critical thinking activities in math

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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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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 ↓

8 thoughts on “20 Math Critical Thinking Questions to Ask in Class Tomorrow”

I would love to see your free math writing prompts, but there is no place for me to sign up. thank you

Ahh sorry about that! I just updated the button link!

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Jun 30 Critical Thinking in Mathematics: Designing High Cognitive Demand Math Tasks

Oh hey, here we are again, talking about my favorite topic: making kids THINK. Let’s get into it.

At the heart of thinking tasks lie the mathematical process skills, including reasoning, problem solving, communicating, conjecturing, and representing. These skills empower students to think critically, analyze information, communicate their ideas effectively, and explore the intricacies of mathematical concepts. Moreover, they go hand in hand with general good thinking skills, such as collaborating, listening actively, sharing ideas, and reflecting on one's own thought processes.

One effective strategy for designing thinking tasks is to take existing activities and transform them into opportunities for deep thinking. By flipping traditional activities, we can infuse them with elements of open-ended exploration, encouraging students to delve into rich problem-solving experiences.

Let's consider a traditional numeracy task where students practice multiplication using flashcards or worksheets. To design a thinking task, we can flip it by presenting students with a numerical pattern and asking them to identify the rule or equation that generates the pattern. This task encourages students to think critically, make observations, and identify mathematical relationships. It goes beyond simple memorization of multiplication facts and invites students to actively engage in problem-solving and pattern recognition. By providing students with opportunities to uncover patterns and think flexibly, we foster their mathematical reasoning skills and promote a deeper understanding of multiplication concepts.

My first year of teaching was with kindergartners. During small group time, I decided to try out a new activity with them. I drew an "open equation" on the table and had them use blocks to make the equation true. Some students had ___ + ___ = 6, others had ___ + ___ + ___ = 10, or even ___ + ___ - ___ = 10. To my surprise, this activity quickly became their favorite during small group sessions. It not only engaged them but also showcased their remarkable ability to think deeply about mathematical concepts. It was a powerful reminder that even our youngest students are capable of high cognitive thinking and can thrive when given the opportunity to engage in meaningful tasks.

When first introducing thinking tasks, it is essential to start with tasks that are slightly lower in complexity and not directly tied to specific content or math standards. This approach allows students to experience success, build confidence, and develop their thinking skills without feeling overwhelmed. By emphasizing the importance of the thinking process rather than the final answer, we create a supportive environment that nurtures students' intellectual growth and fosters a love for learning.

Here are some examples of good thinking tasks that aren't necessarily math-content related:

Provide students with a list of unrelated words or objects (e.g., banana, shoe, cloud, clock). Challenge them to come up with as many unique and imaginative ways these items could be connected or combined.

Present students with logic puzzles or tasks that require them to deduce information based on given clues. For example:

Mary is older than Jane. Jane is older than Sarah. Who is the youngest among them?

There are five houses in a row, each painted a different color. The red house is to the left of the blue house. The green house is next to the yellow house. Which color house is in the middle?

Offer students puzzles that involve visual patterns, rotations, or transformations. For example, ask students to determine the missing piece in a sequence of shapes or to identify the next shape in a pattern.

These tasks are designed to facilitate that mindset shift for students. They allow time for students to start working on those thinking skills as well as collaboration.

After students have started shifting their mindset and are comfortable with the routine, you can incorporate tasks related to your current concept. Take a look at your curriculum or unit plans and ask yourself, "What is the concept here?" and "What is the math students need to be doing?" Then you can look for or create tasks that address the mathematical skills alongside sense-making.

Let's say you are working on a unit on area and perimeter. Traditionally, you might want students to solve the area and perimeter of many different shapes. You may even let them work in groups or play a game. But how could we still have them working on the concepts of area and perimeter and using deep thinking skills?

Consider providing tasks like these:

You have a length of fencing material that is 30 feet long. Your task is to create as many different rectangular enclosures as possible using the entire length of the fencing material.

Imagine you are designing the floor plan for your dream house or an amusement park. Create a floor plan that includes different rooms or attractions. Calculate the area of each room or attraction and consider how you can optimize the use of space. Be creative and make sure to label your dimensions.

Crystal decides that she wants fringe put all the way around the rug. If the rug maker puts fringe around the rugs, how much fringe will he need for each rug? Use pictures, equations, or words to model your thinking.

Jana is designing a daycare center for small dogs. She wants to design different rectangular pens for her dogs to play. Each pen must have a total area between 49 and 100 square feet.

