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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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The Power of One Good Math Question

By focusing on authentic moments of inquiry, elementary students engage in critical thinking in math class.

Most of the math problems we present to elementary students are scripted. They might come from the curriculum we are teaching, or maybe they are a three-act math task we learned at a workshop or found in a blog. But often the best problems are the ones that we had not planned and are instead based in the real life of the classroom. There is a lot of power in a single, authentic question.

Moments of Inquiry in Math Class

Everyday life presents lots of interesting math problems. The best of these inquiry opportunities come from questions the students themselves pose if we stop and listen to what they are asking. No one works on problems like these in class every day, and they shouldn’t. But an openness to tackling something that comes from actual experience connects the classroom to the underlying power of mathematics to help us make sense of the world. 

One day, Maggie, who was new to teaching first grade, went to retrieve a box of dominoes she had set aside to use for the next unit. Dominoes are a great manipulative for first grade because they encourage subitizing (recognizing small numbers without counting), and they help students see fact families. For instance, a single two-dot/three-dot domino can show all of these: 2+3=5, 3+2=5, 5–2=3, 5–3=2.

Instead of finding neatly organized sets, she found a box full of jumbled dominoes. When she met with Steven, the math specialist who was coaching her, they both looked at the plastic container and had the same sinking feeling: It was going to take a while to sort them back into sets. Neither of them had a good sense of how many sets were even in the box or how many dominoes constituted a set. But this felt like a good question to think about, so instead of doing the sorting themselves, they brought the problem to the students. 

presenting students with the task

Maggie presented the bin of dominoes to her class and explained that there were many sets mixed together. Students had some prior knowledge of what individual dominoes looked like, but for this exercise, the only additional information that students had was that there would not be any duplicates in a single set. There was no explanation of how many dominoes were in a full set or clues about how to organize them.

The class split into small groups and set to work. The students had the opportunity to approach the task in any way that made sense to them. Some students sorted the dominoes based on one half of the dominoes’ pips. Some students sought out patterns within the full collection of dominoes. For example, one group looked at how many had one pip on one side and six on the other. Some students focused primarily on casting aside duplicates or bringing them to another group that could use them. 

The first completed set of dominoes cast a hush over the room—the excitement was palpable. Now, with a visual cue, students noticed patterns that they had been grappling with. Students observed how the group had arranged them: a complete row of dominoes with six pips on the bottom, moving up the ladder to finally one domino without any pips on either side. Students asked all sorts of questions about where their peers had started and how they thought about the sequence. They noticed that the total number of pips in each row increased as they worked their way down from top to bottom. Students shared how organizing it this way made it easier to notice which dominoes were duplicates within the set. 

making one big question work

First of all, the task was clear and compelling. It was a single question that was easy to understand, but there was not a single path toward a solution. There were curricular connections—pattern making, subitizing, and number properties (a nice physical model for the commutative property)—but the students had the freedom to figure out their own approach. The students had to do the thinking, the organizing, and the planning. They had ownership over the problem . Moreover, it was a question that caught their curiosity, and they wanted to know the answer.

These aren’t the only questions that Maggie’s class has considered this year. A picture of a sundial led to looking at Roman numerals and other number systems. A poll about favorite shapes led to a lively discussion about whether a heart was a shape or not (and introduced the word cardioid !). In order to choose questions that guide conversation, here are some guidelines: 

1. Make it real. Kids can tell if the question is a setup or something you really want to know. 

2. Keep it simple. Frame the question in the simplest way possible. Simple questions leave the most room for creativity and thinking. 

3. Stay out of their way. Often we rush in with too much structure and over-scaffold the problem. When we do that, we reduce the thinking, and it becomes about doing what is expected rather than solving the problem. When we hand students a list of questions to guide them or a form for their answers, it becomes another worksheet to fill out, and filling out the worksheet correctly becomes the goal. Let the answer to the question be the goal. 

4. Let them struggle. Don’t jump in to help. Don’t make suggestions. Limit yourself to asking questions and only answering questions with questions. 

5. Celebrate the solution. Or, if there are no solutions that emerge, celebrate that we couldn’t figure it out. That happens too. 

6. If there is a natural audience, share the results. Neither Maggie nor Steven knew how many sets of dominoes there were until the students told them. That in itself was worth celebrating. 

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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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Tips to Improve Critical Thinking Skills with 1st Grade Math Word Problems

Last Updated on May 31, 2022 by Thinkster

Developing critical thinking skills with math word problems is incredibly important. Students should move beyond simple rote memorization and fact-finding to understand the thought process and concept behind those facts.

