominence in the recently revised British Columbia curriculum, she felt it was time.

June, as it turned out, was interested in neither co-planning nor co-teaching. What she wanted from me was simply a collection of problems she could try with her students. The first one I gave her was a Lewis Carroll problem that I’d had much success with, with students of different grade levels: If 6 cats can kill 6 rats in 6 minutes, how many will be needed to kill 100 rats in 50 minutes?

June used it the next day. It did not go well. A forest of arms immediately shot up, and June moved frantically around the room answering questions. Many students gave up quickly, so June also spent much effort trying to motivate them to keep going. In general, there was some work attempted when June was close by and encouraging the students, but as soon as she left the trying stopped. This continued for the whole period.

The following day I was back with a new problem. The results were as abysmal as they had been on the first day. The same was true the third day. Over the course of three 40-minute classes, we had seen little improvement in the students’ efforts to solve the problems, and no improvements in their abilities to do so. So June decided it was time to give up.

I wanted to understand why the results had been so poor, so I stayed to observe June and her students in their normal routines. After three full days of observation, I began to discern a pattern. That the students were lacking in effort was immediately obvious, but what took time for me to realize was that the students were not thinking. More alarming was the realization that June’s teaching was predicated on an assumption that the students either could not or would not think.

Once I realized this, I proceeded to visit 40 other mathematics classes in a number of schools. In each class, I saw the same thing—an assumption, implicit in the teaching, that the students either could not or would not think. Under such conditions it was unreasonable to expect that students were going to be able to spontaneously engage in problem solving.

This motivated me to find a way to build, within these same classrooms, a culture of thinking. I wanted to build what I now call a thinking classroom—one that’s not only conducive to thinking but also occasions thinking, a space inhabited by thinking individuals as well as individuals thinking collectively, learning together, and constructing knowledge and understanding through activity and discussion.

Over 14 years, and with the help of over 400 K–12 teachers, I’ve been engaged in a massive design-based research project to identify the variables that determine the degree to which a classroom is a thinking or non-thinking one, and to identify the pedagogies that maximize the effect of each of these variables in building thinking classrooms. From this research emerged a collection of 14 variables and corresponding optimal pedagogies that offer a prescriptive framework for teachers to build a thinking classroom.

1. The type of tasks used: Lessons should begin with good problem solving tasks. In the beginning of the school year, these tasks need to be highly engaging, non-curricular tasks. Later these are gradually replaced with curricular problem solving tasks that then permeate the entirety of the lesson.

2. How tasks are given to students: As much as possible, tasks should be given verbally. If there are data, diagrams, or long expressions in the task, these can be written or projected on a wall, but instructions should still be given verbally.

3. How groups are formed: At the beginning of every class, a visibly random method should be used to create groups of three students who will work together for the duration of the class.

4. Student work space: Groups should stand and work on vertical non-permanent surfaces such as whiteboards, blackboards, or windows. This makes the work visible to the teacher and other groups.

5. Room organization: The classroom should be de-fronted, with desks placed in a random configuration around the room—away from the walls—and the teacher addressing the class from a variety of locations within the room.

6. How questions are answered: Students ask only three types of questions: proximity questions, asked when the teacher is close; “stop thinking” questions—like “Is this right?” or “Will this be on the test?”; and “keep thinking” questions—ones that students ask in order to be able to get back to work. The teacher should answer only the third type of question.

7. How hints and extensions are used: The teacher should maintain student engagement through a judicious and timely use of hints and extensions to maintain a balance between the challenge of the task and the abilities of the students working on it.

8. Student autonomy: Students should interact with other groups frequently, for the purposes of both extending their work and getting help. As much as possible, the teacher should encourage this interaction by directing students toward other groups when they’re stuck or need an extension.

9. When and how a teacher levels their classroom: When every group has passed a minimum threshold, the teacher should pull the students together to debrief what they have been doing. This should begin at a level that every student in the room can participate in.

10. Student notes: Students should write thoughtful notes to their future selves. They should have autonomy as to what goes in the notes and how they’re formatted. The notes should be based on the work already on the boards done by their own group, another group, or a combination.

11. Practice questions: Students should be assigned four to six questions to check their understanding. They should have freedom to work on these questions in self-selected groups or on their own, and on the vertical non-permanent surfaces or at their desks. The questions should not be marked or checked for completeness—they’re for the students’ self-evaluation.

12. Formative assessment: Formative assessment should be focused primarily on informing students about where they are and where they’re going in their learning. This will require a number of different activities, from observation to check-your-understanding questions to unmarked quizzes where the teacher helps students decode their demonstrated understandings.