What is the biggest perimeter you can make with a rectangle that has an area of 24?

You can see that some of these tasks are perfect for the beginning of the unit, and some are great for after students have been taught some vocabulary. The beauty is that the point of these tasks isn't just the mathematical thinking but the process skills they practice.

Similarly, when teaching a unit on place value, you could have students work on problems where they fill in the hundreds, tens, and ones of certain numbers. But what if you had them try these tasks:

Dylan has 634 cubes in a pile. How many groups of a hundred could he make? Any left over? How many groups of ten could he make? Any left over?

Pencils come in cases of 100, packs of 10, or as single pencils. Show me what an order of 283 would look like.

Designing tasks doesn't always have to be laborious or difficult. It can be as simple as flipping your task from asking for a solution to asking for a question. For example, in a unit on rounding, instead of asking what 83 rounds to, try asking students to make a list of numbers that are close to 83 and far from 83. Be sure to have them defend and explain their thinking.

AUBREETEACHES.COM

By incorporating these different types of thinking tasks into your teaching, you can create a dynamic and engaging learning environment that promotes critical thinking, problem-solving, and mathematical reasoning. These tasks not only help students develop their thinking skills but also foster a love for learning and a deeper understanding of mathematical concepts. So, embrace the power of thinking tasks and unlock the potential of your students' minds!

Happy math-ing!

Jul 5 Lions, Tigers, and WORD PROBLEMS - OH MY!

Jun 26 Supercharge Your Math Stations with Choice Boards

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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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Critical Thinking Math Problems: Examples and Activities

David has been an educator for over 20 years. He holds a bachelor's degree in communications and journalism as well as a master's degree in education. He has taught English, language arts, and social studies to students from both middle and high school.

Table of Contents

Critical thinking in math, real world problem solving, asking questions, bellringers, project-based learning, lesson summary, learning outcomes.

Critical thinking is a key factor in separating those students who can 'do' math from those who truly understand what they're doing. When students do math, they can perform computations and explain concepts because they've learned formulas and definitions through practice and rote memorization. They don't necessarily know why the formula works, but they can use it. Likewise, they may not know how some ancient mathematician defined the concept, but they know the definition.

On the other hand, students who've been taught to think critically in math can explain why a formula works, and they can trace the steps used to define a concept. Not only can they solve a problem, they can explain the logic behind the process they used to reach a solution.

Think of it this way: sooner or later, most math students learn the Pythagorean theorem and its related formula. Students can become adept at using the formula A squared + B squared equals C squared to find the length of the hypotenuse or one of the sides. They can solve problems involving right triangles using the formula, provided they are given enough information. Students who have been taught to think critically can explain why the Pythagorean theorem works. More importantly, they know when and how to apply the Pythagorean theorem to solve a problem even if right triangles aren't an obvious part of the solution.

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• 0:02 Critical Thinking in Math
• 1:22 Real World Problem Solving
• 2:28 Asking Questions
• 3:22 Bellringers
• 4:02 Puzzles
• 4:58 Project-Based Learning
• 5:45 Lesson Summary

Math textbooks only go so far when it comes to presenting real world problems that require mathematical solutions. Texts are organized around concepts, making it easy for students to see what strategies they need to use to solve a problem. If the chapter is on the quadratic formula, students automatically know they will use that formula at some point to answer every question, even a complex word problem. Critical thinking kicks in when students have a variety of options for solving a problem. Students apply critical thinking to find the best strategy out of many possible methods to reach a solution.

Here's a problem that requires mathematical critical thinking:

Based on current trends in rising or falling temperatures, predict the average high and low temperatures for five different places on Earth five years from now.

To solve the problem, students will need to analyze data, determine the trends in each place, and select a method for predicting the future temperatures. They may need to use a variety of formulas and statistical tools to form their predictions. Teachers can take this a step further by asking students to explain and defend the methods they used.

To think critically is to follow a clear line of logical steps and reasoning. To solve critical thinking problems, math teachers should model the way they think when solving a problem. Students can internalize a set of questions to ask that will help them think their way to a solution. These questions could include:

• What is the problem? What am I trying to figure out?
• What do I know? What is the given information?
• What do I need to know to solve the problem?
• What problems like this have I solved before?
• What solutions could work? What strategies will work best in this situation?

After students attempt a solution, they can further ask: Why did my solution work? Or they might try to understand why their solution didn't work. Critical thinking activities present the perfect opportunity for students to collaborate and have meaningful conversations using mathematical vocabulary, which is a good sign they have developed a deep understanding of concepts.