In doing so, students are developing strong thinking skills that can help them become successful lifelong learners.

In elementary school, first grade math word problems are a great place to start teaching critical thinking strategies.

Here are some tips to help your first grader think through word problems with a critical mind.

Create a Plan

To be a strong critical thinker, your child needs to take the time to plan and strategize before tackling a problem.

You can teach your child to do this by having her read the problem, then dissect what it is asking.

She can then underline the important information in the problem and create a picture or diagram to represent what the problem is asking.

This ensures that he is taking the steps to carefully outline and identify what the problem is asking.

Teaching these steps early on is also incredibly important, as your child will face multi-step problems and ones with distractors in the future.

Ask “Why?”

One of the keys to critical thinking in math is being able to not just do the problem, but also to explain why.

In first grade math word problems, the “why” is often quite simple to identify, but you should still be asking.

Find out why the child chose to count, add or subtract. Have him explain his reasoning in his own words and help him write it down. Then, talk about how he came to that conclusion, encouraging him to continue to think about the problem and his steps for solving it.

Ask “Does It Make Sense?”

Most first grade math word problems are fairly clear in what they are asking the child to do, and your child should stop and reflect on his answer to see if it makes sense.

For example, if the problem creates a scenario where a person has a certain amount of an item and someone gives him more, the answer should be a larger number than he started with, which you would get by adding. If the child chose to subtract, the answer will be smaller than what you started with.

Use an online math program, like Thinkster, to help with math word problems

Critical thinking is a crucial component of Thinkster Math’s  curriculum .

Thinkster’s curriculum introduces critical thinking problems within the first grade curriculum, giving your child the opportunity to practice and sharper skills and strategies that will help them become incredible lifelong learners and thinkers.

Curious to see your child’s abilities in solving first-grade word problems?

If you’re looking for  online  math   tutoring  to help your child, you can try   Thinkster risk-free .

Thinkster provides a full-fledged  online  tutoring  platform (driven by AI, behavioral, and data science), as well as supplemental  math  worksheets ,  math   homework  help ,  test prep , and more. Our  Parent Insights App  allows you to monitor your  student ‘s work and  learning  improvements at any time.

An elite,  expert  math   tutor  and  online teaching  system work together to help your  student  go beyond just  learning   math  – we want them to master it.

Learn more about our curriculum and teaching style  here .

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Logic Puzzles for Kids: fun ways to teach critical thinking in 1st and 2nd grade

Susan Jones January 4, 2022 6 Comments

This post may contain affiliate ads at no cost to you. See my disclosures for more information.

These logic puzzles are so much fun for kids to practice their critical thinking skills. In this post, I share 5 different types of logic/critical thinking activities that are great for young students to practice! Before I dive in, I wanted to let you know you can watch or listen to all this information in video format below:

Research has shown that critical thinking skills do not develop naturally. Humans need to be put in situations where they can practice these skills in order to get better at them, just like any other subject we teach in school!

The difference is with most subjects, we teach the skills in concrete linear ways (addition, for example). This makes it important to also teach our students how to think outside the box and pose questions in a different way to practice their critical thinking skills. In this blog post, I am going to share some of my favorite logic and critical thinking puzzles that your students can use to solve problems thoughtfully in all areas of learning!

Odd One Out!

Odd One Out! is a fun puzzle game where students have to look at a set of 4 pictures and decide which one doesn’t belong. After they determine the odd one out, they must explain why it doesn’t fit . As you can see in the example below, all four items are body parts, however, three go on your face. Therefore, the foot is the “odd one out.”

Your students will have to give their answer and their explanation when solving the puzzle!

This activity is great for developing vocabulary, characterizing uses, and comparing and contrasting various parts of the different items. You can group pictures together based on their shape, or items that all start with the same letter, or a group of items that all rhyme, to practice a bunch of different skills using this same type of logic puzzle!

Combinations and Pattern Completions:

In these types of logic puzzles, students will combine shapes or complete patterns in their head. For example, in the puzzle below, students have to use spatial reasoning to determine what shape will be made when they add the line with the triangle. All three options show triangles with lines, but only the middle triangle makes sense based on the size and direction of the line. 

Spatial reasoning has so many real-world applications and it’s great for all of us, young and old, to practice developing that skill!

