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20 Math Critical Thinking Questions to Ask in Class Tomorrow

• November 20, 2023

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

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

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

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

Table of Contents

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

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

What skills do we actually want to teach our students?

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

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

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

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

When should I ask these math critical thinking questions?

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

Start small

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

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

Add critical thinking questions to word problems

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

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

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

When you want your students to defend their answers.

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

When you want your students to justify their opinions

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

When you want your students to think outside of the box

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

Let’s Recap:

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

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• Math Worksheets
• 2nd Grade Math
• Logical reasoning

Grade 2 logical reasoning worksheets: Improve your child's thinking skills

Hello, and welcome to our engaging math resource! Today we will discuss a vital topic for Grade 2 students: logical reasoning. This article will provide many learning opportunities and areas in Mathskills4kids.com , where you'll find the best Grade 2 logical reasoning worksheets online. These worksheets are designed to improve your child's thinking skills and apply them in math and the real world.

Logical reasoning involves using facts, rules, and patterns to solve problems and make decisions . Logical reasoning skills are essential for academic success and everyday life.

Our major objective in this resource is to show you why logical reasoning is important for grade 2 students , how to introduce logical reasoning concepts to your child , fun and engaging activities to practice logical reasoning skills , the benefits of logical reasoning worksheets for grade 2 , tips and tricks to help your child solve logical reasoning problems , etc.

Let's get started!

Why logical reasoning is important for Grade 2 students

Logical reasoning is important for grade 2 students because it helps them develop their thinking skills and prepares them for more advanced math and science topics in the future.

Logical reasoning also helps students improve their reading comprehension, writing skills, and creativity. With logical reasoning skills, students can understand different perspectives, evaluate arguments, and draw conclusions.

Logical reasoning also fosters curiosity, confidence, and independence in learning.

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Start practice on Second Grade here

How to introduce logical reasoning concepts to your child.

The best way to introduce logical reasoning concepts to your child is to use everyday examples and situations they can relate to.

For example, you can ask your child questions like:

• What do you think will happen if you leave your ice cream outside on a hot day?
• How do you know that this is a triangle?
• What is the rule for making this pattern ?
• How can you sort these objects into different groups ?
• How can you prove that this statement is true or false?

You can also use games, puzzles, stories, and experiments to introduce logical reasoning concepts to your child. For example, you can play games like tic-tac-toe, chess, sudoku, or riddles with your child.

You can also read stories that involve logic puzzles or mysteries with your child. You can also do simple experiments with your child using household items like water, vinegar, baking soda, or food coloring.

Mathskills4kids fun and engaging activities to practice logical reasoning skills

There are many fun and engaging activities found in Mathskills4kids that you can use to practice logical reasoning skills with your child. Here are some examples:

• Make a treasure map with clues and directions for your child to follow.
• Create a secret code with symbols or letters and have your child decode it.
• Build a model or a structure with blocks or Lego and have your child explain how they did it.
• Make a collage or a picture with shapes and colors and have your child describe it.
• Invent a new game or a toy with rules and instructions for your child to play.

The benefits of Mathskills4kids logical reasoning worksheets for Grade 2: Improve your child's problem-solving and critical thinking abilities

One of the best ways to practice and improve your child’s thinking skills is to use logical reasoning worksheets for grade 2 from Mathskills4kids.com . These Logical reasoning worksheets are designed to challenge and stimulate your child's mind with different problems and questions requiring logic and reasoning. Logical reasoning worksheets for grade 2 can help your child improve their problem-solving and critical thinking abilities by:

• Developing their analytical and deductive skills
• Enhancing their memory and concentration
• Expanding their vocabulary and knowledge
• Increasing their creativity and imagination
• Boosting their confidence and motivation

Tips and tricks to help your child solve logical reasoning problems

Solving logical reasoning problems can be tricky sometimes, but some tips and tricks can help your child solve all the exercises in our Grade 2 logical reasoning worksheets and more.

Here are some of them:

• Encourage your child to read the problem carefully and understand what it is asking.
• Help your child identify the relevant facts, rules, and patterns in the problem.
• Guide your child to use different strategies like drawing diagrams, making tables, using examples, or eliminating options.
• Support your child to check their answers and explain their reasoning.
• Praise your child for their efforts and achievements.

What are some real-life situations where logical reasoning skills are useful?

Logical reasoning skills are useful in real-life situations and school. Here are some examples of how logical reasoning skills can improve your child’s thinking skills in everyday life:

• Planning a trip or an event
• Following directions or instructions
• Making choices or decisions
• Solving conflicts or disputes
• Learning new skills or hobbies

Where to find the best grade 2 logical reasoning resources online

There are many ways to practice logical reasoning with your kids at home or in the classroom. Hence we want to help you discover where to find the best grade 2 logical reasoning resources online to print and use with your Grade 2 students at any time.

These activities are interactive, colorful, and varied, so your kids will always feel excited. They also cover different logical reasoning skills that will readily improve your child’s thinking skills, such as pattern recognition, picture analogy, picture matching, odd one out, and more.

Here are some of the best online Grade 2 logical reasoning worksheets and fun activities that we have found for you:

This website offers a variety of printable logic grid puzzles for kids of different ages and levels. Logic grid puzzles are a type of logic puzzle that require you to use clues and deductive reasoning to fill in a grid with the correct information.

For example, you might have to figure out who likes which color, has which pet, or plays which instrument. These puzzles are great for developing logical thinking, attention to detail, and concentration skills.

This website provides interactive worksheets that you can do online or print out.