Bellringers are short activities students do at the beginning of class as a warm-up exercise. Normally, bellringer activities require students to practice or apply skills they have already learned. Bellringers can also stimulate critical thinking.

For example, a critical thinking math bellringer might ask students to evaluate a pattern and determine a missing piece. For example:

What number would come next in this sequence: 3, 6, 9, 15, 24, _____?

Pattern questions may consist of numbers, shapes, variables, or colors. Part of the bellringer should include asking students to explain how they found the pattern since that's where the critical thinking occurs.

Solving puzzles is an entertaining way to engage students in critical thinking. Sudoku is a popular style of puzzle that requires students to think critically and mathematically. To solve a Sudoku puzzle students fill in columns, rows, and boxes with numbers from one to nine using each number only once in each area.

Many students enjoy brainteasers with a mathematical twist. Here's one that involves understanding the principles of multiplication by zero:

I will take the Philadelphia Phillies. You can have any other team in the major leagues. I will add together the runs the Phillies score in every game this season. You can multiply all your team's runs together from every game this season. At the end of the season, I will probably win. Can you explain why?

The answer is that I can add zero runs from a shutout to my total and continue to build on my score. However, as soon as you multiply by zero from one shutout, your result will be zero.

Project-based learning tasks require students to apply math concepts and strategies while thinking both critically and creatively. While completing the projects, students not only practice thinking and speaking in mathematical terms, they also learn to collaborate with their peers. They have to think critically to respond to each other's ideas, and they have to frame their criticisms constructively.

Imagine all the mathematical critical thinking involved in a project requiring students to design an original product, calculate the cost of manufacturing it, and create a method for marketing the product. Each stage from design to marketing requires a different type of research and different forms of math. In each step, students must think critically to ensure their imaginary product becomes a successful project.

When students use critical thinking in math, they not only know how to solve a problem, but they also understand why the solution works. Likewise, students use critical thinking when they determine the best strategy for solving a problem. Bellringers , puzzles, and project-based learning assignments will teach students to think critically and mathematically.

After studying the lesson, students are prepared to:

• Describe critical thinking in math
• Identify five strategies to develop critical thinking in math
• List examples of how to incorporate critical thinking strategies in math classes

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20 Critical Thinking Activities For Elementary Classrooms: Navigating Fact And Fiction (+Resources)

December 1, 2023 //  by  Seda Unlucay

With the barrage of mainstream news, advertising, and social media content out there, it’s vital for students to think independently and learn to differentiate between fact and fiction.

This series of critical thinking activities, STEM-based design challenges, engaging Math puzzles, and problem-solving tasks will support students in thinking rationally and understanding the logical connection between concepts.

1. Teach Students How to Obtain Verifiable News 

There’s probably no 21st-century skill more important than differentiating between real and fake sources of news. This editable PowerPoint bundle covers traditional media, social networks, and various target audiences and teaches students how to find verifiable facts.

Learn More: Teachers Pay Teachers

2. Watch and Discuss a Critical Reasoning Video

This kid-friendly video teaches students to break arguments down into claims, evidence, and reasoning. Armed with this lifelong learning tool, they will be able to make more informed decisions when consuming all types of information.

Learn More: Brain Pop

3. Complete a Critical Design Challenge

This science and designed-based classroom activity challenges students to find ways to prevent a falling egg from breaking. Pairing it with the classic Humpty Dumpty nursery rhyme is sure to inspire many creative ideas.

Learn More:  Education

4. Critical Community Engagement Activity 

This community engagement activity requires analytical skills to determine what items can be recycled in the classroom and in their neighborhood. By creating recycling bins from reusable cardboard boxes, students have an opportunity to contribute to the environmental well-being of their community while practicing social responsibility.

Learn More: Kaboom

5. Develop Logical Skills with a Then and Now Activity

We may no longer use candles for reading or quill pens for writing, but can your students identify the objects that have replaced them? This activity engages their writing, drawing, and logical skills while giving them a chance to reflect on all the changes in our modern world.

Learn More: Education

6. Play a Critical Thinking Game

This active learning activity requires students to use their critical thinking skills to make comparisons and create meaningful analogies. The fun animal safari theme is sure to inspire many funny and creative ideas!

7. Develop Social-Emotional Problem-Solving Skills 

Through this lesson, students will understand that while conflicts are a normal part of life, it’s vital to have problem-solving skills to resolve them. This is also an excellent opportunity for developing their social awareness and relationship skills.