Similarly, in the complete the pattern puzzle below, students will look at the pattern on the top of the page and have to figure out which option comes next based on what they see. Pattern puzzles are great because students need to use their logic and evidence of what has already come before to make predictions about what comes next!

There are a lot of different critical thinking skills used for solving analogies. Students must figure out the meaning of the words, the uses of the objects, how the words in the first comparison are related, and how the first relationship relates to the second comparison in the analogy! Below is an analogy that I would use with my students:

The most important part when solving these analogies with your class is having them explain how they got their answer. In the example above, it might be easy for a student to say “rain”, but you really want them to verbalize why they knew that. That way, they will have to explain all the relationships and definitions in the analogy and explain the thought-process behind their answer. 

Anyone who has played sudoku knows that the more you practice, the better you get at it. That is why it is so important to keep practicing these logic puzzles with your students!

Sudoku puzzles are great for your students because they need to make quick decisions when determining which number or object goes where. They also need to be able to quickly recognize their mistakes along the way and fix them in order to progress with the puzzle.

Below are two kid-friendly sudoku puzzles you can use in your classroom using numbers or objects:

The above is a “classic” sudoku puzzle with numbers, but you can also use objects like shown below! Students will need to understand the basics of this type of game which is that each image or number can only appear once in each row, column, and block.

Classic Logic Puzzle

Last but not least, I love using a classic logic puzzle. Now listen… these were my nemesis! My brain would get so boggled thinking about how to solve these when I was a kid (and realistically, still now).  Here is an example of a kid-friendly puzzle so you know what I am talking about:

As you can see in the problem above, students can see the age of one child. Then, they have to use logic and reasoning based on the clues to determine the ages of the rest of the children in the puzzle.

Problems like this can be challenging because students need to organize their thoughts and develop a strategy first before they can solve the problem. As I mentioned at the beginning of this post, these are skills that don’t come naturally, so we need to make sure that our students are able to consistently practice these logic puzzles in order to develop their skills. We also need to model how we would solve some of these problems so our students can see the strategies in action. We can’t expect them to just solve them on their own!

All the puzzles and examples above are part of a new unit I created to help students develop their critical thinking and logic skills. I made 40 puzzles for each of the 5 categories above, so this unit has 200 critical thinking and logic puzzles to use in your classroom. What’s great is each puzzle can be displayed to work through in a whole group setting and they are also available in black and white printable versions so students could paste them in a journal and solve on their own!

FREEBIE ALERT : if you follow the link below and preview the product, you can download 10 free puzzle slides from the unit!

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Reader Interactions

February 7, 2022 at 5:28 am

I am so excited to introduce these logic games to my class!! Thank you so much Susan

March 28, 2022 at 4:27 am

June 22, 2022 at 2:01 am

I can not wait to start my new class. These will be part of their morning work tubs.

January 6, 2023 at 11:52 pm

I would like the Logic Puzzles please.

January 25, 2023 at 7:31 pm

These logic puzzles will be great warm ups! Fantastic!!

March 10, 2023 at 2:59 pm

I love these! Such great activities to boost young minds.

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Hello friends.

Welcome to Susan Jones Teaching. When it comes to the primary grades, learning *All Things* in the K-2 world has been my passion for many years! I just finished my M.Ed. in Curriculum and Instruction and love sharing all the latest and greatest strategies I learn with you through this blog and my YouTube channel! I hope you'll enjoy learning along with me :)

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Rich Problems – Part 1

Rich problems – part 1, by marvin cohen and karen rothschild.

One of the underlying beliefs that guides Math for All is that in order to learn mathematics well, students must engage with rich problems. Rich problems allow ALL students, with a variety of neurodevelopmental strengths and challenges, to engage in mathematical reasoning and become flexible and creative thinkers about mathematical ideas. In this Math for All Updates, we review what rich problems are, why they are important, and where to find some ready to use. In a later Math for All Updates we will discuss how to create your own rich problems customized for your curriculum.

What are Rich Problems?

At Math for All, we believe that all rich problems provide:

• opportunities to engage the problem solver in thinking about mathematical ideas in a variety of non-routine ways.
• an appropriate level of productive struggle.
• an opportunity for students to communicate their thinking about mathematical ideas.

Rich problems increase both the problem solver’s reasoning skills and the depth of their mathematical understanding. Rich problems are rich because they are not amenable to the application of a known algorithm, but require non-routine use of the student’s knowledge, skills, and ingenuity. They usually offer multiple entry pathways and methods of representation. This provides students with diverse abilities and challenges the opportunity to create solution strategies that leverage their particular strengths.