The worksheets are based on the topic of animals and their habitats. They involve matching animals to their habitats, finding the odd ones, completing patterns, and more.

These worksheets are perfect for practicing visual discrimination, categorization, and spatial reasoning skills.

These puzzles enhance logical reasoning, analytical thinking, and math skills.

Thank you for sharing the links of MathSkills4Kids.com with your loved ones. Your choice is greatly appreciated.

We hope you enjoyed our Grade 2 logical reasoning worksheets and saw the amazing results in your child's thinking skills .

Thank you for reading, and happy reasoning!

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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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Second Grade Critical Thinking

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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

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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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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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Real World Problem Solving in Second Grade Mathematics

Introduction.

Edgewood Magnet School in New Haven, Connecticut is an arts magnet school, integrating the arts across the curriculum. Students in this environment are encouraged to use the strategies of observation, interpretation, and analysis to increase their thinking skills in every subject. With that mission, both teachers and students use unique and exciting approaches to “the basics” and work together to ensure that all learners are included.

For most second graders, the beginning of the year is a time for refreshing knowledge and skills from first grade. The summer away from direct instruction and opportunities for practice and guidance sometimes means a loss of solid understanding of learned concepts in mathematics. This three- to four-week unit is designed to review and build new understanding of one-step word problem solving using addition and subtraction as students develop skills and strategies they will use all year. The students, through a series of mathematical scenarios, will use the problem types identified in Table 1 of the Common Core Mathematics Glossary which covers addition and subtraction. 1

The Common Core concentrates on a clear set of math skills and concepts. Students learn concepts in an organized way during the school year as well as across grades. The standards encourage students to solve real-world problems. 2

The Common Core calls for greater focus in mathematics. Rather than racing to cover many topics in a mile-wide, inch-deep curriculum, the standards ask math teachers to significantly narrow and deepen the way time and energy are spent in the classroom. This means focusing sharply on the major work of each grade, which for grades Kindergarten through second grade includes concepts, skills, and problem solving related to addition and subtraction.

The New Haven Public School district uses the Math in Focus Singapore Approach, a Common Core-based curriculum for students from Kindergarten to Fifth Grade. The student books and workbooks follow an instructional pathway that includes learning concepts and skills through visual lessons and teacher instruction for understanding the how and why; consolidating concepts and skills through practice, activities and math journals for deep math understanding, hands-on work in pairs and in small groups; and, applying concepts and skills through extensive problem solving practice and challenges to build real world problem solvers. 3

This approach embeds problem solving throughout each lesson and encourages frequent practice in both computation and problem solving. The word problems appear throughout each chapter and progress from 1-step to 2-step to multi-step. Each chapter concludes with a challenging problem or set of problems that require students to solve some non-routine questions. To solve these problems, the students need to draw on their deep prior knowledge as well as recently acquired concepts and skills, combining problem solving strategies with critical thinking skills, including classifying, comparing, sequencing, identifying parts and whole, identifying patterns and relationships, induction and deduction and spatial visualization.

The second grade text begins with numbers to 1000. Students begin by expressing numbers in standard form (231), expanded form (200 + 30 + 1), and word form (two hundred thirty-one). This is accompanied by concrete representations via base ten blocks, and, for two digit numbers and a few three digit numbers, representation by trains of rods, of lengths 1, 10 and 100. This initial chapter also includes sequencing numbers and comparing using greater than and less than terminology, and then moving right into addition and subtraction of two- and three-digits numbers. Here the take-away should be, if you have more hundreds, the tens and ones don’t make any/much difference; and if you have the same number of hundreds, but more tens, then the ones don’t make any/much difference. Most of my students (if not all) struggle from the start! They do not seem to have a solid foundation of understanding numbers to 100 or the concept of place value in general. This unit is designed to get ahead of the frustration that the students feel when pushed too quickly before they have a firm understanding of principles of place value and the properties of operations.

This unit launches the school year with 1-step addition and subtraction problems of all types using numbers to 10. The goal is to spend time practicing basic computations with numbers that student can work comfortably with before jumping right into the district curriculum. Once there is a level of understanding with these problem sets (numbers to 10), students will move on to solving 1-step problems using teen numbers and then onto numbers to 100. Most of the curriculum problems at the start of the year require addition and subtraction of 3-digit numbers. Some students will move quickly through the problem sets with numbers to 100 and will be ready to work with the regular curriculum.

For the duration of the unit, the focus will be steadily on solving and later constructing a collection of word problems that provide robust and balanced practice. Problems sets will be based on a scenario which will provide the substance of the story. Each scenario will allow us to extract several problems, changing the numbers and ensuring each set of numbers makes a reasonable problem. This idea looks like the following: John has 8 crayons in his box. He shares 3 with Sam. How many crayons does John have left in the box? John has some crayons in his box. He shares 3 with Sam. John has 5 crayons left in his box. How many crayons did John start with? John has 5 crayons. Sam has 2 fewer than John. How many crayons does Sam have? John and Sam are sharing crayons. John has 5 and Sam has 3. How many crayons do the friends have together? The two students participate in several crayon-sharing stories that use the same set of numbers but in slightly different situations. Some situations are more obvious and direct while others take more thinking. It is important to provide opportunities for students to work with and solve the different problem types that can be created from one set of numbers. 4

Background: Problem Types

The taxonomy of addition and subtraction problem types as identified in the Common Core State Standards of Mathematics Glossary is a framework that sorts one-step problems into three broad classes: change , comparison , and part-part-whole . Each of the three classes is then separated further into a total of 14 problem types sorted out as follows: change , in which some quantity is either added to or taken away from another quantity over time; comparison , in which one amount is described as more or less than another amount; and part-part-whole , in which an amount is made up of two parts. 5