Learn More: ED Foundations

8. Desert Island Survival Game 

This classic game is sure to inspire student engagement, as they use their critical thinking skills to survive being stranded on a desert island. Students have to watch out for ideological assumptions and question ideas in order to determine the appropriate items to bring.

9. Play a Problem-Solving Treasure Hunt Game 

This exciting game for kids requires them to use key math skills to break a series of codes. With ample time, designated progress monitors, and sharp critical thinking skills, students are sure to find the hidden treasure.

Learn More: Twinkl

10. Use Writing to Increase Critical Empathy

This activity builds writing fluency while giving students a chance to show appreciation for each other. As they reflect emphatically on their classmates’ contributions and character, their base level of kindness and sense of ethical responsibility is bound to increase.

Learn More: Edutopia

11. Learn How to Make Logical Inferences

This activity for kids teaches the critical academic skill of making inferences from a series of texts. Students will surely enjoy playing the role of detective in order to draw their own logical conclusions.

Learn More:  Study

12. Think Critically About Cultural Assumptions 

This engaging activity for students challenges them to think critically about why people from a variety of cultures decorate their bodies. It helps them to break through cultural assumptions while comparing and contrasting the different forms of hand and body painting around the world.

Learn More:  Harmony

13. Big Paper Silent Reflection Activity 

After posing some open-ended questions, students silently write their responses with colored markers on large chart paper. After each group has circulated around the room, students can share their critical reflections and learn from the various perspectives of their classmates.

Learn More:  Slideshare

14. Watch a TED Video About the Socratic Method

Socrates is one of the forefathers of critical thinking, who focused on making his students thinking visible by questioning their logic and reasoning. The accompanying quiz and discussion questions are an excellent way to reinforce student learning.

Learn More:  Ted Ed

15. Brainstorm Ways to Help a Homeless Person

This lesson in civic responsibility teaches students about the causes of homelessness and guides them to find ways to help the homeless in their communities. It develops key problem-solving skills while building critical empathy.

Learn More:  National Homeless.org

16. Guess the Object Game

This video features a series of twenty zoomed-in mystery objects. Students will love using their critical thinking skills to guess each one!

Learn More:  Andy – The ESL Guy

17. Solve Some Challenging Math Brain Teasers

This abundant series of brain teasers is the perfect choice if you’re looking to test your children’s memory and problem-solving skills. Encourage them to use their knowledge of numbers to complete these tricky math problems that are not only designed to challenge your little brainiacs but are also compiled in an easy-to-use format.

Learn More: Mental Up

18. Complete a STEM Elevator Challenge

In this design and engineering-based lesson, students have to build a functional elevator that can carry an object to the top of a structure. It’s a terrific way to encourage cooperative learning while sharpening their problem-solving skills.

Learn More:  Georgia Youth Science and Technology Centers

19. Create the Perfect Farm 

There’s no better way to develop critical thinking skills than by solving real-world problems. This video encourages students to think about ways to feed a growing global population in an environmentally sustainable way.

20. Solve Logic Grid Puzzles

These logic grid puzzles will motivate students to use logical reasoning skills and the process of elimination to solve a series of clues. But be warned, they are highly addictive and difficult to put down once you get started!

Learn More:  Puzzle Baron’s Logic Puzzles

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Critical Thinking Activities – Math Circles

by Liesl - Homeschool Den

A few days ago, I mentioned that we started back into homeschooling with Math Circles rather than jumping into our “normal” math curriculum. What are math circles? From what I understand, they started in Russia where they hosted math contests.  Students competed to answer various word problems. The contest itself was designed to get students intrigued and excited about mathematics. There’s something similar here in the US called the Math Olympiad. But, in general it’s just a form of math enrichment with games, stories or hands-on activities.

At the time I started looking into it, math just wasn’t their favorite time of day. I wanted to change that.  I bought several books and we started going through these.  By far our favorite one is  Mathematical Circle Diaries, Year 1: Complete Curriculum for Grades 5 to 7   Note: The books I mention here are affiliate links.

The kids love the puzzles — like this one that I mentioned a couple of days ago:

Top: Moving just two match sticks, make six.

Bottom:  8 matchsticks are laid out to look like a fish swimming to the left.  Moving just three matchsticks, make the fish swim to the right

They also have been working through logic word problems like on the island of knights and liars, knight always tell the truth and liars always lie… Then the book goes on to set up scenarios and ask who is the knight and who is the liar.  The kids love these and BEG for more!