Rich problems usually have one or more of the following characteristics:

• Several correct answers. For example, “Find four numbers whose sum is 20.”
• A single answer but with many pathways to a solution. For example, “There are 10 animals in the barnyard, some chickens, some pigs. Altogether there are 24 legs. How many of the animals are chickens and how many are pigs?”
• A level of complexity that may require an entire class period or more to solve.
• An opportunity to look for patterns and make connections to previous problems, other students’ strategies, and other areas of mathematics. For example, see the staircase problem below.
• A “low floor and high ceiling,” meaning both that all your students will be able to engage with the mathematics of the problem in some way, and that the problem has sufficient complexity to challenge all your students. NRICH summarizes this approach as “everyone can get started, and everyone can get stuck” (2013). For example, a problem could have a variety of questions related to the following sequence, such as: How many squares are in the next staircase? How many in the 20th staircase? What is the rule for finding the number of squares in any staircase?

• An expectation that the student be able to communicate their ideas and defend their approach.
• An opportunity for students to choose from a range of tools and strategies to solve the problem based on their own neurodevelopmental strengths.
• An opportunity to learn some new mathematics (a mathematical residue) through working on the problem.
• An opportunity to practice routine skills in the service of engaging with a complex problem.
• An opportunity for a teacher to deepen their understanding of their students as learners and to build new lessons based on what students know, their developmental level, and their neurodevelopmental strengths and challenges.

Why Rich Problems?

All adults need mathematical understanding to solve problems in their daily lives. Most adults use calculators and computers to perform routine computation beyond what they can do mentally. They must, however, understand enough mathematics to know what to enter into the machines and how to evaluate what comes out. Our personal financial situations are deeply affected by our understanding of pricing schemes for the things we buy, the mortgages we hold, and fees we pay. As citizens, understanding mathematics can help us evaluate government policies, understand political polls, and make decisions. Building and designing our homes, and scaling up recipes for crowds also require math. Now especially, mathematical understanding is crucial for making sense of policies related to the pandemic. Decisions about shutdowns, medical treatments, and vaccines are all grounded in mathematics. For all these reasons, it is important students develop their capacities to reason about mathematics. Research has demonstrated that experience with rich problems improves children’s mathematical reasoning (Hattie, Fisher, & Frey, 2017).

Where to Find Rich Problems

Several types of rich problems are available online, ready to use or adapt. The sites below are some of many places where rich problems can be found:

• Which One Doesn’t Belong – These problems consist of squares divided into 4 quadrants with numbers, shapes, or graphs. In every problem there is at least one way that each of the quadrants “doesn’t belong.” Thus, any quadrant can be argued to be different from the others.
• “Open Middle” Problems – These are problems with a single answer but with many ways to reach the answer. They are organized by both topic and grade level.
• NRICH Maths – This is a multifaceted site from the University of Cambridge in Great Britain. It has both articles and ready-made problems. The site includes  problems for grades 1–5 (scroll down to the “Collections” section) and problems for younger children . We encourage you to explore NRICH more fully as well. There are many informative articles and discussions on the site.
• Rich tasks from Virginia – These are tasks published by the Virginia Department of education. They come with complete lesson plans as well as example anticipated student responses.
• Rich tasks from Georgia – This site contains a complete framework of tasks designed to address all standards at all grades. They include 3-Act Tasks , YouCubed Tasks , and many other tasks that are open ended or feature an open middle approach.

The problems can be used “as is” or adapted to the specific neurodevelopmental strengths and challenges of your students. Carefully adapted, they can engage ALL your students in thinking about mathematical ideas in a variety of ways, thereby not only increasing their skills but also their abilities to think flexibly and deeply.

Hattie, J., Fisher, D., & Frey, N. (2017). Visible learning for mathematics, grades K-12: What works best to optimize student learning. Thousand Oaks, CA: Corwin Mathematics.

NRICH Team. (2013). Low Threshold High Ceiling – an Introduction . Cambridge University, United Kingdom: NRICH Maths.

The contents of this blog post were developed under a grant from the Department of Education. However, those contents do not necessarily represent the policy of the Department of Education, and you should not assume endorsement by the Federal Government.

Math for All is a professional development program that brings general and special education teachers together to enhance their skills in planning and adapting mathematics lessons to ensure that all students achieve high-quality learning outcomes in mathematics.