Within the group of change problems, there are two subgroups: change-increase , in which a quantity is added to an initial amount and change-decrease , in which a quantity is taken from an initial amount. We might recognize these subgroups more familiarly as “add to” or “take from.” Additionally within each of these subgroups, there are three possible unknown quantities. One scenario to show change-increase : 2 kittens were playing with some yarn. 3 more kittens join them. Now there are 5 kittens playing with the yarn. Using these quantities, the unknown might be the result (2 + 3 = ?), an unknown quantity of change (2 + ? = 5) or an unknown initial amount (? + 3 = 5). In the change-decrease subgroup, there are again three possible unknowns. A scenario for this example: 5 birds are sitting on the branch. 2 fly away. Now there are 3 birds sitting on the branch. Here again the students might solve for the final amount (5 – 2 = ?), the amount of change (5 - ? = 3), or the initial amount (? – 2 = 3). This gives in all six types of change problems.

Similarly comparison problems can also be categorized into two subgroups: comparison-more , in which one quantity is described as more or greater than another, and comparison-less, in which one quantity is described as less or fewer than another. Here again, each of these two subgroups has three possible unknowns, for a total of 6 types. Sam has 6 marbles. James has 8 marbles. James has 2 more marbles than Sam. The unknown quantity may be the lesser amount (? + 2 = 8), an unknown greater amount

(6 + 2 = ?), or the unknown difference (8 – 6 = ?) one quantity that is more and one that is less. Using this same scenario for a set of comparison-less problems, the language need to change from “more than” to “less than.” Here is a way to present this set with the language adjustment: Sam has 6 marbles. James has 8 marbles. Sam has 2 fewer marbles than James.

Part-part-whole problems are a set of two quantities, the parts that, when put together, make up a whole quantity.  This problem type seems very like to change category but in this problem type there is no change over time. The two parts play equivalent roles, which allow for only two possible unknown categories: either a part is unknown or the whole is the unknown. There are 4 large dogs and 3 small dogs. There are 7 dogs in all. One of the parts may be unknown (4 + ? = 7 or ? + 3 = 7) or the unknown may be the size of the whole (4 + 3 = ?). Since the parts are interchangeable, there are only 2 types in this class of problems.

The following chart sort these classes and categories into the framework. Located in Appendix A of this unit is a set of example problems illustrating each of these 14 types.

The Scenarios of the Problems

For second graders, life at school is a large part of their world. Most of my students arrived at Edgewood for their Kindergarten year and stayed through First Grade making the year in second grade essentially their third year at the same school. They are comfortable in the building and know many of the other students. They will become the active players in the math stories that I, and we together, will construct. Activities that occur in the classroom, in the cafeteria, on the playground, and on the bus seem to be recognizable situations that will help with the basic understanding of context.

Additionally, there are opportunities for students to incorporate the topics and learning that occur in the other subjects, such as science, social studies, literacy, art, music and, in our school, dance and drama. One example might be to create set of story problems centered on the life cycle of the butterfly, a unit of study each year in second grade. With the common knowledge the students will be obtaining, this content could become the scenarios for word problems. An example might be: Seven caterpillars climbed up the branch and formed their chrysalises. Later that day, three more caterpillars climbed up the branch and formed their chrysalises. How many chrysalises are hanging from the branch? Similarly, using the characters in a book read together as a class could provide the characters in a new set of problems. Curious George had a bunch of bananas. He ate 4 of them. Now he has 3. How many bananas did Curious George begin with? The use of common or thematic content will not only connect all the thinking and practicing, it will provide tangible and real situations. With an established scenario, students will work with a set of numbers, determining the unknown within each of problems types.

Creating the Problems

A question that is frequently answered with a guess is “What should we do to answer the question to solve the word problem?” The fundamental understanding of what is being asked is not apparent to the students, making the solution inaccessible. Most first graders entering second grade have a basic understanding when the story (problem) is categorized as final unknown or whole unknown , but most other components of the taxonomy are unfamiliar to them or just too difficult to decode. To begin to help them with their thinking, they will use concrete models, such as themselves (2 children are sitting at the reading table, 4 more join them) acting out scenarios. Many basic materials in the classroom – pencils, notebooks, folders, crayons – can be used to create and design scenarios, with each type of problem represented.

Solving the Problems

Following the overall plan of the Singapore Math program, the students will solve problems using the concrete, pictorial and abstract approach. Because this is a standard approach in our district mathematics instruction throughout the year, the students will begin with this set of strategies to solve problem sets.

Word problems are written as stories and scenarios making language a consideration in crafting the problems for the beginning second graders. Word problems are as much about language and reading as they are about math. If the story is not understandable, how can students begin the know what to do with the numbers they’ve been given and the question they’ve been asked? Thus, words and vocabulary need to be appropriate and useful for the variety of reading levels of the incoming students.  The structure of word problems should be understandable and clear, accessible in language as well as numbers. Also, the language, especially the words that express the relationship between the quantities involved, should be discussed to ensure that it is familiar to all students.

This is a clear integration of Language Arts and Mathematics and a method in which students can connect math to the real world, in this case, through the activities they engage in at school. Reading skills and computation skills come together with even the simplest of word problems.

Structure of Problem Collection

The content introduction over the duration of this unit includes a certain sequencing and scaffolding to guide students through the 14 problem types. To begin the unit, students will only be working with numbers to 10. This is an important starting place to ensure that understanding is occurring. Most of my second graders are capable with addition and subtraction to 10, but are not so comfortable with the word problem language. So first, students will be challenged more by the language than the arithmetic. Students will practice figuring out what exactly the problems are asking with problems that they are familiar with before moving on to a new step. Practicing all the problem types will improve and increase strategies and confidence!