13. Summative assessment: Summative assessment should focus more on the processes of learning than on the products, and should include the evaluation of both group and individual work. Summative assessment should not in any way have a focus on ranking students.

14. Reporting out: Reporting out of students’ performance should be based not on the counting of points but on the analysis of the data collected for each student within a reporting cycle. The data need to be analyzed on a differentiated basis and focused on discerning the learning a student has demonstrated.

My research also shows that the variables and accompanying pedagogical tools are not all equally impactful in building thinking classrooms. And there is an optimal sequence for both teachers and students when first introducing these pedagogies. This sequence is presented as a set of four distinct toolkits that are meant to be enacted in sequence from top to bottom, as shown in the chart. When these toolkits are enacted in their entirety, an optimal transformation of the learning environment has been achieved in the vast majority of classrooms.

Open-Ended Questions for Students: How to Craft Them (20+ Examples)

As an educator, your main responsibility is to instill critical thinking skills in your students.

No student becomes successful in their career simply because they memorized and used facts in their jobs. Success comes from the ability to think deeply about the subject matter and interpret it in ways that let them apply it to real-world situations.

It’s hard for students to go beyond their textbooks unless you ask open-ended questions that allow them to engage in such thought processes.

To help you facilitate such discussions in the classroom, we’ll explore a list of open-ended question examples for students. In addition, we’ll also look at ways to craft thoughtful questions and analyze responses with ease.

Open-ended vs. closed-ended questions

The key difference between open-ended and closed-ended questions is that the former has no predefined answer. It encourages the individual to think about the question in their own way and respond accordingly.

As typical university assessments use close-ended questions with specific answers, students tend to think from a one-dimensional perspective. For example, yes/no types of questions .

While the method is sound to test their grasp of a topic’s theoretical roots, more lively discussions are needed to develop other skills.

Also, as open-ended questions require more cognitive effort , it results in a pool of answers that offer more insights compared with simple yes/no questions. This leads to more fruitful discussions in the classroom as students actively participate and put their questions and points of view forward.

Open-ended question examples for students in different subjects

Usually, open-ended questions start with a “what,” “who,” “which,” “why,” or “how.” They force the student to articulate their thoughts in a structured manner and go beyond single-word answers.

If you’re stuck trying to spin up questions for your next lecture, here are a few examples of open-ended questions to get you started:

Arts and Literature

• How does the cultural context of a novel influence its themes and characters?
• How do gender dynamics shape the narratives in classical literature versus contemporary works?
• How has digital media changed traditional forms of art and literature?
• In what ways does the [book you discussed] reflect the societal issues of its time?
• How does the “anti-hero” concept in literature challenge traditional notions of heroism?
• How do the narrative techniques in [specific book] affect your story interpretation?
• How do genetic mutations contribute to the evolution of antibiotic resistance in bacteria?
• Why do you think your environment plays a significant role in your mental health?
• What are the ethical implications of [new medical intervention] in humans?
• Which renewable energy technologies will prove to be sustainable 20 years down the line?
• What do you think about the correlation between psychology and neurobiology?
• How can we improve the method we discussed today to detect earthquakes?
• Which types of rovers do you think are best for a planet like Venus?

Mathematics

• How can mathematical models be used to predict financial markets?
• How can differential equations be applied to model and solve real-world problems in engineering?
• What role does probability theory play in everyday decision-making and risk assessment?
• How does game theory apply to economics?
• What are the mathematical foundations of AI?

Social Studies

• How has social media influenced political discourse and public opinion?
• How do historical events shape current foreign policy decisions in [country]?
• What are the ethical considerations for governments using surveillance technology?
• How do migration patterns affect urban development and demographic shifts?
• How has the concept of work changed with technological advances and the global economy?

Tips to ask open-ended questions and analyze responses

Here are a few tips for integrating this format of questioning within the classroom:

1. Integrate open-ended questions into discussions and homework

Typically, open-ended questions are limited to post-lecture discussions. But it’s essential to include them wherever you can—especially for homework assignments.

It gives learners time to think and even further research the topic to build on their understanding. This lets them develop an argument for their viewpoint, explore different perspectives, and clarify the concept.

For instance, ask them to write a short essay of 250 words or more on the lecture’s topic. As it requires them to articulate their thoughts and identify gaps in their knowledge, it’ll force them to take on further reading.

In the classroom, ask them similar questions and keep following up with statements like “Why do you think that?” or “How would that work?” to help them develop their arguments.