Check Out These 50 First-Grade Math Word Problems of the Day

Desmond saw 5 bunnies.

Opening your daily math lesson with a Math Word Problem of the Day is an excellent way to set the stage for learning. We all know that word problems are difficult for young learners to grasp, even when the mathematical operation portion of the problem is basic.

Incorporate these first grade math word problems one day at a time at the start of your math block to build confidence, critical thinking skills, and a learning community. Students will get used to reading slowly for meaning, while also identifying key information. Encourage students to write out equations and draw pictures to explain their thinking, since this helps them see the light when they are stuck!

Topics covered include addition, subtraction, multiplication, and comparison. All you need to do is post one of these first grade math word problems on your whiteboard or projector screen. Then let kids take it from there!

Want this entire set of word problems in one easy document? Get your free PowerPoint bundle by submitting your email here .

50 First Grade Math Word Problems

1. I had 6 pencils, and my teacher gave me 4 more. How many pencils do I have now?

2. Gina’s dog got 3 treats on Sunday and 0 treats on Monday. How many treats did Gina’s puppy get in all?

3. Joel went to the zoo with his family. During the first hour he was there he saw a bear, 2 tigers, and 3 lions. How many animals did Joel see in his first hour at the zoo?

4. Jackson sorted his toy cars by color. He has 6 blue cars, 5 green cars, and 4 black cars. How many cars does Jackson have in all?

5. Ben has 2 green balloons and 4 yellow balloons. How many balloons does he have altogether?

6. There are 3 kids in the Clark family. Tina is 3, Joshua is 4, and Samantha is 7. If you add up all their ages, what is the sum of the Clark kids?

7. If you go for a swim and 6 of your friends come along, how many friends are swimming in total?

8. Rachel’s mom had some flowers in a vase. 3 of the flowers wilted and Rachel’s mom took them out of the vase. Now there are 5 flowers in the vase. How many flowers were in the vase to start with?

9. Hayden’s cat had a litter of kittens. 3 kittens were gray, 2 kittens were spotted, and 7 kittens were black. How many kittens did Hayden’s cat have?

10. Pedro brought in 3 red leaves and 6 yellow leaves from the playground. How many leaves does he have in all?

11. Gabriella read 3 books on Monday, 6 books on Tuesday, and 4 books on Wednesday. How many books did Gabriella read in all?

12. If you have 3 cats, 2 guinea pigs, and a bunny. How many cute little noses do they have altogether?

13. If there are 3 inches of snow on the ground in the morning and we get 3 more inches of snow by dinner time. How many inches of snow did we get that day?

14. My cat has 4 paws and my brother’s dog has 4 paws. How many paws are there in all?

15. I had 10 pennies, but I lost 2 of them. How many pennies do I have now?

16. Santiago read 7 books over the summer. Ryan read 5 books. How many more books did Santiago read than Ryan?

17. Andrew put 10 stickers on his notebook. When he got to school he noticed some of the stickers had fallen off. Now Andrew only has 6 stickers on his notebook. How many stickers fell off Andrew’s notebook?

18. Nicole likes to help her mom pick tomatoes from their garden. She counted 9 tomatoes in the garden. 6 tomatoes were red and the rest were green. Nicole and her mom picked all the red tomatoes. How many green tomatoes did Nicole and her mom leave in the garden?

19. My sister and I have 20 pennies. If my sister has 10 pennies, how many pennies do I have?

20. The zoo had 8 tigers. 3 of the tigers moved to another zoo. How many tigers were left?

21. Esther read 3 poems. Magenna read some more poems. Altogether they read 7 poems. How many poems did Magenna read?

22. Haley’s dad bought 8 cheeseburgers. Haley ate 1 of them. How many cheeseburgers does Haley’s dad have left?

23. If you boil 7 eggs in water, and the number of eggs that float is one more than the number that sink, how many eggs float?

24. Rasheed loves to eat jellybeans. His favorite jellybeans are the yellow ones. There were 12 jellybeans in his bag. Rasheed removed all the yellow jellybeans and ate them, leaving 6 jellybeans in his bag. How many yellow jellybeans did Rasheed eat?

25. The gym teacher had 5 basketballs. The next week the gym teacher got some new basketballs. Now the gym teacher has 9 basketballs. How many new basketballs did the gym teacher get?

26. Jamal has 6 toy airplanes and his brother has 4 toy airplanes. How many more toy airplanes does Jamal have than his brother?