With addition and subtraction within 10 mastered, the next phase of the unit moves to numbers to 20. The key is to continue with scenarios that are obvious and repeated as new numbers are introduced. An example of this transition would be these parallel problems:

6 students got on the bus at the first stop. 3 students got on the bus at the second   stop. After the second stop, how many students are on the bus? ( change-increase, final unknown)

Some students got on the bus at the first stop. 3 students got on the bus at the second stop. Now there are 9 students on the bus. How many students got on at the first stop? ( change-increase, initial unknown)

These now become:

11 students got on the bus at the first stop. 7 students got on the bus at the second stop. After the second stop, how many students are on the bus? ( change-increase, final unknown)

Some students got on the bus at the first stop. 7 students got on the bus at the second stop. Now there are 18 students on the bus. How many students got on at   the first stop? ( change-increase, initial unknown)

When working with numbers to 20, it is essential that students understand that the “teen” numbers (11-19) are really 10 and some ones. Students should work with numbers within 20, creating equations using their knowledge and skill of making a ten first. In the case of 7 + 6, making a new ten looks like this:

7 + 6 = 7 + 3 + 3 = 10 + 3 = 13

Because 7 needs a 3 to make ten, and 6 is composed of 3 + 3, this equation shows the progression of making 10 and some more. Practicing this method using two ten frames demonstrates the process concretely. In the example above, students use the ten-frames to show 7 and 6 separately. To make the new 10, students will move 3 from the 6, which now shows 10 and 3 more or 13.

As mentioned earlier, it is obvious that the most accessible problem types for students entering the second grade are the change-increase or change-decrease, result unknown and part-part-whole, whole unknown. The general go-to strategy for solving a word problem seems to be to just take the two numbers you see and add them together, or maybe subtract, but often the students are just unsure. It seems that these are the most practiced problem types, which leaves students without balanced experience with all 14 types and ultimately without some strategies to employ as they problem-solve. Students need to see a broad range of problems to gain a strong understanding of how addition and subtraction are used and how they are related to each other. The notion of example sufficiency means students should be exposed to a wide array of examples to provide well-rounded practice with the concept. 6

Teaching Strategies

The approaches for this curriculum unit vary to reflect the learning styles of all students.

The general format is based on the workshop model. The concepts and skills are taught through a series of mini-lessons focused on the objective with the following methods used throughout:

Experiential Learning: Most young students need to begin with hands-on learning. Using concrete models to work out math stories allows students to see the problem and manipulate the pieces as the story progresses. This type of learning is an important first step.

Differentiated Instruction: Lessons and activities will be targeted to maximize learning. The students will use a variety of approaches, working sometimes individually and sometimes in small groups, determined by the complexity of the work. Some students will move more quickly as they master skills and some will need more opportunities for practice.

Cooperative Learning: The students will be given opportunities to work as cooperative groups to create math stories to present to the class. This strategy will allow students to work collaboratively taking on various roles necessary to complete the work, with a focus on success for all.

Classroom Activities

Activity 1: sequenced problem types – problems to 10.

The introduction (and review) portion of the unit covers all problem types but in a sequenced manner. The objective is for students to read and interpret a word problem with guided instruction followed by independent practice. Because of the many problem types, this part will take several days of review and practice before students are comfortable beginning to write their own sets of problems. Based on student need and pace of understanding, I expect this section to be a four- to six-day set of lessons, more if needed.

The sequence is as follows: part-part-whole ; change-increase and change-decrease ; and finally, compare-greater and compare-fewer . The following introductory sessions are designed as a whole group activity, with students either at their desks or gathered on the rug close to the board or easel. The whole group portion should be 20 minutes at most. At the close of each session, I will give students between 5 and 10 similar problems to solve. More capable students can begin to generate their own problems during the independent work time.

Beginning with the fundamentals provides a good opportunity to get to know students’ skills which is helpful in preparing differentiated work and creating groups,

In this lesson, students will interpret real world problems and with the help of manipulatives and pictures, solve part-part-whole stories using addition and subtraction.

6 girls are playing

3 boys are playing with them.

How many children are playing in all?

Begin the story with the whole unknown as in this example. This type of story is perfect for students to act out right in the classroom. Write the story on the board or chart paper and have students volunteer as actors. Once the students have solved the problem, write the math sentence to show what happened: 6 + 3 = 9 students. Explain that the 2 parts (boys and girls) have made a whole (children). With the students still in acting position, present a new approach to this scenario:

9 students are playing.

6 of them are girls.

How many boys are playing?

With this visual example, students should see right away how many. The important concept to demonstrate is that the parts can be determined when the whole and one part are known, in this case 9 is known as the whole and 6 as one part. Again, write the math sentence to show this calculation: 6 + ? = 9 and include the strategy of starting with the whole to determine the missing part as a subtraction sentence 9 – 6 = 3. Practicing both approaches to the solution will help students connect addition and subtraction and recognize how they are used together.

Since this lesson requires students to read story problems, I will pair fluent readers with those who are less fluent, provide counters for those who want them, and allow partners to work together to solve and problems and share the strategies that they used.

I will use two more examples, like the ones below, to demonstrate, remembering to write the word problem on the board as well as the math sentence. I will also reword the problems to have the part as the unknown.

Hannah has 5 red markers.

She has 3 blue markers

How many markers does Hannah have in all?

7 students are drawing with crayons.