2. Craft questions that encourage the development of critical-thinking skills

Design a questionnaire of open-ended questions for the end of each lecture to stimulate critical thinking and problem-solving skills. This will push students to go beyond mere facts and “islands of knowledge” to make connections between seemingly disconnected issues.

Here are a few templates that can help encourage elaboration:

• “What is the impact of…”
• “How would you solve…”
• “Why do you think…”
• “Which factors do you think influence…”
• “What challenges do you foresee in…”
• “What potential solutions would work for…”

Students learn to question the status quo and assess the credibility of sources. This format also helps them get a well-rounded perspective on complex issues.

3. Make sure the question design is simple and effective

A well-crafted question is clear and straightforward. Also, it avoids overly complex language or any form of ambiguity.

The goal is to avoid confusion and keep students on the same topic. One way to do that is to prevent the use of double-barreled or leading questions.

NOT: “What do you think about renewable energy, and how will it impact our environment?”

BUT: “What do you think about renewable energy?”

When you connect the question to real-world scenarios or dilemmas, it’ll make the discussion relatable and engaging . This gives students the much-needed context required to offer meaningful answers.

4. Use technology to create an interactive classroom environment

These days, there are many types of tools available for creating engaging discussions, such as:

• Polling software
• Presentation software
• Digital whiteboards
• Discussion boards

For instance, Poll Everywhere lets you create open-ended questions or surveys that you can use within a remote or in-person session. Students can add their responses anonymously or with their names, and you can discuss the answers in real time.

Alternatively, students can also send in their questions, and you can pick the most common or interesting ones for discussion.

5. Give students a time limit to respond thoughtfully

When you set a time limit, students are compelled to think on their feet. However, it also encourages focused reflection and prioritization of ideas. This prevents overthinking or drifting off-topic, resulting in better answers.

Time constraints also give a sense of what making decisions in the real world is like, especially under pressure. This will ultimately prepare students to handle situations confidently outside the classroom.

6. Create a safe and inclusive environment to encourage responses

When you ask open-ended questions, ensure the classroom environment is safe. You can do that by allowing the students to anonymize their answers, mainly when dealing with sensitive topics.

Tools such as Poll Everywhere let you anonymize responses and moderate live discussions to create a healthy learning environment. Poll Everywhere has a feature that can automatically filter any profanity and censor abusive words. Also, students who have difficulty speaking up in class and sharing their ideas might be more likely to participate now.

When you’re asking follow-up questions, don’t use a judgmental tone. For instance, instead of saying, “Why?” use “Why do you think so?” or something similar. This fosters trust and openness in the classroom.

7. Develop a criteria for assessment of student responses

Create a rubric for assessment to ensure consistency while grading. For example, assign a weighted grade to a student mentioning a specific keyword or concept.

This grading system needs to align with the learning objectives of the course. If students miss out on specific concepts, for example, it shows that they don’t thoroughly understand the topic.

Also, communicate the criteria for grading before or after the assessment so students know what was expected in the assignment.

8. Provide real-time feedback on student responses

When students offer their responses, give them feedback. This is particularly useful in a discussion setting as other students also get to form their opinions.

Feedback should be constructive, focusing on the strengths of the response and offering specific suggestions for enhancement. It builds confidence and motivates students to engage more deeply with the material.

Feedback also provides valuable information by highlighting areas for improvement for both the student and the lecturer. The students know what went wrong with their answers, and the lecturer knows what needs to be improved or focused on in the next lecture.

Engage in lively discussions using Poll Everywhere

Using open-ended questions results in a more interactive and reflective learning environment. But a key part of that is how you implement this learning method in the classroom.

This is where digital tools can play a massive role. For instance, instead of asking open-ended questions in class directly, use a tool such as Poll Everywhere to ask them. Students can all send in their responses without needing to raise their hands and speak to the entire class. Additionally, educators can also moderate responses and grade them in one space, making it an effective tool for learning.

Poll Everywhere allows students to get real-time feedback, participate anonymously, and participate in an inclusive learning environment. This teaches them to think critically while experiencing an interactive mode of learning.

If you’re an educator looking to deploy open-ended questions, schedule a demo with Poll Everywhere today.

Related articles

• Kindergarten
• Greater Than Less Than
• Measurement
• Multiplication
• Place Value
• Subtraction
• Punctuation
• 1st Grade Reading
• 2nd Grade Reading
• 3rd Grade Reading
• Cursive Writing

Math Critical Thinking Questions For Grade 1

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