27. Antonio has some marbles. His brother Alex gives him 5 more. Now Antonio has 8 marbles. How many marbles did Antonio have to begin with?

28. If you have an 8-pack of crayons and you give your friend 3 of them to use during drawing time. How many crayons do you have in your pack now?

29. Emily has 4 pink erasers and some white erasers. She has 7 erasers in all. How many white erasers does Emily have?

30. Angel serves pizza at her birthday party. The pizza has 12 slices. 8 slices of pizza are eaten by Angel and her guests. How many slices of pizza are left?

31. If you have 9 toys on the floor and your little brother has 6 toys on the floor. How many more toys on the floor do you have?

32. There are 8 windows in the classroom. Some of the windows have decorations on them, 2 of them don’t have any directions. How many windows have decorations?

33. On Saturday, you brought home some fish from the pet store. If 15 of your 18 fish have stripes. How many of your fish are without strips?

34. 8 birds flew to the top of a fence. Some birds flew away and 6 birds stayed. How many birds flew away?

35. There were 6 books on Noah’s shelf. Olivia took some of the books. Now there are 2 books on the shelf. How many books did Olivia take?

36. Ethan has some folders in his backpack and 4 folders in his desk. He has 8 folders altogether. How many folders are in his backpack?

37. Liam has 8 t-shirts. 5 of them have superheroes on them, and the rest are solid colors. How many of Liam’s t-shirts are solid colors?

38. Mary was putting together a 20 piece puzzle. After she finished, she discovered that only 18 pieces were there. How many pieces were missing?

39. Nicholas has 7 cousins. Some of his cousins are girls and 3 of his cousins are boys. How many girl cousins does Nicholas have?

40. It snowed for 6 hours on Monday and 4 hours on Tuesday. How many more hours did it snow on Monday?

41. Charlie’s mom baked 12 chocolate chip cookies for dessert. Charlie ate 2 cookies and his mom and 1 cookie. How many chocolate cookies were left?

42. Melanie has 16 purple pens. Dante has 10 blue pens. Melanie has ____ more pens than Dante has.

43. Sofia has 75 pennies in her bank. How many more pennies will she need to have 100 pennies in her bank?

44. There were 9 cups of soda on the table. Some of the cups were knocked over, and 6 were still standing. How many cups of soda were knocked over?

45. Griffin has 20 board games. Some were under his bed, and 15 were in his closet. How many board games were under Griffin’s bed?

46. Antonio spotted 3 deer sitting at the top of a hill, but all he could see were their eyes. How many eyes did Antonio see in all?

47. Desmond saw 5 bunnies. He counted all of their ears. How many bunny ears did Desmond count?

48. Katie counted all of her toes, and then she counted all her mom’s toes. How many toes did Katie count altogether?

49. Which weighs more? A 15-pound red fox or a 24-pound wild turkey?

50. Which weighs more: a 150-pound white-tailed deer or a 110-pound kangaroo?

Enjoying these first grade math word problems? Check out our first grade hub for even more resources.

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Check Out These 50 Second-Grade Math Word Problems of the Day

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ThinkUp! Math

ThinkUp! Math helps teachers deliver high-level, standards-based instruction so that students can develop the confidence they need to succeed.

ThinkUp! Math Addresses 100% of the TEKS and Introduces the 9 Traits of Critical Thinking.™

ThinkUp! Math (Grades 1−8) addresses 100% of the TEKS and integrates the 9 Traits of Critical Thinking into mastery of content and thinking skills. This curriculum helps students build critical thinking skills and connect math to the real world, while giving teachers access to proven instructional strategies for planning content-driven lessons, differentiating instruction, and creating thinking-centered classrooms.

Critical Thinking Interwoven into Math Standards Mastery

Mentoring Minds Math Writer Erica Miller discusses how critical thinking is interwoven into ThinkUp! Math curriculum, instruction and standards mastery.

Take a Look Inside ThinkUp! Math

ThinkUp! Math Product Details

• Teacher Edition and Student Edition include Getting Started, Instruction, Assessment, Intervention, and Extension components that help teachers engage and accommodate all learners.

• Rigorous, standards-aligned content embeds critical thinking and problem-solving skills into lessons, placing an emphasis on mathematical processes as well as the final solution.

• Hands-on activities using manipulatives and pictorial representations connect mathematics to the everyday lives of students.

• Vocabulary activities help students develop math literacy and strengthen communication skills.

• Instruction for 100% of the TEKS equips teachers with in-depth knowledge of the standards.