2 students are drawing with colored pencils.

How many students are drawing?

Continuing with this same idea, the next set of problem types includes change-increase and change-decrease . Although part-part-whole is language that students can adopt and use while discussing their work, the change-increase and change decrease language is a bit trickier. The use of the word change is more appropriate for students to demonstrate that some amount has been either added or subtracted from an initial amount.

Introduce the word problem below which is an example of the unknown result in the change-increase category.

Jason had 8 “caught being good” stickers on his chart at the beginning of the day.

During the school day, he earned 2 more stickers.

How many stickers does Jason have on his chart at the end of the day?

Student can solve the problem as written and, using the same scenario, challenge them to create the change-unknown and initial unknown story. One example might be:

Jason had some “caught being good” stickers on his chart at the

beginning of the day.

At the end of the day, he has 10 stickers.

How many stickers did Jason have at the beginning of the day?

This is an oral activity, with me writing the adjusted version across the board, placing the math sentence underneath. It is important to allow students to work on composing the problem so they can begin the see the relationship between the problems and what the problems are asking.

The goal is for students to understand and not just solve. I can informally assess during the discussion of rewriting the text of the word problem, with more formal assessment later in the unit.

The next category to introduce is the change-decrease problem types. Following the same format as before, I will introduce the result unknown, change unknown and then initial unknown.

Crystal collected 7 leaves for her project.

2 leaves blew away in the breeze.

How many leaves does Crystal have left for her project?

Again, the goal is for students to understand and not just solve.

The third broad class, compare, is more difficult for my 2 nd grade students. This requires the text of the word problems to be very straight-forward. Students should not get tangled up when they are learning to take the data from the problem. Remember that using the exact terminology is not the goal, but rather understanding what the problem is asking. Here are three ways I will present a scenario that shows the problem types comparison-more , and three ways to show comparison-less. Students need to be exposed to and have opportunities to practice all types. Of course, not all of these examples should be used at one time. As I write the problems out on chart paper and post them in the classroom, the students can begin to see and do their own comparing and contrasting as one scenario is explained in different ways. The use of the words “more” and “fewer” should be highlighted and explained as the problem set is introduced and worked on. My role here is to let the students begin to notice the subtle differences in the wording and how it changes the thinking. Simpler is better to start with!

Throughout these introductory sessions, the students and I will brainstorm scenarios that can eventually be used in own word problems. Ideas should generate from school activities and materials, guiding students to think of what students can actually use for manipulatives or, as in the first scenario, be able to act out to solve. By keeping a list of ideas on chart paper as reference material, students won’t struggle with vocabulary or appropriate scenarios; they will be on to the task of crafting their problems. This list will prepare the students for the second part of the unit.

Activity 2: Classroom / school scenarios

As stated earlier, words and vocabulary should be accessible to students and not a challenge or hurdle. The goal is to get to the thinking of the stories and plugging in the information that was gathered during the brainstorming session. To begin this portion, review the charts and add more if students have new ideas. It may be helpful for the purposes of composing word problems to have the information in categories, such as these:

Materials We Use

Classes We Attend

Activities at School

Classmate’s Names

I will create groups of two or three students to have them write problems of their own to share with the class.  Since this lesson requires students to read and write story problems, again, fluent readers and writers with those who are less fluent, provide counters for those who want them, and allow partners to work together to solve and problems and share the strategies that they used.

The goal during this period of time is to challenge students to write the same problem but try it another way, choose a different type as they tell the story. The timing for the student groups to work together will be during arrival time as morning work and during the math workshop portion of math instruction time. This will allow students to work as much as 30 minutes per day with their partners to create some math stories.

I will stress that it is important to keep their collection together as much of their work will become part of the workbook they will create at the end of this unit. Folders and math journals can be helpful, or my collecting the work-in-progress daily is another option.

Activity 3: Science Scenarios

The first unit in 2 nd grade science is investigation and research on the life cycle of the butterfly. Students receive caterpillars at the start of the semester and observe and record the changes the caterpillar’s life. The work that the students do during their science lessons can become the information and scenarios they can use for crafting word problems.

Using all different problem types, we will write several together as a class.  This is an additional opportunity to integrate math very specifically into our science research and work. It is important for students to recognize that, although their learning has been compartmentalized into subject areas, it is essentially impossible to separate it all out into categories. So this portion of the unit uses math, science and reading to help students learn about the life cycle of a butterfly (and other animals as well).

Students will create problem sets that use their daily experiences tracking their caterpillars. Each student has 2-3 caterpillars to observe and record information on, which can become the start of word problems. Examples to start: If Table 3 has 8 caterpillars and 2 caterpillars join that group, how many caterpillars are being observed at Table 3? Here are 28 students in the class. Each student need one cup of caterpillar food.  There are 30 cups of caterpillar food. How many more cups of food are there than students?

There are often students who have great interest in other areas of science. This is an area to encourage if students are excited about sharing their knowledge. Some students will be more inclined to use the unit of study going on in class, but throughout the literacy portion of the day, students are exposed to a great deal of non-fiction, or informational text, that could certainly enrich our science word problems.

Throughout the duration of the science unit, students will continue to write word problems of various types to eventually include in our final project, the workbook. These problems can be written during the morning work session, during math workshop, and at the end of science class. By the end of the unit, each student should have two problems to add to the Science chapter of the workbook.

Activity 4: Creation of Workbook / Publishing Celebration

The goal of this portion of the unit is to sort the word problems into “chapters” and create a workbook to share at the Publication Celebration. Chapters will be titled by subject or category, depending on student choice and teacher suggestion. Ideas include Beginning Stories, Classroom Activities, Playground Fun, Science & Math, and Social Studies Connections. Let students be creative with titles!