We also add in Critical Thinking activities.  The past week the kids have done a Sudoku puzzle. We use the free sets from Krazy Dad.  He has made hundreds and hundreds of Sudoku puzzles for kids in 4×4 squares , 6×6 squares and 8×8 squares  and other sudoku puzzles  (that are even harder!).  For the 4×4 puzzles, you have to fill in the block so that each row, each column and each 2-by-2 block contain all of the digits 1 thru 4. He has easier versions (where more numbers are filled in) and harder versions (where he doesn’t offer as many numbers to start with). He asks for a donation.

This week we pulled out some of the critical thinking puzzles from the Critical Thinking Company’s book,  Building Thinking Skills® Level 2 . This thick book has both math puzzles and activities as well as various language and science activities.

Note: The books I mention here are affiliate links.

Another books we use fairly regularly is  Primary Grade Challenge Math . DD has been going through that book with me. They also have one aimed for older kids, simply called  Challenge Math For the Elementary and Middle School Student .

The Critical Thinking has a wonderful selection Mind Benders (deductive thinking puzzles) for younger and older students.

A year or so ago, I also searched the internet for some math puzzles. We’ve worked through this set of problems as well.  My kids really enjoyed these. The answers are available in the pdf. 🙂

Math Riddles

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Hi i’m liesl.

Do you believe education can be exciting, inspiring, and full of joy? We do too! I love the quote by William Butler Yeats, "Education is not the filling of a pail, but the lighting of a fire." It's about getting the kids involved, engaged, and fired up about learning (while juggling the rest of life too!)

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Activities with Pattern Blocks

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• Critical Thinking

When it comes to math manipulatives, one of the most common things I hear is about not knowing what to do with them. In this post, I share one of my favorite activities with pattern blocks. It’s engaging and promotes critical thinking and communicating mathematically.

“Free to a good home!” 

This was the sign hovering over a pile full of teacher stuff outside of a classroom door. 

Something with bright colors caught my eye, so I rummaged through the pile to see if there was anything there worth my time. 

I pushed the pile apart with my hands to see what was at the bottom. 

Math manipulatives!! 😁

I couldn’t believe my luck! There were trays of Cuisenaire rods and a box of Base 10 Blocks.

A smile came across my face as I quickly scooped up the manipulatives and ran back to my classroom thinking of all the ways I could use these tools with my students. 

Using Manipulatives in the Classroom

One of the most common things I hear from teachers is about not knowing how to best utilize manipulatives. These math tools cost a lot of money but often go unused because teachers are unsure of how to use them.

While I’m an avid collector of all math manipulatives, pattern blocks are one of my favorite math tools because they are versatile and can be used in many different ways in the classroom. And, it’s the one tool most schools seem to have more than enough of. 

In fact, when you inherited your classroom, you may have found gobs of these random shapes, maybe even a few buckets of them in the cabinets. 

And, you probably thought to yourself, “What am I supposed to do with these? We only teach geometry for three weeks!” 

Well friend, did you know pattern blocks can be used for more than your three-week geometry unit? Pattern blocks are amazing tools that can be used all year long!

Pattern blocks include six basic shapes: a yellow hexagon, a red trapezoid, a blue rhombus, a green triangle, an orange square, and a beige rhombus. The pieces are proportional to each other which makes them useful in a variety of ways. 

In addition to analyzing the characteristics of two-dimensional shapes, pattern blocks can also be used to teach fractions . There are even some additional fraction pieces you can add to the set to enhance student learning. 

Critical Thinking Activities with Pattern Blocks

What’s the Common Attribute?” is an engaging activity that promotes critical thinking with pattern blocks. It can be used year round and makes a great starter activity, especially around the time of your geometry unit. The only prerequisite skills needed are some basic vocabulary terms related to shapes, such as sides, angles, congruent, equal, etc. 

The basic idea is to create a Venn Diagram where pattern blocks are placed according to a specific attribute or set of attributes. Students then use the placement of the pattern blocks to determine the common attribute. (See the example above.)

Here’s how the activity works:

1. Choose a rule for the Venn diagram. 

2. Display a Venn Diagram with the blocks in the correct place on a dry erase board or under the document camera.

3. Ask the students, “What’s the common attribute?”

4. Provide students with time to think.

5. Ask students to “turn and talk” to a shoulder partner, face partner, neighbor, or classmate to discuss the answer. 

6. Have students share their responses with the class highlighting important vocabulary.  

Promote Critical Thinking with Good Questions

Important questions to ask during the debrief:

a. What vocabulary is important here?

b. What’s the common attribute of the left side?

c. What’s the common attribute of the right side?

d. What’s the common attribute of the shapes in the middle, or the intersection, of the two circles? 

e. Why is there a shape on the outside of both circles? What does this mean? (It is a part of the set but does not meet the inclusion criteria for either circle.)