• The digital platform features interactive, web-based instruction, real-time student progress monitoring, and digitally enabled capabilities including graphing and drag-and-drop activities.

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Spectrum Grade 1 Critical Thinking Math Workbooks, Ages 6 to 7, 1st Grade Critical Thinking Math, Addition and Subtraction Through 100, Place Value, and Geometry Workbook - 128 Pages (Volume 43) Paperback – April 13, 2017

1st grade Critical Thinking Math Workbook for kids ages 6+

Support your child’s educational journey with Spectrum’s First Grade Critical Thinking Math Workbook that teaches essential 1st grade math skills.

Math books for 1st graders are a great way for children to learn critical thinking skills such as addition, subtraction through 100, place value, geometry, and more through a variety of learning activities that are both fun AND educational!

Why You’ll Love This First Grade Critical Thinking Workbook

• Engaging and educational first grade math activities. “Drawing and counting money”, “Using pictures to add and subtract”, and “Composing 2-D and 3-D shapes” are a few of the fun math activities that incorporate critical thinking for kids to help inspire learning into your child’s classroom or homeschool curriculum.
• Tracking progress along the way. “Check what you know” and “Check what you’ve learned” sections are included at the beginning and end of every chapter. A mid-test and final test are also included in the Spectrum math book to test student knowledge. Use the answer key to track student progress before moving on to new and exciting activities.
• Practically sized for every activity. The 128-page first grade math workbook is sized at about 8 ½ inches x 11 inches―giving your child plenty of space to complete each exercise.

About Spectrum

For more than 20 years, Spectrum has provided solutions for parents who want to help their children get ahead, and for teachers who want their students to meet and exceed set learning goals―providing workbooks that are a great resource for both homeschooling and classroom curriculum.

• 6 chapters of math activities
• Mid-test, final test, and answer key
• “Check what you’ve learned” and “Check what you know” reviews
• Part of series Spectrum
• Print length 128 pages
• Language English
• Publisher Spectrum
• Publication date April 13, 2017
• Grade level 1 and up
• Dimensions 8.4 x 0.31 x 10.8 inches
• ISBN-10 1483835480
• ISBN-13 978-1483835488
• See all details

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• ISBN-10 ‏ : ‎ 1483835480
• ISBN-13 ‏ : ‎ 978-1483835488
• Grade level ‏ : ‎ 1 and up
• Item Weight ‏ : ‎ 10.4 ounces
• Dimensions ‏ : ‎ 8.4 x 0.31 x 10.8 inches
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Find lessons for 1st grade math | tpt, importance of learning math in 1st grade.

It's no secret that mathematics is a foundational subject for students to learn. Math forms the basis for so many other subjects — like science, engineering, and technology — and because of that, it's essential that students develop strong math skills from a young age.

Learning math in 1st grade is an exciting and crucial part of a child's education. First of all, it helps first graders begin to develop critical thinking, logical reasoning, and problem-solving skills, teaching them to think outside the box. It also helps develop their understanding of numbers and basic operations, which are important for everyday life. Lastly, it prepares them for more advanced math topics they will encounter in future.

The key concepts for 1st grade math

In 1st grade math, kids learn simple concepts such as counting, basic addition and subtraction, solving simple word problems, telling time, and money. These mathematical concepts are the building blocks that will help them succeed in the future grades when they tackle more complex topics like place value, and basic fractions.

Counting and Number Recognition

Counting and number recognition are the most fundamental concepts in 1st grade math. As a first grader, a student will learn how to count from 1 to 100 and recognize numbers up to 20. They also learn to identify odd and even numbers, count by twos, fives, and tens, and compare numbers.

Addition and Subtraction

Addition and subtraction are the next math skills that children learn in 1st grade. They'll primarily learn to add and subtract numbers up to 20 with the aid of manipulatives and number lines. Kids also learn to solve simple word problems this this point.

Time and Money

Telling time and counting money are also essential concepts that children learn in 1st grade math. They learn to tell time to the hour and half-hour using both analog and digital clocks. They also learn to count coins and bills and solve simple money word problems.

Strategies to help students learn math skills

Here are some strategies teachers can use to help kids learn math in 1st grade.

Make math fun

Children learn best when they're engaged! Sprinkle a little fun into your math lessons by using games, puzzles, and real-life scenarios. If your students seem to find math boring or uninteresting, you can also try connecting it to one of their interests or hobbies.