Students will submit their work which will include at least one word problem for each chapter. They must also submit the solutions to their problems so that they can be included in an answer key. Each chapter will have at least 25 problems, with examples of all types and with varying levels of difficulty. Word problems can either be typed or hand-written for the final workbook, depending on what the students decide as a class. One workbook per student will need to be copied and bound in some manner for the Celebration.

Two weeks before the Publication Celebration, students will create an invitation to give to their family and friends, inviting them to come for a “Celebration of Problem Solving.” Parents and other VIP guests will spend some time working on word problems, moving around the room, visiting many students. The students will share their own specific work with the guests (the word problems they themselves created) and “help” their visitors figure out the answers.

Each student will have a “Comments” sheet for guests to sign and leave comments on their experience working with the student. I will encourage visitors to stop to talk with each student or as many as they can during their visit.

Additionally, this is an opportunity to have some students work as editors and publishers. Creating the workbook will require review and assembly time and these tasks can be delegated and shared by the students who are interested.

Common Core State Standards for Mathematics,

http://www.corestandards.org/the-standards/mathematics.

Fong, Ho Kheong. Math in Focus Singapore Math by Marshall Cavendish . Final ed. Singapore: Marshall Cavendish Education, 2015.

Fuson, Karen C. Math Expressions . 2011 ed. Orlando, FL: Houghton Mifflin Harcourt ;, 2011.

Howe, Roger. Three Pillars of First Grade Mathematics and Beyond

Howe, Roger, The Most Important Thing for Your Child to Learn about Arithmetic

Howe, Roger and Harold Reiter, The Five Stages of Place Value

Ma, L. Knowing and Teaching Elementary Mathematics , Erlbaum Associates, Mahwah, NJ, 1999.

The Moscow Puzzles: 359 Mathematical Recreations . New York: Dover Publications, 1992.

Polya, George. How to Solve It: A New Aspect of Mathematical Method . New Princeton Science Library ed., 2014.

Appendix A: Problem Set

Change Increase / Result Unknown

7 students are in the classroom. 2 more students join them. How many students are in the classroom now?

Change Increase / Change Unknown

7 students are in the classroom. Some more students join them. Then there were 9 students. How many students join the first 7?

Change Increase / Initial Unknown

Some students are in the classroom. 2 more students joined them. Then there were 9 students. How many students were in the classroom at the beginning?

Change Decrease / Result Unknown

9 students were in the classroom. 2 students went home. How many students are in the classroom now?

Change Decrease / Change Unknown

9 students were in the classroom. Some students went home. Now there are 7 students. How many students went home?

Change Decrease / Initial Unknown

Some students were in the classroom. 2 students went home. Then there were 7 students in the classroom. How many students were in the classroom in the beginning?

Compare More / Difference Unknown

Sam has 10 French fries. Emily has 6 French fries. How many more does Sam have than Emily?

Compare More / Greater Unknown

Sam has 4 more French fries than Emily. Emily has 6 French fries. How many French fries does Sam have?

Compare More / Smaller Unknown

Sam has 4 more French fries than Emily. Sam has 10 French fries. How many French fries does Emily have?

Compare Fewer / Difference Unknown

Sam has 10 French fries. Emily has 6 French fries. How many fewer does Emily have than Sam?

Compare Fewer / Smaller Unknown

Emily has 4 fewer French fries than Sam. Sam has 10 French fries. How many French fries doe Emily have?

Compare Fewer / Greater Unknown

Emily has 4 fewer French fries than Sam. Emily has 6 French fries. How many French fries does Sam have?

Part-Part-Whole / Whole Unknown

Sam has 4 cookies for lunch. He has 2 more for dinner. How many cookies does Sam have?

Sam ate 6 cookies today. He had 4 of them for lunch. How many did he have for dinner?

Appendix B – Implementing Common Core Standards

This unit integrates, quite naturally, literacy and math. Both reading and writing are essential parts of the students’ ability to solve word problems involving both addition and subtraction.

Students will work most specifically toward the Common Core State Standard in Mathematics, 2.OA.A.1 which states that second graders should, by the end of the year, be able to “represent and solve problems involving addition and subtraction within 100 to solve one- step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions. During this unit students will begin solving and crafting word problems with numbers to 10, advance to numbers to 20 and continue on to the 100’s and up to 1000 as they master place value concepts.

This unit also addresses the Language Arts Common Core State Standards of Reading Informational Text, RI.2.1, in which students work on locating key ideas and details by asking and answering such questions as who, what, where, when, why, and how to demonstrate understanding of key details in a text. Throughout this unit on word problems, students will be working asking these questions as they determine what information the math story is providing. As they begin to write their own word problems, they will need to consider these questions to craft a meaningful story for the text of their problem.

• Common Core State Standards for Mathematics, http://www.corestandards.org/the-standards/mathematics.
• Common Core State Standards for Mathematics
• Ho Kheong Fong, Math in Focus Singapore Math by Marshall Cavendish , 8.
• Roger Howe, Three Pillars of First Grade Mathematics and Beyond, 2 .
• Roger Howe, Three Pillars of First Grade Mathematics and Beyond, 1 . Common Core State Standards for Mathematics
• Roger Howe, Three Pillars of First Grade Mathematics and Beyond, 2

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Home » Teacher & Parents Tips » Math Made Easy: Helping Grade 2 Students Thrive in Problem Solving

Math Made Easy: Helping Grade 2 Students Thrive in Problem Solving

Mathematics is an essential subject that students cannot afford to neglect. As early as grade 2, students are introduced to the basics of mathematical concepts such as numbers, addition, subtraction, multiplication, and division. An essential aspect of mathematics is problem-solving. While many students find it challenging, it can be made easy with the right approach. This article will discuss how parents and educators can turn problem-solving woes into victories and equip their grade 2 students with the skills needed to excel in math.