What to Do Next

Once students get the hang of the activity, have them create their own puzzlers– a great math menu activity. Then, share their creations with the class and have students decide “what’s the common attribute?” 

Ready to try it out? Grab a free set of puzzlers using the form below. 

What’s your favorite way to use pattern blocks in the classroom? 

Shametria Routt Banks

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Home » Blog Posts » Math & Technology » Math Riddles to Promote Critical Thinking Skills in Your Classroom

Math Riddles to Promote Critical Thinking Skills in Your Classroom

Have you ever watched your students’ faces light up with a “Eureka!” moment? There’s something incredibly rewarding about seeing young minds solve problems that challenge them. But how can we, as educators, create more of these moments in a way that’s both fun and educational? The answer might just lie in math riddles ! 🤔

Math riddles are not just entertaining puzzles; they are powerful tools for promoting critical thinking and problem-solving skills . In this post, we’ll explore how these clever questions can turn your classroom into a think tank of eager detectives. Plus, I’m excited to share that you can get my Math Riddle QR Code Task Cards for FREE —a resource guaranteed to engage your students and transform your classroom dynamics. So, are you ready to dive into the world of math riddles and unlock the potential of your students? Let’s get started!

This post may contain affiliate links to Amazon for your convenience. As an Amazon Associate, I earn from qualifying purchases, which do not cost any extra for you. Please see the   full disclosure here .

What is Critical Thinking, and Why Do Students Need It?

Critical thinking is the ability to analyze facts to form a judgment. In the classroom, it’s about going beyond memorization and recall to apply, analyze, and evaluate information. But why is this important?

In today’s fast-paced world, the ability to think critically is more valuable than ever. Students equipped with these skills can navigate complex problems, make informed decisions, and approach challenges with creativity and resilience.

Critical thinking in math, especially, teaches students to question assumptions, consider multiple solutions, and rigorously test their ideas. This not only enhances their mathematical abilities but also prepares them for real-world challenges where answers are not always clear-cut.

Getting Students to Think More Deeply

Thinking is the hardest work there is, which is probably the reason so few engage in it.      Henry Ford

One of my favorite things to do as a teacher is pushing my students to think more deeply.

So instead of just giving my former 2nd graders straight math drills to memorize, I would give them math riddles instead.

Promoting critical thinking through math riddles pushes students to engage in several different learning skills at once.

Students must read carefully to comprehend the riddle. Then, they have to complete the math computation in order to solve the riddle.

I love this because it combines ELA and Math content for my students.

Math Riddle Example:

This image below gives an example of a math riddle. Students engage in problem-solving skills as they work through each problem.

Math Riddles help promote critical thinking and place value practice. I absolutely LOVE being able to address and giving meaningful practice with more than one learning standard.

Ways to Use Math Riddles in Your Classroom

Incorporating math riddles into your classroom can be both fun and incredibly beneficial for student learning. Here are some creative ways to do it:

• Math Starter : Kick off your class with a math riddle to get those brains buzzing.
• Morning Work : Let students start their day with a puzzle, setting a positive tone for the day.
• Early Finishers : Keep those fast workers engaged with challenging riddles instead of busy work.
• Brain Breaks : Inject a quick, fun break into long periods of work with a stimulating riddle.
• Team Challenges : Foster teamwork and communication by having students work together to solve riddles.
• Homework Assignments : Include riddles as part of homework to make it more engaging.
• Math Centers : Create a riddle station for students to visit during math center time.
• Bulletin Boards : Post riddles on your bulletin board for an interactive display.
• Exit Tickets : Use a riddle as an exit ticket to assess understanding in a fun way.
• Weekly Challenges : Offer a riddle of the week for extra credit or just for fun.
• Parent Involvement : Share riddles with parents to engage them in their child’s learning.
• Interactive Notebooks : Have students record and solve riddles in their math notebooks.

Check Out These Related Posts!

• The BEST Math Read Alouds Ever
• Teaching Critical Thinking with Task Cards

Infusing Technology with Math Riddles

In addition to pushing my students beyond just rote memorization math practice, these QR Codes also give them practice with technology. My students absolutely love QR Codes anyway. Honestly, I love them too! They give students a chance to see their answers immediately. That is less grading for me and it gives students instant feedback.

