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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.

Table of Contents

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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K-5 Math Centers

K-5 math ideas, 3rd grade math, make teaching 3rd grade math less intimidating, thinking critically with fractions and number lines.

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Fractions Day 16: Word Problems and Critical Thinking

Well . . . I promised a little update on the problem solving from the other day, so here goes!

What I often do toward the end of a unit is provide students with a class period or two to work collaboratively or on their own on an assortment of word problems.  Some of the problems are right at the level I would expect them to be able to do and others “push” and help them work on their “problem attack” and perseverance.  While they work, I can circulate and coach as they get started–but then my real goal is to be able to pull small groups and individuals to work on “issues” that have come up in recent lessons.

During this round of problem solving, I wanted to pull students who are still “iffy” on equivalent fractions, on comparing fractions, and on addition/subtraction with like denominators, so I got my collection of problems ready so the students would be focused while I pulled groups.

Here is one way I organize the problems:

This is a little cheap “tent” pocket chart that I think I got a few years ago at “The Bullseye Store”  It has those pockets on both sides.

So . . . on each of my two problem solving days, I did a 15 minute review minilesson to keep cycling back through those concepts covered over the last weeks and then I sent my students off to work in their math notebooks on the variety of problems.  I DO give a little “problem talk” about the problems (8 choices this time) so the students know who the problem is about (often students in the class) and what is happening.  In this collection there was a friendship bracelet problem (I KNEW which 3 girls would make a beeline for that one), a “travel team” soccer problem, a kitten problem, a candy store problem, a “Training for a 5K” problem . . . you get the picture.  Students often gravitate toward problems with topics that interest them no matter what the math content is!  I will also give a warning if I think the problem is particularly challenging or one that I call a good “warm up” which is the sign to those who are hesitant to TRY THAT ONE FIRST!

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Understanding Fractions

Hands-on thinking activities teaching fraction fundamentals.

Grades: 2-4

Mathematics

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This 64-page math book for Grades 2-4 uses fun, step-by-step lessons to provide a thorough foundation in understanding fractions. The book begins with the meaning of fractions and their many uses - and ends with the simple math of comparing, adding, and subtracting fractions both visually and numerically. These easy-to-understand, hands-on, thinking activities build confidence by providing an understanding of fractions that is relatable to daily life. This book includes cut-out fraction circles that enable teachers to demonstrate key concepts and provide students with a tactile experience to reinforce the lesson and aid in learning new concepts. Helpful teacher notes are provided along with clear explanations for answers.

• Meaning of fractions
• Writing and using fractions
• Finding common denominators
• Simple adding and subtracting of fractions

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Fractions and Measurement: Critical Thinking (Gr. 4)

Scott Foresman, an imprint of Pearson

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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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10 Brilliant Math Brain Teasers

Tap into rigorous problem-solving and critical thinking with these playful math brain teasers for middle and high school students.  

To break the ice during the first few awkward moments of class in the new school year, high school math teacher Lorenzo Robinson uses an unusual strategy: He reads his students’ minds.

Here’s how the mystical feat unfolds: Each student picks a number between 1 and 100. Next, they use calculators to add, subtract, multiply, and divide their way through a set of predetermined numbers. At the end, everyone ends up with the same answer: 427. Robinson isn’t psychic, of course, but because the mechanics of the teaser are always the same, regardless of which initial numbers his students select, he’s able to correctly “guess” their final result—much to their amazement. 

Starting off the lesson with a math brain teaser sets a playful tone and lowers the stakes for kids, “generating a buzz around my class,” Robinson says. “It makes students feel as though this class is not going to be scary, it’s going to be interesting. ‘We’re going to be learning, but we’re also going to have some fun.’” 

Robinson thinks of math brain teasers as a variation on brain breaks —a brief respite from dense curricular material that gives kids time to pause and process. They can also provide an opportunity to build relationships and community as kids put their heads together to find solutions. Good brain teasers can be sneaky: They get kids developing problem-solving and critical thinking skills. 

Meanwhile, before introducing a new one, Robinson works through the problem himself, identifying questions that students might have along the way and making sure his class has the background knowledge to understand how the teaser works. It’s important, he says, to provide a few minutes for kids to examine and discuss the teaser. Ask them to observe, highlight, and share things that stand out. 

“The most powerful reaction is when a kid doesn’t get the correct answer,” Robinson says, and they ask to try the problem again. “They want to feel what the other kids are feeling, that educational euphoria. They want to do it again because they want to be right.” That organic intellectual curiosity is hugely helpful in high school math, Robinson says, because it can be “parlayed into the other stuff that we do.”

We combed through dozens of math brain teasers to find 10 good ones—including several of Robinson’s tried-and-true favorites.  