Table of Contents

The Importance of Problem Solving in Grade 2 Math

Problem-solving is an essential skill that students need to master to excel in math. It involves critical thinking, analysis, and decision-making. It also helps students develop their reasoning abilities and enables them to apply logic in real-life situations. In grade 2 math, problem-solving skills are essential as they help students understand mathematical concepts better. Students who can solve problems are more confident and enjoy math more than those who struggle.

Turning Problem-Solving Woes into Victories

Many students, especially in grade 2, find problem-solving challenging. However, with the right approach, it can be turned into a victory. One way to turn problem-solving woes into victories is by breaking down the problem into smaller parts. Encourage your child to read the problem carefully and identify the key elements. Once they have identified these elements, they can begin to solve the problem step by step. This approach helps students understand the problem better and reduces anxiety.

Another way to turn problem-solving woes into victories is by practicing regularly. The more students practice, the more comfortable they become with problem-solving. Encourage your child to practice regularly and provide them with different types of problems to solve. As they solve more problems, their confidence will increase, and they will become more efficient problem-solvers.

Strategies for Effective Problem Solving in Math

There are several strategies that students can use to solve problems effectively. One of the most effective strategies is the use of visual aids. Encourage your child to draw diagrams or pictures to help them understand the problem better. This approach helps students visualize the problem and enables them to make better decisions.

Another strategy is to use real-life situations to solve problems. This approach helps students understand how math can be applied in real-life situations. For example, if you want to teach your child about fractions, you can use pizza slices to help them understand the concept better.

Lastly, encourage your child to work with a partner or in a group. Group work helps students learn from one another and can be an effective way to solve problems. It also helps students develop their social skills and enables them to work collaboratively.

Fun and Engaging Math Activities for Grade 2 Students

Learning math can be fun and engaging. There are several math activities that parents and educators can use to help grade 2 students develop their problem-solving skills. One such activity is math games. Games such as Sudoku, Math Bingo, and Math Jeopardy can be used to teach students math concepts while making learning fun.

Another activity is math puzzles. Puzzles such as crosswords, word searches, and logic puzzles can be used to develop critical thinking and problem-solving skills. Additionally, math stories can be used to teach math concepts while making learning fun. Math stories can be found in storybooks or online, and they provide an interactive way to teach math concepts.

Developing Critical Thinking Skills through Math

Mathematics is an excellent way to develop critical thinking skills. Critical thinking involves analyzing, interpreting, and evaluating information to make informed decisions. In math, critical thinking is essential as it helps students understand mathematical concepts and apply them in real-life situations.

Encourage your child to think critically when solving problems. Teach them to ask questions and to consider different solutions to a problem. Additionally, encourage them to explain their reasoning and to justify their solutions. These skills are essential in problem-solving and can be applied in other areas of their lives.

Providing Support and Encouragement for your Child

Providing support and encouragement is essential when helping your grade 2 child excel in math. Encourage your child to ask questions and to seek help when they need it. Additionally, provide them with a positive learning environment and praise their efforts and progress. Celebrate their successes and encourage them to keep learning and practicing.

Equipping Your Child for Math Success in Grade 2

Mathematics is an essential subject that requires problem-solving skills. By turning problem-solving woes into victories, providing support and encouragement, and using effective strategies and fun activities, parents and educators can help grade 2 students excel in math. With the right approach, learning math can be fun and engaging while developing critical thinking skills that are essential in all areas of life.

2nd Grade Fast Math Success Workbook

2nd Grade Fast Math Success Workbook: Math Worksheets Grade 2: Numeration, Addition, Subtraction, Telling Time and More with Answers

• Comparing Numbers Within 200
• Ordering Numbers Within 200
• Skip Counting: Count By 1s and 2s
• Place Value: Ones, Tens, and Hundreds
• Addition: 1 through 100
• Subtraction: 1 through 100
• Addition: Missing Number – 1 through 100
• Subtraction: Missing Number – 1 through 100
• Ordering Numbers – 1 through 1000
• Comparing Numbers – 1 through 1000
• Counting: Count by 4 to 6
• Addition and Subtraction: Double Digit
• Addition and Subtraction: Missing Number – Double Digit
• Addition: Triple Addend – 1 through 100
• Mixed Operations: 1 through 100
• Write the Numbers Before, After, and Between
• Addition and Subtraction: 1 through 1000
• Telling Time
• Time Passages
• Addition and Subtraction Games
• Final Review

MathBear: Math Workbook Grade 2

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Math Practice Workbook Grade 2: 3051 Questions to Master Essential Math Skills (Numeration, Addition, Subtraction, Multiplication, Telling Time and More) With Answer Key

• Circle the Numbers
• Comparing Numbers
• Addition: Double Digit
• Subtraction: Double Digit
• Addition: Missing Number
• Subtraction: Missing Number
• Number Before, After and Between
• Addition: Triple Digit
• Subtraction: Triple Digit
• Basic Multiplication

MathBear: Homeschool Math Workbook Grade 2

MathBear: Homeschool Math Workbook Grade 2: 2nd Grade Homeschool Math Practice Workbook: Addition, Subtraction, Multiplication, Place Value with Answers