Related Post: How I Save Time Grading with ZipGrade

When a student gets a problem incorrect, they go back and rework the math riddle–either independently or with a partner.

I’ve noticed how this also pushes their critical thinking because finding their own math mistake involves deeper thinking. Plus, it is a great exercise in showing grit and perseverance; something my kids definitely need!

Other Ways to Promote Critical Thinking Skills

Beyond math riddles, there are numerous strategies to encourage critical thinking in the classroom. Here are five additional ideas:

• Socratic Seminars : Engage students in discussions based on asking and answering questions to stimulate critical thinking.
• Problem-Based Learning : Present real-world problems for students to solve collaboratively.
• Debates : Organize debates on various topics to develop reasoning and argumentation skills.
• Reflection Journals : Encourage students to reflect on their learning processes and outcomes.
• Creative Projects : Assign projects that require innovative thinking and problem-solving.

How To Get Your FREE Download of these Math Riddles:

If you are not on my email list, be sure to subscribe to get this FREEBIE! The free products in my TpT store aren’t always the same as the ones I give to my subscribers.

This resource has additions that you can only get by signing up here.

If you are using a school email address, this process may not work for you. Many districts now block outside emails!

So use a personal email address that you check often, and you should be ready to roll!

I send all new FREEBIES to current subscribers automatically. If you haven’t already gotten yours, please check your SPAM or be sure that you confirmed your email with me.

Now that the “techy” talk has been covered, we can all go push our students to think more critically with some fun math riddles!

By integrating math riddles and these strategies into your teaching toolkit, you’re not just teaching math; you’re nurturing curious, independent thinkers ready to tackle the challenges of tomorrow.

Remember, fostering a classroom environment where questions are welcomed and challenges are embraced is key to developing critical thinking skills. And, don’t forget to grab your FREE Math Riddle QR Code Task Cards to get started on this exciting journey! 🎉

Happy Teaching,

The Butterfly Teacher

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5 Ways to Stop Thinking for Your Students

Too often math students lean on teachers to think for them, but there are some simple ways to guide them to think for themselves.

Who is doing the thinking in your classroom? If you asked me that question a few years ago, I would have replied, “My kids are doing the thinking, of course!” But I was wrong. As I reflect back to my teaching style before I read Building Thinking Classrooms by Peter Liljedahl (an era in my career I like to call “pre-thinking classroom”), I now see that I was encouraging my students to mimic rather than think .

My lessons followed a formula that I knew from my own school experience as a student and what I had learned in college as a pre-service teacher. It looked like this: Students faced me stationed at the board; I demonstrated a few problems while students copied what I wrote in their notes. I would throw out a few questions to the class to assess understanding. If a few kids answered correctly, I felt confident that the lesson had gone well. Some educators might call this “ I do, we do, you do .”

What’s wrong with this formula? When it was time for them to work independently, which usually meant a homework assignment because I used most of class time for direct instruction, the students would come back to class and say, “The homework was so hard. I don’t get it. Can you go over questions 1–20?” Exhausted and frustrated, I would wonder, “But I taught it—why didn’t they get it?”

Now in the “peri-thinking classroom” era of my career, my students are often working at the whiteboards in random groups as outlined in Liljedahl’s book. The pendulum has shifted from the teacher doing the thinking to the students doing the thinking. Do they still say, “I don’t get it!”? Yes, of course! But I use the following strategies to put the thinking back onto them.

5 Ways to Get Your Students to Think

1. Answer questions with a refocus on the students’ point of view. Liljedahl found in his research that students ask three types of questions: “(1) proximity questions—asked when the teacher is close; (2) stop thinking questions—most often of the form ‘is this right’ or ‘will this be on the test’; and (3) keep thinking questions—questions that students ask so they can get back to work.” He suggests that teachers acknowledge “proximity” and “stop thinking questions” but not answer them.

Try these responses to questions that students ask to keep working:

• “What have you done so far?” 
• “Where did you get that number?” 
• “What information is given in the problem?” 
• “Does that number seem reasonable in this situation?”  

2. Don’t carry a pencil or marker. This is a hard rule to follow; however, if you hold the writing utensil, you’ll be tempted to write for them . Use verbal nudges and hints, but avoid writing out an explanation. If you need to refer to a visual, find a group that has worked out the problem, and point out their steps. Hearing and viewing other students’ work is more powerful .