Number Magic: I’ll Bet Your Number is… 427

• Start by having students pick any number between 1 and 100. 
• Add 28. 
• Multiply that number by 6. 
• Subtract 3. 
• Divide that number by 3. 
• Subtract 3 more than your original number. 
• Add 8. 
• Subtract 1 less than your original number. 
• Multiply that number by 7. 

And voilà, you’ll correctly identify each student’s final result as 427. Courtesy of: Lorenzo Robinson  

Can Your Shoe Size Tell Your Age? 

• Start with your shoe size. If you are a half size—for example, size 8.5—round up to 9.
• Multiply your shoe size by 5. 
• Add 50. 
• Multiply that number by 20. 
• Subtract the year you were born—for example, 1991. Add 1 if you already had your birthday this year. 

The first digit(s) are your shoe size, and the last two digits are your age.  Courtesy of: Lorenzo Robinson.  

Cutting Across a Cross

Ask students to draw a cross on a sheet of paper. Drawing one on the board as a point of reference is helpful. Next, ask students to draw two straight lines that will segment or cut the cross into pieces. The goal is to produce the most pieces.

The solution can be found here .  Sourced from: MathisFun.com .

Number Magic: I’ll Bet Your Final Number is… 5  

• Start with a positive number. Students shouldn’t say the number out loud.
• Square that number. 
• Add 10x the original number to what you have now. 
• Add 25 to the result of the previous step. 
• Now take the square root of that number, rounding to the nearest whole number. 
• Subtract your original number.
• Before students share their final figure, reveal that you guess their collective result is 5. 

Courtesy of: Lorenzo Robinson.

Birthday Math 

Have students work in pairs and share the following instructions with their partner:

• Start with the number 7.
• Multiply that by the month of your birth. For example, if you were born in September, you’d use the number 9 to represent your birth month. 
• Subtract 1. 
• Multiply that number by 13. 
• Add the day of your birth. 
• Add 3. 
• Multiply that number by 11. 
• Subtract the month of your birth. 
• Subtract the day of your birth. 
• Divide by 10.
• Add 11 to that number. 
• Divide by 100. 

The result on the calculator screen should be their partner’s birthday.  Sourced from: Dr. Mike’s Math Games for Kids .

Coin Conundrum

Ask students to imagine that they have two coins that total 30 cents in value. Have them try to figure out what the two coins are, only providing them with a singular piece of information: One of the coins is not a nickel. The answer: A quarter and a nickel. (Only one of the coins is not a nickel.)

Sourced from: WeAreTeachers .

The Phone Number Trick  

• Ignoring your area code, type the first three digits of your phone number into a calculator.
• Multiply that number by 80. 
• Add 1. 
• Multiply that number by 250. 
• Add the last four digits of your phone number. 
• Add the last four digits of your phone number again. 
• Subtract 250. 
• Divide this number by 2. Do you recognize your phone number?

Courtesy of: Lorenzo Robinson. 

A Number Challenge

For a slightly more independent teaser, challenge students to produce a math equation that works using these four numbers—2, 3, 4, and 5—as well as a plus (+) and equal sign (=). Students can work individually, in pairs, or in small groups as they try to create a valid equation. The answer: 2 + 5 = 3 + 4.

Sourced from: WeAreTeachers .  

Math Mind Reader 

Students can work in pairs with this teaser. One person will start off by holding the calculator so their partner cannot see it; the other person can read the steps aloud to the partner with the calculator. 

• The student with the calculator starts by choosing a whole number from 1 to 20 and writing it down on a piece of paper without letting their partner see it. 
• Next, the student with the calculator enters their secret number into the calculator. 
• Multiply that number by 3. 
• Add the secret number, then subtract 5. 
• Multiply by 3, then multiply by 3 again. 
• Add the secret number, then subtract the number of their favorite month (you don’t have to know what month it is). For example, 9 represents the ninth month of the year, September. 
• Multiply by 3, then multiply by 3 again, and then again a third time. 
• Add the secret number, then subtract their favorite day of the month (again, you don’t have to know what it is on your end). 
• Ask them to show the non-calculator partner the result. At this stage, the non-calculator partner can guess the original secret number, even though what appears on the screen may be a very large number. 

If the result is negative, their secret number is 1.

If the result has only three digits, their secret number is 2.

In all other cases, ignore the last three digits, and then add 2 to get the secret number! 

Sourced from: Dr. Mike’s Math Games for Kids .

What’s Unique About This Number?

After writing the number 8,549,176,320 on the board, ask students to observe the number and tell you everything they think is unique about the number.

Answer: It is the digits 0 to 9 in alphabetical order (eight, five, four, nine, one, seven, six, three, two, zero), but it’s surprising and fun to see what students come up with. This number can also be evenly divided by the digits 1 through 9 except for the number 7, for example. 

Sourced from: MathisFun.com . 

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.

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