Practice makes perfect

Practice is essential in building a strong foundation in math. Encourage students to practice regularly, both at school and at home. Use worksheets, online resources, and math games from TPT to help children practice. And don't forget to acknowledge their achievements and efforts, a little positive encouragement is crucial to motivate students to continue learning.

Use visuals

Visual aids like charts, graphs, and manipulatives can help children understand abstract concepts better. The use of visuals can help explain math concepts to kids and better engage them in their learning.

How to find 1st grade math lessons

Educators can save time preparing 1st grade math lessons with resources created by experienced teachers. Simply search the TPT marketplace for "1st grade math," and filter by grade level, price, and/or resource type to find materials that've been proven to work in classrooms like yours. No matter what you’re teaching, there are plenty of lessons and activities sold by Sellers on TPT that are tailored to meet your students' skill levels.

Frequently asked questions

What math should first grader know.

By the end of 1st grade, a student should be able to count, sequence read, and write numbers up to 100. First graders should also be able to add and subtract small numbers. As part of math learning, students in first grade are also taught about telling time and counting money. Going into 2nd grade, they should know how to read an analog clock, and understand the value of money in addition to being able to count coins and bills. For example, they may learn that four quarters equal a dollar.

What types of math lessons are available on TPT?

There are many different types of math resources sold by Sellers on TPT. Some popular math lessons include: telling time, counting money, addition and subtraction, and word problems.

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First Grade Thinking Skills & Key Concepts: Teacher's Manual

Teaches beyond most state & common core standards.

Critical Thinking

Components Sold Separately

First Grade Thinking Skills & Key Concepts

• Paperback Book - $22.99
• eBook - $22.99

Description and Features

Teaching Support The student book can be used with a free, downloadable, answer PDF ( get it here ) or with this detailed, 224-page Teacher's Manual which can be purchased separately. This separate Teacher's Manual provides instructions to teach the lessons using research-proven methods that promote students' thinking:  direct instruction, cooperative learning, whole sentence responding, and language integration activities. The Teacher's Manual physical book is in black and white, but the eBook version is in color.

Product Details

General License - Download

SOFTWARE LICENSE AGREEMENT

IMPORTANT-READ CAREFULLY

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.

The Critical Thinking Co.™ hereby grants to you a non-exclusive license to use the software product identified above (the "Software") and the accompanying printed materials and User Manual (the "Documentation") on the terms set forth below.

1. GRANT OF LICENSE. The Critical Thinking Co.™ grants you the right to install and use this Software Product, provided that this software will be installed only in the quantity and for the computer system(s) indicated at the time of your order for the Software.

2. COPYRIGHT. The Software Product and Documentation are protected by copyright laws and international copyright treaties as well as other intellectual property laws and treaties. Therefore, you must treat the Software Product like any other copyrighted material. You may not remove, modify, or alter any of The Critical Thinking Co.'s™ copyright or trademark notices from any part originally contained in or otherwise created by the Software Product, including any notices contained in the Documentation.

3. RESTRICTIONS. You may not modify, translate, reverse engineer, decompile, disassemble, or create derivative works based on the Software, or any portion thereof. The Software Product is licensed as a single product. This Software Product can be installed on a computer as a whole and shall not be separated in parts or disassembled to parts or pieces. You may not rent, lease, or lend the Software or Documentation to any other party without the written permission of The Critical Thinking Co.™. The License is in effect until terminated. The License will terminate automatically if you fail to comply with the limitations described herein. On termination, you must destroy all copies of the Software and Documentation.

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.

6. MISCELLANEOUS. This Agreement represents the complete agreement concerning this license between the parties and supersedes all prior agreements and representations between them. This Agreement may be amended only in writing executed by both parties. The acceptance of any purchase order placed by you is expressly made conditional on your assent to the terms set forth herein, and not those contained within your purchase order. If any provision of this Agreement is held to be unenforceable for any reason, such provision shall be reformed only to the extend necessary to make it enforceable and the remainder of this Agreement shall nonetheless remain in full force and effect. If you acquired this product in the United States, the laws of the State of California govern this Agreement. If this product was acquired outside the United States, then local laws may apply. Should you have any questions concerning this Agreement, or if you desire to contact The Critical Thinking Co.™ for any reason, please write to The Critical Thinking Co.™, PO Box 1610, Seaside, CA 93950-1610, USA; send a fax to 831-393-3277; send email to [email protected]; call 800-458-4849; or refer to The Critical Thinking Co.™'s Website at http://www.criticalthinking.com/ .

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