3. We instead of I . When I assign a handful of problems for groups to work on at the whiteboards, they are tempted to divvy up the task. “You do #30, and I’ll do #31.” This becomes an issue when they get stuck. I inevitably hear, “Can you help me with #30? I forgot how to start.”

I now require questions to use “we” instead of “I.” This works wonders. As soon as they start to ask a question with “I,” they pause and ask their group mates. Then they can legitimately say, “ We tried #30, and we are stumped.” But, in reality, once they loop in their group mates, the struggling student becomes unstuck, and everyone in the group has to engage with the problem.

4. Stall your answer. If I hear a basic computation question such as, “What is 3 divided by 5?” I act like I am busy helping another student: “Hold on, I need to help Marisela. I’ll be right back.” By the time I return to them, they are way past their question. They will ask a classmate, work it out, or look it up. If the teacher is not available to think for them, they learn to find alternative resources.

5. Set boundaries. As mentioned before, students ask “proximity” questions because I am close to them. I might reply with “Are you asking me a thinking question? I’m glad to give you a hint or nudge, but I cannot take away your opportunity to think.” This type of response acknowledges that you are there to help them but not to do their thinking for them.

When you set boundaries of what questions will be answered, the students begin to more carefully craft their questions. At this point of the year, I am starting to hear questions such as, “We have tried solving this system by substitution, but we are getting an unreasonable solution. Can you look at our steps?” Yes!

Shifting the focus to students doing the thinking not only enhances their learning but can also have the effect of less frustration and fatigue for the teacher. As the class becomes student-centered, the teacher role shifts to guide or facilitator and away from “sage on the stage.”

As another added benefit, when you serve as guide or facilitator, the students are getting differentiated instruction and assessment. Maybe only a few students need assistance with adding fractions, while a few students need assistance on an entirely different concept. At first, you might feel like your head is spinning trying to address so many different requests; however, as you carefully sift through the types of questions you hear, you will soon be comfortable only answering the “keep thinking” questions.

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Math Detective® Beginning

Higher-order thinking • reading • writing in mathematics.

Grades: 3-4

Mathematics

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Description and Features

This 110-page book uses topics and skills drawn from national math standards to prepare your students for advanced math courses and assessments that measure reasoning, reading comprehension, and writing in math. Students read a short story that includes a chart, table, or graph. Next they answer critical thinking questions to improve their understanding of the math concept and develop their critical thinking (comprehension) skills. Students can't just scan the story for answers—they must carefully analyze and synthesize the information from the text and the chart, table, or graph to explain and support their answers. The questions in Math Detective® Beginning are modeled after questions found on high-stakes math assessments, but require more critical thinking. These problems are excellent preparation for assessments that require students to explain and support their answers. Stories are age-relevant, high-interest, and show students that math is integral to everyday activities. This book contains a lesson that explains the concept of evidence, a chart of activity topics and key ideas to help parents and teachers select activities, and detailed answers. The activities in Math Detective® Beginning are organized around these math concepts:      •  Number and Numeration      •  Patterns      •  Operations      •  Geometry and Spatial Sense      •  Probability      •  Statistics

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This is a legal agreement between you (a single entity, company, or educational institution) and The Critical Thinking Co.™ for the software accompanying this agreement, which includes computer Software and associated Documentation. By installing this Software on a computer, you agree to be bound by the terms of this agreement. If you do not agree to the terms of this agreement, promptly erase all copies of the software in your possession and return any Software packaging associated with this order within sixty (60) days of purchase to the place from which you obtained it for a full refund.

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4. WARRANTIES. The Critical Thinking Co.™ expressly disclaims any warranty for the Software Product. The Software and Documentation is provided "as is" without warranty of any kind, either expressed or implied, including, without limitation, the implied warranties or merchantability, fitness for a particular purpose, or non-infringement. The entire risk arising out of use or performance of the Software remains with you. If media within this package is defective, remove the software application from your device(s) and return any software packaging associated with this order to The Critical Thinking Co.™ within 60 days of the date of purchase, and they will replace it at no charge.

5. NO LIABILITY FOR CONSEQUENTIAL DAMAGES. In no event shall The Critical Thinking Co.™ or its suppliers be liable for any damages whatsoever (including, without limitation, damages for loss of business profits, business interruption, loss of business information, or any other pecuniary loss) arising out of the use of or inability to use this Software Product, even if The Critical Thinking Co.™ has been advised of the possibility of such damages. Because some states/jurisdictions do not allow the exclusion or limitation of liability for consequential or incidental damages, the above limitation may not apply to you.

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