• Place Value
• Commutative Property
• Addition Games
• Subtraction Games

MathBear: Math Curriculum Workbook Grade 2

MathBear: Math Curriculum Workbook Grade 2: 2nd Grade Math Curriculum: Numeration, Place Value, Addition and Subtraction, Telling Time with Answers

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• Number Before, After, or Between
• Number Lines
• Place Value: Ones, Tens, Hundreds
• Subtraction
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• Introduction to Multiplication
• Measure the Rectangles
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MathBear: Math Practice Grade 2: 2nd Grade Math Practice Workbook: Addition, Subtraction, Multiplication, Place Value, Telling Time, Commutative Property with Answers

MathBear: Math Skills Workbook Grade 2

MathBear: Math Skills Workbook Grade 2: 2nd Grade Math Skills Practice Workbook: Addition, Subtraction, Basic Multiplication, Place Value, Math Games, and More With Answers

All Seasons Math Tests Grade 2

All Seasons Math Tests Grade 2 (Student's Edition): 100 Math Practice Pages Grade 2: Timed Math Tests: For Classroom and Homeschool

Kids Math Book Ages 6-8

Kids Math Book Ages 6-8: Math Practice workbook Grade 1-3: Addition, Subtraction, Place Value, Telling Time

• Addition Target
• Subtraction Target
• Addition Square
• Ordering Numbers: 1 to 100
• Addition Table
• Subtraction Table
• Addition: Triple Addend
• Numbers Before, After, and Between
• What time was and will it be?

Math Workbook Grade 2: Addition and Subtraction

MathBear: Math Workbook Grade 2: Addition and Subtraction: 2nd Grade Double Digit Addition and Subtraction Workbook with Answers

• Addition: within 100
• Subtraction: within 100
• Basic Addition with Regrouping
• Basic Subtraction with Regrouping

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These incredibly powerful, flexible activities can be used with a variety of content and contexts.

These games are chosen for their simplicity and depth.

Problems that resist easy solutions while encouraging perseverance and deeper understanding.

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Every student deserves to have the opportunity to problem-solve and engage in genuine mathematical thinking. Rich tasks are designed to make these rich learning experiences possible. We’ve written these tasks to launch quickly, engage students, and promote the habits of mind mathematicians need: perseverance & pattern-seeking, courage & curiosity, organization & communication.

This free video PD series will help you get the most out of the tasks below.

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100+ Critical Thinking Questions for Students To Ask About Anything

Critical thinkers question everything.

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

“Who” Critical Thinking Questions

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

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

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

• Makes the decisions?

“What” Critical Thinking Questions

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

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

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

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

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

“Where” Critical Thinking Questions

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

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

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

“When” Critical Thinking Questions

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

• Is this acceptable?
• Is this unacceptable?

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

• Has this happened before?

“Why” Critical Thinking Questions

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

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

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

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

“How” Critical Thinking Questions

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

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

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

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

More Critical Thinking Questions

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

• Can you give me an example?

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

• Is ______ a fact or an opinion?

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

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

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

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

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Time: Critical Thinking (Gr. 2)

Scott Foresman, an imprint of Pearson

Featured 2nd grade resources.

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Second Grade Thinking Skills & Key Concepts

Teaches beyond most state & common core standards.

Critical Thinking

Full curriculum

Components Sold Separately

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

Second Grade Thinking Skills & Key Concepts: Answer PDF

• Paperback Book - $21.99
• eBook - $21.99

Description and Features

This highly-effective, standards-based, 160-page book is a research-based instructional program that teaches beyond most state and Common Core standards by:

• Improving children's observation and description skills
• Developing academic vocabulary
• Developing thinking skills that underlie content learning (describing/defining, identifying similarities and differences, sequencing, and classifying)
• Improving students' understanding of key concepts in mathematics, social studies, and science
• Students completing structured exercises to write sentences and paragraphs
• Carefully sequencing lessons to develop thinking skills
• Employing language integration techniques to teach thinking skills and key concepts

Academic Vocabulary Development The program builds academic vocabulary using these important concepts: describe, compare and contrast, and classify shapes, position, patterns, matter, water, weather, land forms, bodies of water living and non-living things, communities, our country. Observation Skills Observation lessons involve concrete examples using detailed photographs to develop observation skills. The student book provides activities that students may use to clarify their thinking and learning by peer and class discussion. Spatial Thinking Skills     • Describing Shapes – naming shapes, finding shapes to match a description, describing characteristics of a shape     • Similarities and Differences – matching and combining shapes, producing equal figures, figure completion     • Sequences – recognizing and producing the next figure in a sequence     • Classification – classifying by shape and/or color, forming classes, depicting overlapping classes     • Using positional and directional words

Verbal Thinking Skills     • Describing – matching a picture to a description, describing people, animals, or objects shown in pictures, part/whole analysis     • Similarities and Differences – selecting similar people, animals, or objects, explaining similarities and differences     • Sequences – ranking objects or people by a significant characteristic     • Classifications – explaining characteristics of a class, exceptions, sorting into classes     • Analogies – naming the kind of analogy or completing the analogy

Mental Models This book teaches the characteristics outlined in its mental models needed to describe or define a concept. How We Know It Works     • Increased scores on language proficiency and cognitive abilities tests     • Increased scores on normed or criterion-referenced achievement tests     • Proficient student writing     • Increased number of students placed in advanced classes and subsequent successful performance

Teaching Support This student book can be used with a free, downloadable, answer PDF ( get it here ) or with a detailed, 192-page Teacher's Manual which can be purchased separately . The 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.

Watch a short presentation on this highly effective product. View Online | PowerPoint | PDF

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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